Math 9.64 (Edited makeMixedNum), C#

Math 9.64 (Edited makeMixedNum)

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//Rextester.Program.Main is the entry point for your code. Don't change it.
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using ShuffleExtension;
using System.Threading;
using System.Data;
using MathSpace;
using CountExtension;
namespace Rextester
{

public class Program {
        
        public int ratio1;
        public int ratio2;
        public int ratio3;
        public int num1, num2, num3;
        
        public static void Main(String[] args){
            
            makeMixedNum();
            //LCM(12,10,5);
            //LCM3Q();
           // makeDeciDivQ();
            
            //simultQ();
            //makeDivQ3by2();
            //addSub2Q();
        }
        
        public static void LCMQ() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " lcm = " + lcm(left,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)==1 && Math.Abs(left-right)<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " lcm = " + lcm(left,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (1)","Find the LCM (or lowest common multiple) of each pair of numbers",20);
            
        }
        
        public static void LCM3Q() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " @lcm(" + left + "," + right + ")=" + lcm(left,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (lcm(left,right)<120 && Fraction.GCD(left,right)==1 && Math.Abs(left-right)<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + " and " + right + " @lcm(" + left + "," + right + ")=" + lcm(left,right));
                } 
            }
            
            while(count<150) {
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                    
                }
            }
            
            while (count>=150 && count<170) {
             
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)==1 && Math.Abs(max(left,middle,right)-min(left,middle,right))<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (3)","Find the LCM (or lowest common multiple) of each set of numbers",20);
        }
        
        public static void LCM2Q() {
            
            List<string> lcmQ = new List<string>();
            int count=0;
            while(count<100) {
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)!=1 && lcm(left,right)!=left && lcm(left,right)!=right) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                    
                }
            }
            
            while (count>=100 && count<130) {
             
                int left = Rand.Next(2,100);
                int middle = Rand.Next(2,100);
                int right = Rand.Next(2,100);
                
                if (left!=middle && middle!=right && lcm(left,middle,right)<120 && GCD(left,middle,right)==1 && Math.Abs(max(left,middle,right)-min(left,middle,right))<20) {
                
                    count++;
                    lcmQ.Add("        \\item " + left + ", " + middle + ", " + right + " @lcm(" + left + "," + middle + "," + right + ")=" + lcm(left,middle,right));
                } 
            }
            
            lcmQ.Shuffle();
            Print(lcmQ,"Lowest Common Multiple (2)", "Find the LCM (or lowest common multiple) of each pair of numbers", 20);
        }
        
        public static void Reversal() { // finds the 4-digit reverse number
        
            for (int a = 0; a<10;a++){
                    
                    for (int b = 0; b<10;b++){
                    
                        for (int c = 0; c<10;c++){
                        
                            for (int d = 0; d<10;d++){
                                
                                double n = 9;
                                if ((n*1000*a+n*100*b+n*10*c+n*d)==(1000*d+100*c+10*b+a)) {
                                    
                                    Console.WriteLine(a+""+b+""+c+""+d);
                                }
                            }
                        }
                    }
                }
        
        }
        
        public static int Tens(){ // randomises 10 or 100
         
            int rand = Rand.Next(0,2);
            
            if (rand==0) {
                
                return 10;
                
            }
            
            else 
                
                return 100;
               
        }
        
        public static int Tens2() { // returns 1, 10 or 100 randomly
            
            int rand = Rand.Next(0,3);
            
            if (rand==0) {
                return 1;
            }
            
            else if (rand==1) {
                return 10;
            }
            
            else return 100;
               
        }
        
         public static void addSub3Q() { // add and sub 3 terms
            
             string title = "Addition \\& Subtraction (3 term) (2)";
             List<string> addsubQ = new List<string>();
             DataTable dt = new DataTable();
             int n1, n2, n3;
             
             for (int k=0; k<9000; k++){
                 int[] n = new int[3];
                 
                 n[0] = Rand.Next(101,1000);
                 n[1] = Rand.Next(11,1000);
                 n[2] = Rand.Next(11,1000);
                 int[] op = new int[2];
                 op[0] = Rand.Next(0,2);
                 op[1] = Rand.Next(0,2);
                 string[] operand = new string[2];
                 operand[0] = "+";
                 operand[1] = "-";
                 int result;
                 if (n[0]-n[1]>=0&& (n[0]-n[1])-n[2]>=0 && (n[0]+n[1]+n[2]<1000) && addsubQ.Count()<300){
                     
                     result = Convert.ToInt32(dt.Compute(n[0]+operand[op[0]]+n[1]+operand[op[1]]+n[2], null));
                     addsubQ.Add("        \\item \$\\mathmakebox[3.0cm][r]{"+n[0]+operand[op[0]]+n[1]+operand[op[1]]+n[2]+"}=\\underline{\\hspace{2cm}}\$");
                     //Console.WriteLine(result);
                 }
                
             }
             
             //Console.WriteLine(addsubQ.Count());
             //addsubQ.Shuffle();
             PrintArithmetic(addsubQ, title);
         
         }

public static void addSubQ() { // add and sub questions
            
            string title = "Addition \\& Subtraction (1)";
            List<string> addQ = new List<string>();
            for (int k=0; k<2; k++){
                    
                for (int i=10; i<=99; i++){
                                
                    for (int j=10; j<=99; j++){
                                   
                        if (i+j<100) addQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"+"+j+"}=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                    }   
                }   
            }
            
            List<string> subQ = new List<string>();
            for (int k=0; k<2; k++){
                
                for (int i=10; i<=99; i++){

for (int j=2; j<=99; j++){
                        
                        if (i>j && i%10>j%10){subQ.Add("        \\item \$\\mathmakebox[1.5cm][r]{"+i+"-"+j+"}=\\underline{\\hspace{2cm}}\$");}
                        
                    }
        
                }
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(addQ.Count());
            //Console.WriteLine(subQ.Count());
            addQ.Shuffle();
            subQ.Shuffle();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.Shuffle();
            //PrintArithmetic(questions, title);
            
        }
        
        public static void addSub2Q() { // add and sub questions
            
            string title = "Addition \\& Subtraction (2 Digits)";
            List<string> addQ = new List<string>();
            while(addQ.Count()<150){
                    
                int i = Rand.Next(11,100);
                int j = Rand.Next(11,100);
                int result = i+j;
                        if (i+j<100) addQ.Add("        \\item \$"+i+"+"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)"); //\\mathmakebox[1.45cm][r]{  
                    
                
            }
            
            List<string> subQ = new List<string>();
            for (int k=0; k<2; k++){
                
                int i = Rand.Next(11,100);
                int j = Rand.Next(11,100);
                int result = i-j;
                                   
                if (i>j){subQ.Add("        \\item \$"+i+"-"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)");}
                        
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(addQ.Count());
            //Console.WriteLine(subQ.Count());
            addQ.Shuffle();
            subQ.Shuffle();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            PrintAnswerKey(questions, title, 30);
            
        }
        
        public static void multDivQ() { // mult and div questions
            
            string title = "Multplication \\& Division (1)";
            List<string> multQ = new List<string>();
            DataTable dt = new DataTable();
            for (int k=0; k<4; k++){
                    
                for (int i=2; i<=9; i++){
                                
                    for (int j=2; j<=9; j++){
                                   
                        if (multQ.Count()<200) multQ.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\times"+j+"}=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                    }   
                }   
            }
            
            List<string> divQ = new List<string>();
            for (int k=0; k<4; k++){
                
                for (int i=10; i<=100; i++){

for (int j=2; j<=9; j++){
                        
                        if (divQ.Count()<200 && i>j && i%j==0 &&i/j<10){divQ.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}
                        
                    }
        
                }
            }
            
            List<string> questions = new List<string>();
            //Console.WriteLine(multQ.Count());
            //Console.WriteLine(divQ.Count());
            
            questions.AddRange(multQ);
            questions.AddRange(divQ);
            questions.Shuffle();
            PrintArithmetic(questions, title);
            
        }

public static void makeMultQ(int lower1, int upper1, int lower2, int upper2) {
            
            string title = "Multplication  (1)";
            List<string> questions = new List<string>();
            for (int k=0; k<12; k++){
                    
                for (int i=lower1; i<=upper1; i++){
                                
                    for (int j=lower2; j<=upper2; j++){
                                   
                        questions.Add("        \\item \$"+i+"\\times"+j+"=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
                    }   
                }   
            }
            
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            
        }
        
		public static void makeMultQ3by1() {
            
            string title = "Multplication (3 by 1 Digits)";
            List<string> questions = new List<string>();
            for (int k=0; k<300; k++){
            
			int i = Rand.Next(101,1000);
			int j = Rand.Next(11,100);
			i = Rand.Next(101,1000);
			i = Rand.Next(101,1000);
			j = Rand.Next(2,10);
			j = Rand.Next(2,10);
				questions.Add("        \\item \$"+i+"\\times"+j+"=\\underline{\\hspace{2cm}}\$"); //\\mathmakebox[1.45cm][r]{  
            
            }
            
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            //Console.WriteLine(questions.Count());
        }
		
        public static void makeDivQ(int lower1, int upper1, int lower2, int upper2) {
            
            string title = "Division (2 by 1 digits) General";
            List<string> questions = new List<string>();
            for (int k=0; k<4; k++){
                
                for (int i=lower1; i<=upper1; i++){

for (int j=lower2; j<=upper2; j++){
                        
                        if (i>j){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}
                        
                    }
        
                }
            }
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            
        }
		
        public static void makeDivQ3by1() {
            
            string title = "Division (2 by 1 digits) General";
            List<string> questions = new List<string>();
            
            for (int k=0; k<100; k++) {
            int i = Rand.Next(101,1000);
            int j = Rand.Next(2,10);
            
                if (i>j){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"\\div"+j+"}=\\underline{\\hspace{2cm}}\$");}

}
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
            
        }
        
        
		public static void makeDivQ3by2() {
            
            string title = "Division (3 by 2 digits)";
            List<string> questions = new List<string>();
            
            while(questions.Count()<150) {
                int i = Rand.Next(101,1000);
                int j = Rand.Next(11,100);
                int result = i/j;
                if (i>j && i%j==0) { questions.Add("        \\item \$"+i+"\\div"+j+"=\\underline{\\hspace{2cm}}\$"+result+"\\)"); }

}
            questions.Shuffle();
            
           // PrintArithmetic(questions, title);
            
            PrintAnswerKey(questions, title, 30);
            
        }
        
        public static void makeDeciQ(){
            
            string title = "Decimal Arithmetic General";
            // Division
            List<string> divQ = new List<string>();
            for (int i=0; i<6500; i++) {
                int tens = Tens();
                double argument = Math.Truncate(Rand.NextD(1.0,99.99)*tens)/tens;
                
                decimal num1 = Rand.Next(2,100);
                int dividend = Rand.Next(2,1000);
                decimal result = dividend/num1;
                int count = BitConverter.GetBytes(decimal.GetBits(result)[3])[2];
                
                //Console.WriteLine(count);
                if(count<4 && divQ.Count()<120) {
                    //Console.WriteLine("{0}/{1}={2}", dividend,num1, dividend/num1);
                    divQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+dividend+"\\div"+num1+"}=\\underline{\\hspace{2cm}}\$");
                }
                
                
            }
            
            //Multiplication
            List<string> multQ = new List<string>();
            
            for (int i=0; i<120; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund;
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    hund = 10;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                double result = num1*num2;
                if ( (Math.Floor(num1)!=num1 || Math.Floor(num2)!=num2) && multQ.Count()<120) {
                    multQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"\\times"+num2+"}=\\underline{\\hspace{2cm}}\$");
                }
            }
            
            //Add
            List<string> addQ = new List<string>();
            
            for (int i=0; i<120; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund = Tens();
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    //hund = 100;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    //hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                double result = num1+num2;
                addQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"+"+num2+"}=\\underline{\\hspace{2cm}}\$");
            }
            
            //Subtract
            List<string> subQ = new List<string>();
            
            for (int i=0; i<300; i++) {
                double number = Rand.NextD(1.0,99.99);
                int hund = Tens();
                double num1;
                if (number>=10) {
                    num1 = Math.Truncate(number*10)/10;
                    //hund = 100;
                }
                
                else {
                    num1 = Math.Truncate(number*100)/100;
                    //hund = 10;
                }
                
                double num2 = Math.Truncate(Rand.NextD(2,hund)*hund)/hund;
                if(num1>num2) {
                    double result = num1-num2;
                    subQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+num1+"+"+num2+"}=\\underline{\\hspace{2cm}}\$");
                }
                
            }
            List<string> questions = new List<string>();
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.AddRange(multQ);
            questions.AddRange(divQ);
            
            questions.Shuffle();
            PrintArithmetic(questions,title);
        }
        
        public static void makeDeciDivQ() {
         
            string title = "Decimal Division General";
            // Division
            List<string> divQ = new List<string>();
            for (int i=0; i<6500; i++) {
                int tens = Tens();
                
                
                decimal divisor = (decimal) Rand.Next(2,100)/Tens2();
                decimal dividend = (decimal) Rand.Next(2,1000)/Tens2();
                decimal result = dividend/divisor;
                int resultInt = Convert.ToInt32(result);
                int count = BitConverter.GetBytes(decimal.GetBits(result)[3])[2];
                
                //Console.WriteLine(count);
                if(count<4 && divQ.Count()<120) {
                    //Console.WriteLine("{0}/{1}={2}", dividend,num1, dividend/num1);
                    divQ.Add("        \\item \$\\mathmakebox[3cm][r]{"+dividend+"\\div"+divisor+"}=\\underline{\\hspace{2cm}}\$");
                }
                //if (divisor!=1 && count<4 && resultInt.Count()<4) Console.WriteLine(dividend+ " / " +divisor + " = " + result);
//                if (count<4 && resultInt.Count()<4 ) Console.WriteLine((int)result);
                if (
                    !(BitConverter.GetBytes(decimal.GetBits(divisor)[3])[2]==0 && BitConverter.GetBytes(decimal.GetBits(dividend)[3])[2]==0 
                      && BitConverter.GetBytes(decimal.GetBits(result)[3])[2]==0) && divisor!=1 && count<4 && divQ.Count()<120) {
                
                      
                    Console.WriteLine(dividend+ " / " +divisor + " = " + result);
                }
            
            
        
            }
        
        }
              
        /*public static void makeDeciQ(double upper1) {
            
            string title = "Division (2 by 1 digits) General";
            List<string> addquestions = new List<string>();
            List<string> subquestions = new List<string>();
            List<string> multquestions = new List<string>();
            List<string> divquestions = new List<string>();
            string[] op = new string[4] {"+", "-", "\\times", "\\div"};

for (int i=1; i<=upper1; i++){
                
                int operand = Rand.Next(1,4);
                double[] num = new double[2] {Math.Truncate(Rand.NextD(1.0,99.99)*100)/100, Rand.Next(2,999)};
                
                decimal num1 = Convert.ToDecimal(num[1]));
                //if (operand==2){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                    
                
                if (operand==4 && num[2]%num1==0){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                    
                //else if (operand==1) {questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
                //else if (operand==3) {questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+num[0]+op[operand]+num[1]+"}=\\underline{\\hspace{2cm}}\$");}
            }
            
            //questions.Shuffle();
            
            //PrintArithmetic(questions, title);
            
        }*/
                                    
        public static void makeSubQ2by2(int lower1, int upper1, int lower2, int upper2){
            
			string title = "Subtraction (2 by 2 Digits)";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            for (int i=lower1; i<=upper1; i++){
            //for (int i=10; i<100;i++){
                
                for (int j=lower2; j<=upper2; j++){
                //for (int j=10; j<100;j++){   
                   
                    if (i!=j && i+j<100){questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"-"+j+"}=\\underline{\\hspace{2cm}}\$");}
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            //Console.WriteLine(questions.Count());
            
            PrintArithmetic(questions, title);
            /*for (int i=0; i<questions.Count(); i++){
                
                if(i==0){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+(i/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}
                Console.WriteLine(questions[i]);
               
                if (i!=0 && (i+1)%30==0){
                  
                    
                    Console.WriteLine("\\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\pagebreak[4]");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);
                }
            }*/
        }
        
        public static void makeAddQ2by1(int lower1, int upper1, int lower2, int upper2){
            
			string title = "Subtraction (2 by 2 Digits)";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            for (int i=lower1; i<=upper1; i++){
            //for (int i=10; i<100;i++){
                
                for (int j=lower2; j<=upper2; j++){
                //for (int j=10; j<100;j++){   
                   
                    questions.Add("        \\item \$\\mathmakebox[1.45cm][r]{"+i+"+"+j+"}=\\underline{\\hspace{2cm}}\$");
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            PrintArithmetic(questions, title);
           
        }
		
        public static void makeAlg() { // algebraic questions
            
            int[] n = new int[10];
            
            for (int j=0; j<50; j++) {
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(1,10);
                }
                char[] op = new char[] {'+','-'};
                int x = Rand.Next(0,2);
                int y = Rand.Next(0,2);
                int z = Rand.Next(0,2);
                Console.WriteLine("\$\\dfrac{{{7}(x{4}{0})}}{{{1}}}{6}\\dfrac{{{8}(x{5}{2})}}{{{3}}}=\$\\\\",n[0],n[1],n[2],n[3],op[x],op[y],op[z],n[4],n[5]);
            }

}

public static void makeQ(int lower1, int upper1, int lower2, int upper2){
         
            for (int i=lower1; i<=upper1; i+=9){

for (int j=lower2; j<=upper2; j+=9){

Console.WriteLine("        \\item \$"+i+"\\operation"+j+"=\$");                   
            
                }
              
            }

}
        
        public static void makeFracQ(){
        
            string title = "Algebra Simplification Introduction";
            string exerciseTitle = "Simplify the algebraic expressions";
            int m=0;
            int i_final=30000;
            int incre= 0;
            
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            string mathbox = "\\mathmakebox[1.45cm][r]{";
            string[] op = new string[2] {"(", ")("};
            string end =")=\\)";
            
            List<string> questions = new List<string>();
            
            
            //for (int i=lower1; i<=upper1; i+=9){
            for (int i=1; i<100;i++){
                
                //for (int j=lower2; j<=upper2; j+=9){
                for (int j=10; j<100;j++){   
                    
                    int num1 = Rand.Next(1,10);
                    int num2 = Rand.Next(1,10);
                    int denom1 = Rand.Next(2,10);
                    int denom2 = Rand.Next(2,10);
                    int mixed1 = Rand.Next(0,10);
                    int mixed2 = Rand.Next(0,10);
                    
                    if (num1!=denom1 && num2!=denom1 && num1<denom1 && num2<denom1){questions.Add("        \\item \$"+mixed1+"\\dfrac{"+num1+"}{"+denom1+"}+"+mixed2+"\\dfrac{"+num2+"}{"+denom1+"}=\\underline{\\hspace{2cm}}\$");}
                   /*if (i>j) {
                       
                       questions.Add("        \\item \$"+i+"-"+j+"=\$");
                       
                   }*/
                   
                }
                
            }
            questions.Shuffle();
            
            //Console.WriteLine(questions.Count());
            
            for (int i=0; i<questions.Count(); i++){
                
                if(i==0){

}
                    
                }
               
            }
             
        }*/

public static void makeAlgebra(){
        
            //string[] vari = new string[24] {"a","b","c","d","f","g","h","k","m","n","p","q","r","s","t","u","v","w","x","y","z","\\delta", "\\epsilon", "\\phi"};
            string[] vari = new string[21] {"a","b","c","ab","bc","ac","abc","x","y","z","xy","yz","xz","xyz","k","m","n","km","kn","mn","kmn"};
            //var[0] = "a";
            //var[1] = "b";
            //var[2] = "c";
            
            int n=-1; // n is the random number of variables per question
            int m=0;
            int i_final=30000;
            int incre= 0;
            string title = "Algebra Simplification Introduction";
            string exerciseTitle = "Simplify the algebraic expressions";
            string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
            
            string[] op = new string[4] {"+","-","(", ")("};
            int operand = Rand.Next(0,1);
            //string end =")=\\)";
            string end = "=\\)";
            for (int i=1; i<=i_final; i++) {

int num2=Rand.Next(0,7);  // range of number of different variables per question
                int num = Rand.Next(2,5); // range of number of total variables per question
                int consts=Rand.Next(-9,10); // range of coefficients of the variables
                while (true) {
                    consts=Rand.Next(-9,10);
                    if (consts==0) {
                        consts=Rand.Next(-9,10);
                    }
                    else break;
                }
                if(i==1){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\textbf{Exercise "+(m/30+1)+". "+exerciseTitle+".}\\\\");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}

if (n==-1){ //first variable of each question
                    Console.Write("        \\item \\(");
                }
                
                if (n==0){
                Console.Write(consts+vari[num2+7*incre]+op[operand]);
                
                }
            
                else if (n>0 && n<num){
                    Console.Write(consts+vari[num2+7*incre]+op[operand]);
                }
                n++;                
                if (n==num){ 
                    m++;
                    Console.Write(consts+vari[num2+7*incre]);
                    Console.Write(end);
                    Console.WriteLine();
                    
                    if (m%30==0) {
                        incre=Rand.Next(0,3);
                        Console.WriteLine("\\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\pagebreak[4]");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\textbf{Exercise "+(m/30+1)+". "+exerciseTitle+".}\\\\");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                    
                    Console.Write("        \\item \\(");
                    n=0;
                }
                
                else if (n>num){
                    m++;
                    Console.Write(consts+vari[num2+3*incre]);
                    Console.Write(end);
                    Console.WriteLine();
                    
                    if (m%30==0) {
                        incre=Rand.Next(0,3);
                        Console.WriteLine("\\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\pagebreak[4]");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        //Console.WriteLine("\\large Promatics Education Centre\\\\[1.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\textbf{Exercise "+((m+30)/30+1)+". "+exerciseTitle+".}\\\\");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                    
                    Console.Write("        \\item \\(");
                    n=0;
                }

/* if(i==i_final){
                    Console.WriteLine("\\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    
                }*/

}
            
            
        }
        
     
        public static void makeDiv4by2()     {
            
            for (int i =0; i<10000; i++) {
                  
                int dividend = Rand.Next(1001,10000);
                int divisor = Rand.Next(11,99);

if (dividend%divisor==0) {
                Console.WriteLine("        \\item \$"+dividend+"\\div"+divisor+"=\$");
                    
                }
            }
        }
        
        public static void makeSciNot(){
            
            for (int i=0; i<100; i++){
                
                int num1 = Rand.Next(1,10);
                int dec1 = Rand.Next(1,10);
                int num2 = Rand.Next(1,10);
                int dec2 = Rand.Next(1,10);
                int exp = Rand.Next(-9,10);
                int plusminus = Rand.Next(-1,2);
                if (num1>num2 && exp != exp+plusminus){
                    
                Console.WriteLine("        \\item \${0}.{3} \\times 10^{{{2}}}+{1}.{4} \\times 10^{{{5}}}=\$",num1,num2,exp,dec1,dec2,exp+plusminus);
                }
            }
        }
        
        public static void DN(){
            
            //st<string> sign = new List<string>(new string[] {"+","-","*","/"});
            List<char> sign = new List<char>(new char[] {'+','-','*','/'});
            
            for (int i=0;i<100;i++){
                
                string question = "{0}{1}{2}{3}{4}{5}{6}";
                int pick1= Rand.Next(0+sign.Count());
                int pick2= Rand.Next(0+sign.Count());
                int pick3= Rand.Next(0+sign.Count());
                int num1=Rand.Next(-9,10);
                int num2=Rand.Next(-9,10);
                int num3=Rand.Next(-9,10);
                int num4=Rand.Next(-9,10);
                string num1_str, num2_str, num3_str, num4_str;
                bool num1_b = num1<0;
                bool num2_b = num2<0;
                bool num3_b = num3<0;
                bool num4_b = num4<0;
                
                if (num1_b && !num2_b && !num3_b && !num4_b) {
                    num1_str = "("+num1.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                    
                }
                
                else if (num2_b && !num1_b && !num3_b && !num4_b){
                    num2_str = "("+num2.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num3_b && !num1_b && !num2_b && !num4_b){
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num4_b && !num1_b && !num2_b && !num3_b){
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b &&!num3_b && !num4_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num3_b && !num2_b && !num4_b){ 
                    num1_str = "("+num1.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num4_b && !num2_b && !num3_b){
                    num1_str = "("+num1.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num3_b && !num1_b && !num4_b){
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num4_b && !num1_b && !num3_b){
                    num2_str = "("+num2.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num3_b && num4_b && !num1_b && !num2_b){
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b && num3_b && !num4_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num3_b && num4_b && !num2_b){
                    num1_str = "("+num1.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num1_b && num2_b && num4_b && !num3_b){
                    num1_str = "("+num1.ToString()+")";
                    num2_str = "("+num2.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1_str,sign[pick1],num2_str,sign[pick2],num3,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else if (num2_b && num3_b && num4_b && !num1_b){
                    num2_str = "("+num2.ToString()+")";
                    num3_str = "("+num3.ToString()+")";
                    num4_str = "("+num4.ToString()+")";
                    Console.WriteLine(question,num1,sign[pick1],num2_str,sign[pick2],num3_str,sign[pick3],num4_str);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
                
                else {
                    Console.WriteLine(question,num1,sign[pick1],num2,sign[pick2],num3,sign[pick3],num4);
                    Console.WriteLine(num1+sign[pick1]+num2+sign[pick2]+num3+sign[pick3]+num4);
                }
              
            }

}
        
         public static void makeMixedNum() {
            
            int numQ = 150;
            string title = "Fraction Arithmetic (General)";
            int[] n = new int[10];
            List<string> questions = new List<string> ();
            
            //Add
            List<string> addQ = new List<string> ();
            
            while (addQ.Count()<numQ) {
                //n[0] = Rand.Next(10,400); // for prime factorization

n[0]=Rand.Next(3,8);
                n[1]=Rand.Next();

for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(1,13);
                    n[1] = Rand.Next(2,13);
                    n[3] = Rand.Next(2,13);
                    n[4] = Rand.Next(2,10);
                    n[5] = Rand.Next(2,10);
                }
                int y = Rand.Next(0,2);
                int z = Rand.Next(0,2);
                //Console.WriteLine("\$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+op[x]+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}=\$");
                if (n[1]!=n[3] && n[0]<n[1] && n[2]<n[3]) {
                    double n0 = (double)n[0];
                    double n1 = (double)n[1];
                    double n2 = (double)n[2];
                    double n3 = (double)n[3];

Fraction left = new Fraction(n[4],n[0],n[1]);
                    Fraction right = new Fraction(n[5],n[2],n[3]);
                    Fraction result = (left + right).toMixed().Simplify();
                    // if the result is small enough (denominator <=20)
                    if (result.denom <= 20 && result.integer<=20 && n[0]!=n[1] && n[2]!=n[3]) {

if (result.integer!=0) {
                            if (result.num!=0) {
                                addQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+result.integer+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                            }
                            else addQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+result.integer+"\\)");
                        }
                        else addQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"+"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");

}
                }
            }
                        
            //Sub
            List<string> subQ = new List<string> ();
            
            while (subQ.Count()<numQ) {
                //n[0] = Rand.Next(10,400); // for prime factorization

n[0]=Rand.Next(3,8);
                n[1]=Rand.Next();

if (result.integer!=0) {
                            if (result.num!=0) {
                                subQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+result.integer+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                            }
                            else subQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+result.integer+"\\)");
                        }
                        else subQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[0]+"}{"+n[1]+"}"+"-"+n[5]+"\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");

}
                }
            }
            
            //Mult
            List<string> multQ = new List<string> ();
            
            int q = numQ/2;
            int m = 5;
            int m2 = 15;
            
            while (multQ.Count()<q/m) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                   
					if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
						
						multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
					}
                                
            }
            
            while (multQ.Count()<(q/m)*2) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                   
                if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                    multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
                                
            }
            
            while (multQ.Count()<(q/m)*3) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                   
                if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                    multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
                                
            }
            
            while (multQ.Count()<(q/m)*4) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                   
                if (GCD(n[0],n[1])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                    multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
                                
            }
            
            while (multQ.Count()<(q/m)*5) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                   
                if (GCD(n[2],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                    multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
                                
            }
            
            while (multQ.Count()<q+q/m) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                }
            }
            
            while (multQ.Count()<q+(q/m2)*2) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                    
                }
            }
            
                    
            
            while (multQ.Count()<q+(q/m2)*3) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                }
            }
                    
            
            while (multQ.Count()<q+(q/m2)*4) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                }
            }
                    
            
            while (multQ.Count()<q+(q/m2)*5) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction mixed, right regular fraction
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]<n[3]) {
                    
                    //Console.WriteLine(n[0] + "/" + n[1] +" " +n[4] + " " + n[6] +"/"+n[1]);
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                }
            }
            
            while (multQ.Count()<q+(q/m2)*6) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
        
            while (multQ.Count()<q+(q/m2)*7) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }

while (multQ.Count()<q+(q/m2)*8) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
            
            while (multQ.Count()<q+(q/m2)*9) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
            
            while (multQ.Count()<q+(q/m2)*10) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // left fraction regular, right mixed
                if (n[0]<n[1] && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    //Console.WriteLine(" " + n[2] + "/" + n[3] +" " +n[5] + " " + n[7] +"/"+n[3]);
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
                
            while (multQ.Count()<q+(q/m2)*11) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
            
            while (multQ.Count()<q+(q/m2)*12) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
			
			while (multQ.Count()<q+(q/m2)*13) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[1],n[2])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
			
			while (multQ.Count()<q+(q/m2)*14) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[0],n[1])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
			while (multQ.Count()<q+(q/m2)*15) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left * right).Simplify();
                Fraction leftMixed = left.toMixed();
                n[4] = (int) leftMixed.Integer;
                n[6] = (int) leftMixed.Num;
                
                Fraction rightMixed = right.toMixed();
                n[5] = (int) rightMixed.Integer;
                n[7] = (int) rightMixed.Num;
                
                // both mixed fractions
                if (n[0]>n[1] && n[0]%n[1]!=0 && n[2]>n[3] && n[2]%n[3]!=0) {
                    
                    if (GCD(n[2],n[3])!=1 && GCD(n[0],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                    
                        multQ.Add("        \\item \$"+n[4]+"\\dfrac{"+n[6]+"}{"+n[1]+"}"+"\\times"+n[5]+"\\dfrac{"+n[7]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                    }
                                       
                }
            }
			
            
            
            //Div
            List<string> divQ = new List<string> ();
            
            while (divQ.Count()<numQ) {
                    
                for (int i =0; i<n.Length; i++){
                    n[i] = Rand.Next(2,100);

}
                
                Fraction left = new Fraction (n[0],n[1]);
                Fraction right = new Fraction (n[2],n[3]);
                Fraction result = (left / right).Simplify();
                   
                if (GCD(n[0],n[3])!=1 && GCD(n[1],n[2])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                
                    divQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
                   
                else if (GCD(n[0],n[1])!=1 && GCD(n[2],n[3])!=1 && result.denom <20 && result.num <20 && n[0]!=n[1] && n[2]!=n[3]) {
                
                    divQ.Add("        \\item \$\\dfrac{"+n[0]+"}{"+n[1]+"}"+"\\div\\dfrac{"+n[2]+"}{"+n[3]+"}="+"\\underline{\\hspace{3cm}}\$"+"\\dfrac{"+result.num+"}{"+result.denom+"}\\)");
                }
            }
            
            questions.AddRange(addQ);
            questions.AddRange(subQ);
            questions.AddRange(multQ);
            questions.AddRange(divQ);
            questions.Shuffle();
            string exerciseTitle = "Calculate and express the answer in simplest forms";
            PrintFraction(questions, title, exerciseTitle);
            PrintAnswerKey(questions, title, 20);

}
        
        public static Fraction[] simultF(int[] c, int[] d) {
            
            Fraction x, y;
           //int[] c = new int[3];
           //int[] d = new int[3];
            if(c.Length != 3 && d.Length!=3)
               throw new ArgumentException("array should be int[3]");

int yLeft = c[0]*d[2]-d[0]*c[2];
            int yRight = c[0]*d[1]-d[0]*c[1];
            y = new Fraction(yLeft, yRight);
            
            Fraction xLeft = c[2]-c[1]*y;
            int xRight = c[0];
            x = new Fraction(xLeft,xRight);
            
            Fraction[] z = new Fraction[] {x,y};
            //Console.WriteLine("x = {0}, y = {1}",x,y); 
            return z;
            
        }
        
        public static double[] simultD(int[] c, int[] d) {
            
            double x,y;
           //int[] c = new int[3];
           //int[] d = new int[3];
            if(c.Length != 3 && d.Length!=3)
               throw new ArgumentException("array should be int[3]");
            
            y = (double) (c[0]*d[2]-d[0]*c[2] ) / (c[0]*d[1]-d[0]*c[1]);
            x = (double) (c[2]-c[1]*y)/c[0];
            
            double[] z = new double[] {x,y};
            //Console.WriteLine("x = {0}, y = {1}",x,y); 
            return z;
        }
        
        public static void simultQ() {
            
            int[] c = new int[6];
            int count = 0;
            
            List<string> questions = new List<string>();
            
            int[] numArray = new int[] {-9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9};
            while (questions.Count()<100 || count <100 ) {
            
                for (int i = 0; i<c.Length; i++) {

c[i] = numArray[Rand.Next(1,17)];
                }

if (c[0]*c[4]!=c[3]*c[1]) {

Fraction[] result = simultF(new int[] {c[0], c[1], c[2]}, new int[] {c[3], c[4], c[5]});
                    Fraction parse;
                    // 
                    //if (Math.Abs(result[0]*result[1])<200 && result[0]%1==0 && result[1]%1==0 && result[0]+result[1]!=0 && result[0]*result[1]!=0) {
                    if (Math.Abs((result[0]*result[1]).toDeci())<200 && result[0].Num+result[1].Num!=0 && result[0].Num*result[1].Num!=0 && Math.Abs(result[0].num)<10 && Math.Abs(result[0].denom)<10 && Math.Abs(result[1].num)<10 && Math.Abs(result[1].denom)<10) {
                        count++;
                        if (c[1]<0 && c[4]>0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]);
                            //questions.Add(c[3]+"x + "+ c[4]+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else if (c[1]>0 && c[4]<0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x + "+ c[1]+"y &= "+c[2]);
                            //questions.Add(c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else if (c[1]<0 && c[4]<0) {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]+" \\\\ "+c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                            }
                            //questions.Add(c[0]+"x - "+ Math.Abs(c[1])+"y &= "+c[2]);
                            //questions.Add(c[3]+"x - "+ Math.Abs(c[4])+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                        
                        else {
                            // if x is a fraction but y is not
                            if (Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+result[1].Simplify()+"$"); 
                            }
                            
                            // if x is not a fraction but y is
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            
                            // if x and y are fractions
                            else if (Fraction.TryParse(result[0].ToString(), out parse) && Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = \\frac{"+result[0].Simplify().Num+"}{"+result[0].Simplify().Denom+"}, y = "+"\\frac{"+result[1].Simplify().Num+"}{"+result[1].Simplify().Denom+"}$"); 
                            }
                            else if (!Fraction.TryParse(result[0].ToString(), out parse) && !Fraction.TryParse(result[1].ToString(), out parse)) {
                                questions.Add("        \\item \$\\begin{array}{rl}"+c[0]+"x + "+ c[1]+"y &= "+c[2]+" \\\\ "+c[3]+"x + "+ c[4]+"y &= "+c[5] + "\\end{array}\$ \\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$"); 
                            }
                            //questions.Add(c[0]+"x + "+ c[1]+"y &= "+c[2]);
                            //questions.Add(c[3]+"x + "+ c[4]+"y &= "+c[5]);
                            //questions.Add("\\\\@$x = "+result[0].Simplify()+", y = "+result[1].Simplify()+"$");
                        }
                    }
                }
            } 
            questions.Shuffle();
            string title = "Simultaneous Equations";
            string exerciseTitle = "Solve for $x$ and $y$";
            Print(questions, title, exerciseTitle, 20);
            
        }
        
        /*****************************************************
        /////////////////////LATEX CODES//////////////////////
        *****************************************************/
        
        public static void PrintArithmetic<T>(List<T> list, string title) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{16pt}{25pt}\\selectfont", "        \\setlength\\itemsep{10pt}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        //Console.WriteLine("\\subsection{Exercise "+(i/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%30==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine("\\subsection{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void PrintArithmetic<T>(List<T> list, string title, int questions) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{16pt}{25pt}\\selectfont", "        \\setlength\\itemsep{10pt}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        //Console.WriteLine("\\subsection{Exercise "+(i/questions+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%questions==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-33mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine("\\subsection{Exercise "+((i+questions)/questions+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void Print<T>(List<T> list, string title, string exerciseTitle) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+(i/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%30==0){
                      
                        
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+((i+30)/30+1)+". "+exerciseTitle+".}");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static void PrintAnswerKey<T>(List<T> list, string title, int questions) {
            
            int p = 5; // number of pages before new page
            Console.WriteLine();
            Console.WriteLine("%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%");
            Console.WriteLine();
            Console.WriteLine("\\newpage");
            Console.WriteLine();
            Console.WriteLine("\\newgeometry{");
            Console.WriteLine(" a4paper,");
            Console.WriteLine(" total={170mm,257mm},");
            Console.WriteLine(" left=15mm,");
            Console.WriteLine(" top=20mm,");
            Console.WriteLine(" bottom=20mm,");
            Console.WriteLine(" right=15mm");
            Console.WriteLine(" }");
            Console.WriteLine("\\fontsize{10pt}{10pt}\\selectfont");
            Console.WriteLine();
            Console.WriteLine("\\section{"+title+" Answer Key}");
            
            for (int i=0; i<list.Count(); i++){
                    
                if(i==0){

Console.WriteLine("\\textbf{p"+(i/questions+1)+"}");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");

}
                                      
                Console.WriteLine(list[i]);

if (i!=0 && (i+1)%(questions*p)==0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\newpage");
                    Console.WriteLine();
                    Console.WriteLine("\\textbf{p"+((i+questions)/questions+1)+"}");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                }
                
                if (i!=0 && (i+1)%questions==0 && (i+1)%(questions*p)!=0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\textbf{p"+((i+questions)/questions+1)+"}");
                    Console.WriteLine("\\begin{multicols}{5}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                }
                
                
            }
        }
        
        public static void Print<T>(List<T> list, string title, string exerciseTitle, int questions) {
        
            //string title = "Title ()";
            //string exerciseTitle = "Instructions";
            //int m=0;
            //int i_final=30000;
            //int incre= 0;

string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};

string[] op = new string[2] {"(", ")("};
            //string end = ")=\\)";

for (int i=0; i<list.Count(); i++){
                    
                if(i==0){

Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\subsection{Exercise "+(i/questions+1)+". "+exerciseTitle+".}");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);

}
                Console.WriteLine(list[i]);

if (i!=0 && (i+1)%questions==0){

Console.WriteLine("    \\end{enumerate}");
                    Console.WriteLine("\\end{multicols}");
                    Console.WriteLine();
                    Console.WriteLine("\\newpage");
                    Console.WriteLine();
                    Console.WriteLine("\\begin{figure}[ht!]");
                    Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                    Console.WriteLine("\\end{figure}");
                    Console.WriteLine();
                    Console.WriteLine("\\vspace{-15mm}\\begingroup");
                    Console.WriteLine("\\centering");
                    Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                    Console.WriteLine("\\endgroup");
                    Console.WriteLine();
                    Console.WriteLine(latex[0]);
                    Console.WriteLine("\\subsection{Exercise "+((i+questions)/questions+1)+". "+exerciseTitle+".}");
                    Console.WriteLine("\\begin{multicols}{2}");
                    Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                    Console.WriteLine(latex[1]);
                }
            }
        }
        
        public static void PrintFraction<T>(List<T> list, string title, string exerciseTitle) {
        
        //string title = "Title ()";
        //string exerciseTitle = "Instructions";
        //int m=0;
        //int i_final=30000;
        //int incre= 0;
        
        string[] latex = new string[] {"\\fontsize{12pt}{16pt}\\selectfont", "        \\setlength\\itemsep{2em}"};
        
        string[] op = new string[2] {"(", ")("};
        //string end = ")=\\)";
        
        for (int i=0; i<list.Count(); i++){
                    
                    if(i==0){
    
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+(i/20+1)+". "+exerciseTitle+".}");
                        //Console.WriteLine("\\begin{tasks}(2)");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
    
                    
                    }
                    Console.WriteLine(list[i]);
                   
                    if (i!=0 && (i+1)%20==0){
                      
                        
                        //Console.WriteLine("\\end{tasks}");
                        Console.WriteLine("    \\end{enumerate}");
                        Console.WriteLine("\\end{multicols}");
                        Console.WriteLine();
                        Console.WriteLine("\\newpage");
                        Console.WriteLine();
                        Console.WriteLine("\\begin{figure}[ht!]");
                        Console.WriteLine("\\vspace{-23mm}\\hspace*{-23mm}\\includegraphics[scale=0.9]{Logo.jpg}");
                        Console.WriteLine("\\end{figure}");
                        Console.WriteLine();
                        Console.WriteLine("\\vspace{-15mm}\\hspace*{-10mm}\\begingroup");
                        Console.WriteLine("\\centering");
                        Console.WriteLine("\\LARGE "+title+" \\\\[0.5em]");
                        Console.WriteLine("\\endgroup");
                        Console.WriteLine();
                        //Console.WriteLine(latex[0]);
                        Console.WriteLine("\\subsection{Exercise "+((i+20)/20+1)+". "+exerciseTitle+".}");
                        //Console.WriteLine("\\begin{tasks}(2)");
                        Console.WriteLine("\\begin{multicols}{2}");
                        Console.WriteLine("    \\begin{enumerate}[label=\\arabic*)]");
                        Console.WriteLine(latex[1]);
                    }
                }
        }
        
        public static long GCD(long a, long b)
        {
            return b == 0 ? a : GCD(b, a % b);
        }
        
        public static long GCD(long a, long b, long c)
        {
            return GCD(a, GCD(b,c));
        }
        
         public static void LCM(int a, int b) {

int lcm;

int a_r=a;
             int b_r=b;
             int d=max(a_r,b_r);
             
             while(d>1) {
                 
                 if (a_r%d==0 && b_r%d==0) {
                     
                     int a_r_temp=a_r/d;
                     int b_r_temp=b_r/d;
                     a_r=a_r_temp;
                     b_r=b_r_temp;
                     lcm=d*a_r*b_r;
                     break;
                     
                 }
               
                 d--;

}
             
             lcm=d*a_r*b_r;
             Console.WriteLine("LCM({0},{1}): {2}", a,b,lcm);
         }
        
        public static int lcm(int a, int b) {

int lcm;

}
             
             return d*a_r*b_r;
             //Console.WriteLine("LCM({0},{1}): {2}", a,b,lcm);
         }
             
             
            
        public static void LCM(int a, int b, int c) {
     
            Console.WriteLine("LCM("+a+","+b+","+c+"): " + lcm(a,lcm(b,c)));
        }

public static int lcm(int a, int b, int c) {
     
            return lcm(a,lcm(b,c));
            
        }
        
        public static int max(int a, int b) {
            
            if (a>b){
                return a;
            }
            else if (b>a){
                return b;
            }
            else {
                return a;
            }
        }
        
        public static int max(int a, int b, int c) {

return max(a,max(b,c));
        }

public static int min(int a, int b) {
            
            if (a>b){
                return b;
            }
            else if (b>a){
                return a;
            }
            else {
                return a;
            }
        }
        
        public static int min(int a, int b, int c) {

return min(a,min(b,c));
        }

public static void Pyth(int lowerBound, int upperBound) {
            //Your code goes here
                       
            for (int i=lowerBound; i<=upperBound; i++) {
                
                for (int j=lowerBound; j<=upperBound; j++){
                    
                    double c = Math.Sqrt(Math.Pow(i,2)+Math.Pow(j,2));
                    if (c%1==0){
                        
                        Console.WriteLine("(a,b,c) = (" + i + "," + j + "," + c + ")");
                    }
                }
            }
        }
        
        public static void areaTrapezoid(double top, double bottom, double height) {
            
            double area = (top+bottom)*height/2;
            Console.WriteLine("Area: {0}", area);
    
        }

public static void volumeCylinder ( double radius, double height) {
            
            double vol = radius*radius*Math.PI*height;
            Console.WriteLine("Volume: {0}", vol);
        
        }

public static void sAreaCylinder(double radius, double height) {
            
            double s_area = 2*calcAreaCircle(radius) + calcAreaCircle(radius)*height;
            Console.WriteLine("Surface Area: {0}", s_area);
        }

public static void Circumf(int radius){
            
            double circ = 2*radius*Math.PI;
            Console.WriteLine("Circumference: {0}", circ);
        }
                
    
        public static void areaCircle(double r){
            double area = r*r*Math.PI;
            Console.WriteLine("Area: {0}", area);
        }
        
        public static double calcAreaCircle(double r){
        
            return r*r*Math.PI;
    
        }
        
        public static double calcCircumCircle(double r){
            
            return 2*r*Math.PI;
        }
    
        public static double sAreaCone(int r, int l) {

return Math.PI*r*r+Math.PI*r*l;
		}

public static double volumeCone(int r, int h){
			
			return Math.PI*r*r/3;
		}

public static void SimplifyRatio(int ratio1, int ratio2, int ratio3) {
            
            int divisor;
            if (ratio1>ratio2 && ratio1>ratio3) {
                divisor = ratio1;
             }
            else if (ratio2>ratio1 && ratio2>ratio3) {
                divisor = ratio2;
            }
            else divisor = ratio3;

int ratio1_reduce = ratio1;
            int ratio2_reduce = ratio2;
            int ratio3_reduce = ratio3;
            while (divisor!=1) {

if(ratio1_reduce%divisor==0 && ratio2_reduce%divisor==0 && ratio3_reduce%divisor==0){
                int ratio1_reduce_temp = ratio1_reduce/divisor;
                int ratio2_reduce_temp = ratio2_reduce/divisor;
                int ratio3_reduce_temp = ratio3_reduce/divisor;

ratio1_reduce = ratio1_reduce_temp;
                ratio2_reduce = ratio2_reduce_temp;
                ratio3_reduce = ratio3_reduce_temp;
                divisor--;
            }
            else divisor--;

}
            
            Console.WriteLine(ratio1+":"+ratio2+":"+ratio3+" = "+ratio1_reduce+":"+ratio2_reduce+":"+ratio3_reduce);
        }
        
        public static void checkAlgebra(){
            
            for (int x = -40; x<40; x++) {
                
                int a = 62*x-68;
                int b = 35;
                
                if (a%b==0){
                        
                    Console.WriteLine(x);
                }
            }
            
            
        }

public static void addLineBreak(int linesPerSection, int totalLines) {
         
            for (int i=0; i<=totalLines; i++) {
                
                if (i%linesPerSection==0) {
                    
                    Console.WriteLine("Break");
                    
                }
                
                else Console.WriteLine("No");
                
            
            }
        }
                 
        public static void circleX(double x, double radius) {
            
            Console.WriteLine("("+x+", "+Math.Round(Math.Sqrt(radius*radius-Math.Pow(x,2)),3)+")");
            
        }
        
        public static void circleY(double y, double radius) {
          
            Console.WriteLine("("+y+", "+Math.Round(Math.Sqrt(radius*radius-Math.Pow(y,2)),3)+")");
            
        }
        
        public static void angle(double x1, double y1, double x2, double y2, double x3, double y3) {
         
            double l12 = Math.Pow((x1-x2),2) +Math.Pow((y1-y2),2);
            double l13 = Math.Pow((x3-x1),2) +Math.Pow((y3-y1),2);
            double l23 = Math.Pow((x3-x2),2) +Math.Pow((y3-y2),2);
            
            double lhs = (l13-l12-l23)/(-2*Math.Sqrt(l12)*Math.Sqrt(l23));
            double angle2 = Math.Acos(lhs);
            //double angle2 = Math.Round(Math.Acos()*100,3);
            
            //Console.WriteLine(angle2 + " degrees C");
            Console.WriteLine(l12 + " " + l23 + " " + l13);
            Console.WriteLine(lhs);
                Console.WriteLine(angle2*360/(2*Math.PI)+" degrees");
        }
        
        
    }
    
    public static class Rand
    { 
        /// <summary> 
        /// Random number generator used to generate seeds, 
        /// which are then used to create new random number 
        /// generators on a per-thread basis. 
        /// </summary> 
        private static readonly Random globalRandom = new Random(); 
        private static readonly object globalLock = new object();

/// <summary> 
        /// Random number generator 
        /// </summary> 
        private static readonly ThreadLocal<Random> threadRandom = new ThreadLocal<Random>(NewRandom);

/// <summary> 
        /// Creates a new instance of Random. The seed is derived 
        /// from a global (static) instance of Random, rather 
        /// than time. 
        /// </summary> 
        public static Random NewRandom() 
        { 
            lock (globalLock) 
            { 
                return new Random(globalRandom.Next()); 
            } 
        }

/// <summary> 
        /// Returns an instance of Random which can be used freely 
        /// within the current thread. 
        /// </summary> 
        public static Random Instance { get { return threadRandom.Value; } }

/// <summary>See <see cref="Random.Next()" /></summary> 
        public static int Next() 
        { 
            return Instance.Next(); 
        }

/// <summary>See <see cref="Random.Next(int)" /></summary> 
        public static int Next(int maxValue) 
        { 
            return Instance.Next(maxValue); 
        }

/// <summary>See <see cref="Random.Next(int, int)" /></summary> 
        public static int Next(int minValue, int maxValue) 
        { 
            return Instance.Next(minValue, maxValue); 
        }

/// <summary>See <see cref="Random.NextDouble()" /></summary> 
        public static double NextDouble() 
        { 
            return Instance.NextDouble(); 
        }

/// <summary>See <see cref="Random.NextBytes(byte[])" /></summary> 
        public static void NextBytes(byte[] buffer) 
        { 
            Instance.NextBytes(buffer); 
        } 
        
        public static double NextD(double minValue, double maxValue) {
            
            return Instance.NextDouble()*(maxValue-minValue)+minValue;
        }
    } 
}

namespace ShuffleExtension {
    
    public static class ShuffleExtend {
        
        //private static readonly Random rnd = new Random();
        
        public static void Shuffle<T>(this IList<T> list) {
        
            int n = list.Count; 
       
            while (n > 1) {
            
                int k = (Rextester.Rand.Next(0, n) % n);
                n--;
                T value = list[k];
                list[k] = list[n];    
                list[n] = value;
        
            }
            
        }
    }
}

namespace CountExtension {
    
    public static class CountExtension {
        
        public static int Count(this int n) {
            //return (Value == 0 ? 1 : ((int)Math.Floor(Math.Log10(Math.Abs(Value))) + 1));
            return (n == 0 ? 1 : (int)Math.Log10(Math.Abs(n)) + 1);
        
        } 
        
    }
}

namespace MathSpace {

public struct Fraction
    {
        public long num;
        public long denom;
		public long integer;
        public long Num
        {
            get
            {
                return num;
            }
            set
            {
                num = value;
            }
        }
        public long Denom
        {
            get
            {
                return denom;
            }
            set
            {
                denom = value;
            }
        }
		public long Integer
		{
			get
			{
				return integer;
			}
			set
			{
				integer = value;
			}
		}
		
        public Fraction(int num, int denom)
        {
            // num + denom - 
            if (num > 0 && denom < 0) {
                this.num = -num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // num - denom +
            else if (num < 0 && denom > 0 ) {
                this.num = -Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // both positive or negative or zero
            else {
                this.num = Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
        }
        public Fraction(long num, long denom)
        {
            // num + denom - 
            if (num > 0 && denom < 0) {
                this.num = -num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // num - denom +
            else if (num < 0 && denom > 0 ) {
                this.num = num;
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
            // both positive or negative or zero
            else {
                this.num = Math.Abs(num);
                this.denom = Math.Abs(denom);
                this.integer = 0;
            }
        }
        public Fraction(int integer, int num, int denom)
        {
            if (num*denom<0) throw new ArgumentException("Numerator and Denominator must be positive.");
            
            // all + or only two +
            if (integer * num * denom > 0 ) {
               this.integer = Math.Abs(integer);
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
            // if an odd -
            else {
               this.integer = -integer;
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
        }
        public Fraction(long integer, long num, long denom)
        {
            if (num*denom<0) throw new ArgumentException("Numerator and Denominator must be positive.");
			 // all + or only two +
            if (integer * num * denom > 0 ) {
               this.integer = Math.Abs(integer);
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
            // if an odd -
            else {
               this.integer = -integer;
               this.num = Math.Abs(num);
               this.denom = Math.Abs(denom); 
            }
        }
        
        public Fraction (Fraction left, int right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }
        
        public Fraction (int left, Fraction right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }
        
        public Fraction (Fraction left, Fraction right)
        {
            Fraction result = left/right;
            this.num = result.num;
            this.denom = result.denom;
            this.integer = 0;
        }

public Fraction toMixed()
        {
            if (this.integer == 0 && (this.num < 0 || this.denom < 0))
            {
                return new Fraction(this.num / this.denom, Math.Abs(this.num % this.denom), Math.Abs(this.denom));
            }
            else if (this.integer == 0 && (this.num * this.denom > 0))
            {
                return new Fraction(this.num / this.denom, this.num % this.denom, this.denom);
            }
            else return new Fraction(this.integer + this.num / this.denom, this.num % this.denom, this.denom);
        }
        
        public Fraction toImproper()
        {
            if (this.integer!=0 && this.integer<0) {
                return new Fraction (-(Math.Abs(this.integer)*Math.Abs(this.denom)+Math.Abs(this.num)),Math.Abs(this.denom));
            }
            
            else if (this.integer!=0 && this.integer>0) {
                return new Fraction (Math.Abs(this.integer)*Math.Abs(this.denom)+Math.Abs(this.num),Math.Abs(this.denom));
            }
            else return new Fraction (this.num,this.denom);
        }
        
        public override string ToString()
        {
            if (this.denom == 0)
            {
                return "Div by 0";
            }
            
            // if fraction is proper or improper fraction
            if (this.denom != 1 && this.integer == 0 && this.num%this.denom!=0)
            {
                // if fraction is negative (either num or denom negative but not both)
                if ((this.num < 0 || this.denom < 0 ) && !(this.num<0 && this.denom<0) )
                {
                    this.denom = Math.Abs(this.denom);
                    return this.num + "/" + this.denom;
                }
                // if fraction is positive
                else return num + "/" + denom; // + ", " + num/denom + " " + num%denom + "/" + denom;
            }
			
			//if fraction is mixed number
			else if (this.denom != 1 && this.integer != 0 && this.num%this.denom!=0)
            {
                var new_integer = Math.Abs(this.integer) + this.num/this.denom;
                var new_num = this.num % this.denom;
                this.integer = new_integer;
                this.num = new_num;
                // if fraction is negative (either num or denom negative but not both)
                if (this.integer < 0)
                {
                    return this.integer + " " + this.num + "/" + this.denom;
                }
                // if fraction is positive
                else return this.integer + " " + this.num + "/" + this.denom;
            }

// if denom not 1 and numerator is a multiple of the denominator (ie. 4/2 ==> 2) and not mixed number (result is integer)
            else if (this.num % this.denom == 0 && this.integer==0)
            {
                return (this.num / this.denom).ToString();
            }
            
			// if denom not 1 and numerator is a multiple of the denominator (ie. 4/2 ==> 2) and mixed number (result is integer)
			else if (this.num % this.denom == 0 && this.integer!=0)
            {
                return (this.integer+(this.num / this.denom)).ToString();
            }
			
            // if denominator is 1, ie., whole number and not mixed number
			
			else if (this.integer!=0) {
				return (integer+num).ToString();
			}
			
            else return num.ToString();
			
        }

public Fraction Simplify()
        {
            int divisor = Convert.ToInt32(GCD(this.num, this.denom));
            if (this.denom != 0 && this.integer==0 && this.num >0)
            {
                return new Fraction(this.num / divisor, this.denom / divisor);
            }
            
            else if (this.denom != 0 && this.integer==0 && this.num <0)
            {
                return new Fraction(-Math.Abs(this.num / divisor), Math.Abs(this.denom / divisor));
            }
            
            else if (this.denom != 0 && this.integer!=0)
            {
                 return new Fraction(this.integer, this.num / divisor, this.denom / divisor);
                
            }
                
            else return new Fraction (this.num, this.denom);

}
        public static long GCD(long a, long b)
        {
            return b == 0 ? a : GCD(b, a % b);
        }
        
        public Fraction Reciprocal()
        {
            return new Fraction(this.Denom, this.Num);
        }

public static Fraction operator +(Fraction left, Fraction right)
        {
            Fraction result;
			if (left.integer==0 &&right.integer==0){
                result = new Fraction(left.num * right.denom + right.num * left.denom, left.denom * right.denom);
                
            }
			else { 
				//result = new Fraction((left.integer*left.denom+left.num)*right.denom+(right.integer*right.denom+right.num)*left.denom, left.denom * right.denom);
				result = (new Fraction(left.integer+right.integer, left.num * right.denom + right.num * left.denom, left.denom * right.denom)).toMixed();
			}
            return result.toMixed().Simplify();
        }

public static Fraction operator +(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = new Fraction(left * right.denom + right.num, right.denom);
            }
            else {
                result = (new Fraction(left+right.integer, right.num, right.denom)).toMixed();
            }
            return result.Simplify();
        }

public static Fraction operator +(Fraction left, int right)
        {
            Fraction result;
            if (left.integer==0) {
                result = new Fraction(left.num + left.denom * right, left.denom);
            }
    
            else {
                result = (new Fraction(left.integer+right, left.denom)).toMixed();
            }
            return result.Simplify();
        }
        
        public static Fraction operator -(Fraction frac)
        {
            if (frac.integer==0) {
                return new Fraction(-frac.num,frac.denom);
            }
            else return (new Fraction (-frac.integer,frac.num,frac.denom)).toMixed();
                
        }

public static Fraction operator -(Fraction left, Fraction right)
        {
            Fraction result;
            if (left.integer==0 && right.integer==0) {
                result = (new Fraction(left.num * right.denom - right.num * left.denom, left.denom * right.denom)).toMixed();
            }
            
            else {
                if (((left.integer*left.denom+left.num)/left.denom)>=((right.integer*right.denom+right.num)/right.denom)) {
                    result = (left.toImproper()-right.toImproper()).toMixed();
                }
                else result = (left.toImproper()-right.toImproper()).toMixed();
            }
            return result.Simplify();
        }

public static Fraction operator -(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = new Fraction(left * right.denom - right.num, right.denom);
            }
            else result = (new Fraction(left * right.denom - right.toImproper().num, right.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator -(Fraction left, int right)
        {
            Fraction result;
            if (left.integer==0) {
                result = new Fraction(left.num - left.denom * right, left.denom);
            }
            // if mixed numbers
            else result = (new Fraction(left.toImproper().num - left.denom * right, left.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator *(Fraction left, Fraction right)
        {
            Fraction result;
            
            if (left.integer==0 && right.integer==0){
                result = new Fraction(left.num * right.num, Math.Abs(left.denom * right.denom));
            }
            // if mixed numbers
            else result = (left.toImproper()*right.toImproper()).toMixed();
                
            return result.Simplify();
        }

public static Fraction operator *(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0){
                result = new Fraction(left * right.num, right.denom);
            }
            else result = (new Fraction(right.toImproper().num * left, right.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator *(Fraction left, int right)
        {
            Fraction result;
            // if improper fraction
            if (left.integer==0){
                result = new Fraction(left.num * right, left.denom);
            }
            // if mixed numbers
            else result = (new Fraction(left.toImproper().num * right, left.denom)).toMixed();
            
            return result.Simplify();
        }

public static Fraction operator /(Fraction left, Fraction right)
        {
            Fraction result;
            if (left.integer==0 &&right.integer==0){
                result = left * right.Reciprocal();
            }
            else result = (left.toImproper() * right.toImproper().Reciprocal()).toMixed();
                
            return result.Simplify();
        }

public static Fraction operator /(int left, Fraction right)
        {
            Fraction result;
            if (right.integer==0) {
                result = left * right.Reciprocal();
            }
            else result = left * right.toImproper().Reciprocal();
            
            return result.Simplify();
        }

public static Fraction operator /(Fraction left, int right)
        {
            Fraction rightRecip = new Fraction(1,right);
            Fraction result;
            if (left.integer==0) {
                result = left * rightRecip;
            }
            else {
                result = left.toImproper() * rightRecip;
            }
            return result.Simplify();
        }

public static int LCM(int a, int b)
        {
            int lcm;
            int a_r = a;
            int b_r = b;
            int d = max(a_r, b_r);

while (d > 1)
            {
                if (a_r % d == 0 && b_r % d == 0)
                {
                    int a_r_temp = a_r / d;
                    int b_r_temp = b_r / d;
                    a_r = a_r_temp;
                    b_r = b_r_temp;
                    lcm = d * a_r * b_r;
                    break;
                }
                d--;
            }
            lcm = d * a_r * b_r;
            return lcm;
        }

public static int LCM(long a, long b)
        {
            int lcm;
            long a_r = a;
            long b_r = b;
            int d = Convert.ToInt32(max(a_r, b_r));

while (d > 1)
            {
                if (a_r % d == 0 && b_r % d == 0)
                {
                    long a_r_temp = a_r / d;
                    long b_r_temp = b_r / d;
                    a_r = a_r_temp;
                    b_r = b_r_temp;
                    lcm = Convert.ToInt32(d * a_r * b_r);
                    break;
                }
                d--;
            }
            lcm = Convert.ToInt32(d * a_r * b_r);
            return lcm;
        }

public static int max(int a, int b)
        {

if (a > b)
            {
                return a;
            }
            else if (b > a)
            {
                return b;
            }
            else
            {
                return a;
            }
        }

public static long max(long a, long b)
        {

if (a > b)
            {
                return a;
            }
            else if (b > a)
            {
                return b;
            }
            else
            {
                return a;
            }
        }
		
        public double toDeci() 
        {  
            if (this.integer==0) {
                return (double) this.num/this.denom;
            }
            else {
                return (double) (this.integer*this.denom+this.num)/this.denom;
            }
        }
        
        public static Fraction toFrac(double deci)
        {
            /*List<double> d = new List<double>();
            List<double> z = new List<double>();
            List<double> n = new List<double>();*/

double[] d = new double[6];
            double[] z = new double[6];
            double[] n = new double[6];
            z[1] = deci; //X
            d[0] = 0;
            d[1] = 1;

for (int i = 1; i < 5; i++)
            {
                z[i + 1] = 1 / (z[i] - Math.Floor(z[i]));
                d[i + 1] = d[i] * Math.Floor(z[i + 1]) + d[i - 1];
                n[i + 1] = Math.Round(z[1] * d[i + 1]);
            }
            int num, denom;
            num = (int)n[5];
            denom = (int)d[5];

return new Fraction(num, denom);
        }

/*        public static Fraction RealToFraction(double value, double error)
                {
                    if (error <= 0.0 || error >= 1.0)
                    {
                        throw new ArgumentOutOfRangeException("error", "Must be between 0 and 1 (exclusive).");
                    }

int sign = Math.Sign(value);

if (sign == -1)
                    {
                        value = Math.Abs(value);
                    }

if (sign != 0)
                    {
                        // error is the maximum relative error; convert to absolute
                        error *= value;
                    }

int n = (int)Math.Floor(value);
                    value -= n;

if (value < error)
                    {
                        return new Fraction(sign * n, 1);
                    }

if (1 - error < value)
                    {
                        return new Fraction(sign * (n + 1), 1);
                    }

// The lower fraction is 0/1
                    int lower_n = 0;
                    int lower_d = 1;

// The upper fraction is 1/1
                    int upper_n = 1;
                    int upper_d = 1;

while (true)
                    {
                        // The middle fraction is (lower_n + upper_n) / (lower_d + upper_d)
                        int middle_n = lower_n + upper_n;
                        int middle_d = lower_d + upper_d;

if (middle_d * (value + error) < middle_n)
                        {
                            // real + error < middle : middle is our new upper
                            upper_n = middle_n;
                            upper_d = middle_d;
                        }
                        else if (middle_n < (value - error) * middle_d)
                        {
                            // middle < real - error : middle is our new lower
                            lower_n = middle_n;
                            lower_d = middle_d;
                        }
                        else
                        {
                            // Middle is our best fraction
                            return new Fraction((n * middle_d + middle_n) * sign, middle_d);
                        }
                    }
                }*/

public static Fraction Parse(string input)
        {
            if (String.IsNullOrWhiteSpace(input)) {
                throw new ArgumentNullException();
            }

//var instance = new Fraction();

// checks if there is more than one "/"
            if (input.IndexOf("/") != input.LastIndexOf("/")) {
                throw new ArgumentException();
            }
            //return instance;

int v;

// 
            if (input.IndexOf("/") != -1)
            {
                if (int.TryParse(input.Substring(0, input.IndexOf("/")), out v)
             && int.TryParse(input.Substring(input.IndexOf("/") + 1), out v))
                {
                    int num1 = int.Parse(input.Substring(0, input.IndexOf("/")));
                    int denom1 = int.Parse(input.Substring(input.IndexOf("/") + 1));
                    var frac = new Fraction(num1, denom1);
                    return frac;
                }
                else throw new IndexOutOfRangeException();
            }
            else // if 
            {
                if (int.TryParse(input, out v))
                {
                    return new Fraction(int.Parse(input), 1);
                }

else throw new IndexOutOfRangeException();
            }

}

public static bool TryParse(string input, out Fraction frac)
        {
            if (string.IsNullOrWhiteSpace(input))
            {
                frac = new Fraction(0, 0);
                return false;
            }

if (input.IndexOf("/") == -1 || input.IndexOf("/") != input.LastIndexOf("/"))
            {
                frac = new Fraction(0, 0);
                return false;
            }

long v;
            if (long.TryParse(input.Substring(0, input.IndexOf("/")), out v)
             && long.TryParse(input.Substring(input.IndexOf("/") + 1), out v))
            {

frac = new MathSpace.Fraction(1, 1);
                v = 1;
                return true;
            }
            else frac = new Fraction(0, 0); return false;
        }

public static Fraction ConvertFrom(object obj)
        {
            Fraction frac = new MathSpace.Fraction(0, 0);
            if (obj.GetType() == frac.GetType())
            {
                frac = (Fraction) obj;
                return frac;
            }
            else throw new NotSupportedException();
        }

public static double ConvertToDecimal(Fraction frac)
        {
            return Convert.ToDouble(frac.Num) / Convert.ToDouble(frac.Denom);
        }

public static double operator +(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) + right;
            return result;
        }

public static double operator +(double left, Fraction right)
        {
            double result = left + ConvertToDecimal(right);
            return result;
        }

public static double operator -(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) - right;
            return result;
        }

public static double operator -(double left, Fraction right)
        {
            double result = left - ConvertToDecimal(right);
            return result;
        }

public static double operator *(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) * right;
            return result;
        }

public static double operator *(double left, Fraction right)
        {
            double result = left * ConvertToDecimal(right);
            return result;
        }

public static double operator /(Fraction left, double right)
        {
            double result = ConvertToDecimal(left) / right;
            return result;
        }

public static double operator /(double left, Fraction right)
        {
            double result = left / ConvertToDecimal(right);
            return result;
        }

public static Fraction Pow(Fraction frac, int n)
        {
            long num_new = (long) Math.Pow(frac.Num, n);
            long denom_new = (long) Math.Pow(frac.Denom, n);
            return new MathSpace.Fraction(num_new, denom_new);
        }
    }
}

Show compiler warnings [ + ] Show input
Compilation time: 0,3 sec, absolute running time: 0,64 sec, cpu time: 0,16 sec, average memory usage: 22 Mb, average nr of threads: 5

\begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 1. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $5\dfrac{7}{13}\times1\dfrac{15}{24}=\underline{\hspace{3cm}}$\dfrac{9}{1}\) \item $1\dfrac{8}{9}\times1\dfrac{13}{17}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $1\dfrac{6}{54}\times\dfrac{9}{85}=\underline{\hspace{3cm}}$\dfrac{2}{17}\) \item $\dfrac{36}{81}\div\dfrac{7}{84}=\underline{\hspace{3cm}}$\dfrac{16}{3}\) \item $6\dfrac{9}{12}+3\dfrac{1}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $5\dfrac{2}{11}\times\dfrac{9}{27}=\underline{\hspace{3cm}}$\dfrac{19}{11}\) \item $\dfrac{21}{45}\div\dfrac{56}{72}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $1\dfrac{1}{15}\times7\dfrac{4}{8}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $\dfrac{10}{52}\times3\dfrac{2}{8}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $8\dfrac{2}{8}-9\dfrac{8}{12}=\underline{\hspace{3cm}}$17\dfrac{11}{12}\) \item $7\dfrac{9}{10}+9\dfrac{2}{8}=\underline{\hspace{3cm}}$17\dfrac{3}{20}\) \item $3\dfrac{4}{6}-9\dfrac{5}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \item $\dfrac{28}{90}\times\dfrac{21}{14}=\underline{\hspace{3cm}}$\dfrac{7}{15}\) \item $2\dfrac{18}{19}\times2\dfrac{25}{35}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $8\dfrac{7}{8}-5\dfrac{3}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{8}\) \item $1\dfrac{2}{6}\times2\dfrac{2}{20}=\underline{\hspace{3cm}}$\dfrac{14}{5}\) \item $\dfrac{10}{72}\times2\dfrac{24}{30}=\underline{\hspace{3cm}}$\dfrac{7}{18}\) \item $\dfrac{23}{34}\times1\dfrac{3}{69}=\underline{\hspace{3cm}}$\dfrac{12}{17}\) \item $\dfrac{45}{36}\div\dfrac{18}{8}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \item $4\dfrac{6}{9}-7\dfrac{1}{4}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 2. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $6\dfrac{3}{4}-8\dfrac{1}{10}=\underline{\hspace{3cm}}$14\dfrac{17}{20}\) \item $2\dfrac{4}{8}-8\dfrac{4}{9}=\underline{\hspace{3cm}}$10\dfrac{17}{18}\) \item $\dfrac{45}{20}\div\dfrac{66}{16}=\underline{\hspace{3cm}}$\dfrac{6}{11}\) \item $3\dfrac{8}{10}-2\dfrac{4}{6}=\underline{\hspace{3cm}}$6\dfrac{7}{15}\) \item $9\dfrac{1}{6}-5\dfrac{1}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{4}\) \item $\dfrac{26}{32}\div\dfrac{26}{16}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $5\dfrac{4}{6}+7\dfrac{2}{9}=\underline{\hspace{3cm}}$12\dfrac{8}{9}\) \item $6\dfrac{1}{2}-2\dfrac{3}{5}=\underline{\hspace{3cm}}$9\dfrac{1}{10}\) \item $\dfrac{24}{72}\times\dfrac{40}{30}=\underline{\hspace{3cm}}$\dfrac{4}{9}\) \item $9\dfrac{1}{2}-7\dfrac{1}{7}=\underline{\hspace{3cm}}$16\dfrac{9}{14}\) \item $\dfrac{48}{66}\div\dfrac{56}{88}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $4\dfrac{3}{12}+8\dfrac{1}{10}=\underline{\hspace{3cm}}$12\dfrac{7}{20}\) \item $\dfrac{36}{18}\div\dfrac{28}{8}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $\dfrac{72}{33}\div\dfrac{40}{15}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{36}{48}\div\dfrac{7}{35}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{90}{55}\div\dfrac{72}{44}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $1\dfrac{2}{7}\times1\dfrac{5}{90}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $9\dfrac{9}{12}+4\dfrac{3}{4}=\underline{\hspace{3cm}}$14\dfrac{1}{2}\) \item $6\dfrac{8}{12}-9\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{4}{15}\) \item $5\dfrac{5}{6}-9\dfrac{2}{8}=\underline{\hspace{3cm}}$15\dfrac{1}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 3. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $7\dfrac{1}{4}+2\dfrac{1}{5}=\underline{\hspace{3cm}}$9\dfrac{9}{20}\) \item $9\dfrac{1}{12}-4\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{7}{12}\) \item $\dfrac{8}{64}\div\dfrac{40}{80}=\underline{\hspace{3cm}}$\dfrac{1}{4}\) \item $3\dfrac{5}{10}-8\dfrac{7}{8}=\underline{\hspace{3cm}}$12\dfrac{3}{8}\) \item $5\dfrac{6}{7}-9\dfrac{3}{6}=\underline{\hspace{3cm}}$15\dfrac{5}{14}\) \item $9\dfrac{8}{12}-7\dfrac{5}{6}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $\dfrac{55}{5}\div\dfrac{99}{42}=\underline{\hspace{3cm}}$\dfrac{14}{3}\) \item $9\dfrac{3}{12}+7\dfrac{6}{9}=\underline{\hspace{3cm}}$16\dfrac{11}{12}\) \item $\dfrac{24}{48}\times7\dfrac{1}{3}=\underline{\hspace{3cm}}$\dfrac{11}{3}\) \item $7\dfrac{1}{4}+8\dfrac{5}{6}=\underline{\hspace{3cm}}$16\dfrac{1}{12}\) \item $2\dfrac{6}{9}-6\dfrac{2}{5}=\underline{\hspace{3cm}}$9\dfrac{1}{15}\) \item $\dfrac{66}{46}\div\dfrac{48}{92}=\underline{\hspace{3cm}}$\dfrac{11}{4}\) \item $6\dfrac{11}{12}+4\dfrac{2}{8}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $9\dfrac{6}{12}-4\dfrac{7}{8}=\underline{\hspace{3cm}}$14\dfrac{3}{8}\) \item $7\dfrac{7}{10}-9\dfrac{4}{8}=\underline{\hspace{3cm}}$17\dfrac{1}{5}\) \item $\dfrac{15}{45}\div\dfrac{64}{60}=\underline{\hspace{3cm}}$\dfrac{5}{16}\) \item $3\dfrac{7}{17}\times\dfrac{3}{58}=\underline{\hspace{3cm}}$\dfrac{3}{17}\) \item $1\dfrac{17}{68}\times1\dfrac{5}{7}=\underline{\hspace{3cm}}$\dfrac{15}{7}\) \item $\dfrac{72}{21}\div\dfrac{56}{14}=\underline{\hspace{3cm}}$\dfrac{6}{7}\) \item $4\dfrac{3}{9}-7\dfrac{7}{12}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 4. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $4\dfrac{4}{6}+6\dfrac{8}{9}=\underline{\hspace{3cm}}$11\dfrac{5}{9}\) \item $3\dfrac{5}{10}+9\dfrac{1}{5}=\underline{\hspace{3cm}}$12\dfrac{7}{10}\) \item $4\dfrac{2}{10}+4\dfrac{4}{8}=\underline{\hspace{3cm}}$8\dfrac{7}{10}\) \item $5\dfrac{3}{12}-9\dfrac{9}{10}=\underline{\hspace{3cm}}$15\dfrac{3}{20}\) \item $8\dfrac{6}{10}-6\dfrac{3}{4}=\underline{\hspace{3cm}}$15\dfrac{7}{20}\) \item $2\dfrac{1}{4}+8\dfrac{3}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $6\dfrac{8}{9}+8\dfrac{10}{12}=\underline{\hspace{3cm}}$15\dfrac{13}{18}\) \item $\dfrac{27}{24}\times\dfrac{88}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $5\dfrac{4}{12}-9\dfrac{2}{4}=\underline{\hspace{3cm}}$14\dfrac{5}{6}\) \item $7\dfrac{4}{6}-6\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $4\dfrac{10}{12}+5\dfrac{5}{6}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $\dfrac{98}{78}\div\dfrac{21}{18}=\underline{\hspace{3cm}}$\dfrac{14}{13}\) \item $2\dfrac{7}{9}-9\dfrac{5}{6}=\underline{\hspace{3cm}}$12\dfrac{11}{18}\) \item $2\dfrac{4}{8}-8\dfrac{9}{12}=\underline{\hspace{3cm}}$11\dfrac{1}{4}\) \item $9\dfrac{3}{9}+9\dfrac{3}{4}=\underline{\hspace{3cm}}$19\dfrac{1}{12}\) \item $9\dfrac{6}{7}+6\dfrac{6}{12}=\underline{\hspace{3cm}}$16\dfrac{5}{14}\) \item $7\dfrac{3}{6}+6\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{3}{4}\) \item $4\dfrac{2}{8}-6\dfrac{5}{12}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $\dfrac{80}{16}\div\dfrac{25}{60}=\underline{\hspace{3cm}}$\dfrac{12}{1}\) \item $\dfrac{51}{9}\div\dfrac{74}{37}=\underline{\hspace{3cm}}$\dfrac{17}{6}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 5. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $6\dfrac{6}{9}-2\dfrac{3}{4}=\underline{\hspace{3cm}}$9\dfrac{5}{12}\) \item $\dfrac{22}{9}\times\dfrac{35}{77}=\underline{\hspace{3cm}}$\dfrac{10}{9}\) \item $\dfrac{16}{12}\div\dfrac{8}{10}=\underline{\hspace{3cm}}$\dfrac{5}{3}\) \item $3\dfrac{1}{6}+3\dfrac{1}{10}=\underline{\hspace{3cm}}$6\dfrac{4}{15}\) \item $\dfrac{60}{35}\div\dfrac{24}{56}=\underline{\hspace{3cm}}$\dfrac{4}{1}\) \item $5\dfrac{8}{9}+4\dfrac{2}{4}=\underline{\hspace{3cm}}$10\dfrac{7}{18}\) \item $2\dfrac{4}{6}-6\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{1}{6}\) \item $4\dfrac{3}{10}-8\dfrac{3}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{20}\) \item $3\dfrac{5}{10}-5\dfrac{1}{6}=\underline{\hspace{3cm}}$8\dfrac{2}{3}\) \item $9\dfrac{1}{2}+7\dfrac{7}{9}=\underline{\hspace{3cm}}$17\dfrac{5}{18}\) \item $3\dfrac{2}{10}+7\dfrac{4}{8}=\underline{\hspace{3cm}}$10\dfrac{7}{10}\) \item $5\dfrac{6}{12}-6\dfrac{2}{4}=\underline{\hspace{3cm}}$-12\) \item $1\dfrac{20}{32}\times2\dfrac{10}{39}=\underline{\hspace{3cm}}$\dfrac{11}{3}\) \item $\dfrac{77}{99}\div\dfrac{12}{18}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $\dfrac{12}{21}\div\dfrac{32}{76}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $2\dfrac{2}{3}+3\dfrac{8}{10}=\underline{\hspace{3cm}}$6\dfrac{7}{15}\) \item $\dfrac{52}{90}\times\dfrac{80}{64}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $3\dfrac{1}{10}-6\dfrac{6}{12}=\underline{\hspace{3cm}}$9\dfrac{3}{5}\) \item $3\dfrac{4}{8}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$6\dfrac{1}{3}\) \item $7\dfrac{3}{4}-5\dfrac{4}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 6. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $5\dfrac{3}{5}+3\dfrac{9}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{20}\) \item $\dfrac{33}{44}\div\dfrac{72}{66}=\underline{\hspace{3cm}}$\dfrac{11}{16}\) \item $9\dfrac{4}{10}-9\dfrac{3}{12}=\underline{\hspace{3cm}}$18\dfrac{13}{20}\) \item $\dfrac{2}{4}\div\dfrac{21}{6}=\underline{\hspace{3cm}}$\dfrac{1}{7}\) \item $7\dfrac{3}{5}-5\dfrac{1}{2}=\underline{\hspace{3cm}}$13\dfrac{1}{10}\) \item $5\dfrac{1}{12}+6\dfrac{6}{8}=\underline{\hspace{3cm}}$11\dfrac{5}{6}\) \item $\dfrac{90}{45}\div\dfrac{21}{49}=\underline{\hspace{3cm}}$\dfrac{14}{3}\) \item $3\dfrac{5}{15}\times1\dfrac{8}{10}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{10}{33}\times\dfrac{99}{9}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $3\dfrac{5}{12}-3\dfrac{1}{6}=\underline{\hspace{3cm}}$6\dfrac{7}{12}\) \item $\dfrac{60}{50}\div\dfrac{30}{15}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $4\dfrac{2}{8}-6\dfrac{9}{10}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $5\dfrac{2}{8}+7\dfrac{11}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{6}\) \item $8\dfrac{6}{12}-8\dfrac{5}{9}=\underline{\hspace{3cm}}$17\dfrac{1}{18}\) \item $\dfrac{34}{2}\div\dfrac{50}{5}=\underline{\hspace{3cm}}$\dfrac{17}{10}\) \item $5\dfrac{1}{10}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$7\dfrac{3}{5}\) \item $5\dfrac{3}{4}+5\dfrac{2}{5}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $\dfrac{13}{26}\div\dfrac{12}{14}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $3\dfrac{8}{10}-6\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{20}\) \item $\dfrac{57}{96}\times\dfrac{16}{3}=\underline{\hspace{3cm}}$\dfrac{19}{6}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 7. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $4\dfrac{5}{12}+4\dfrac{5}{10}=\underline{\hspace{3cm}}$8\dfrac{11}{12}\) \item $\dfrac{92}{23}\div\dfrac{7}{14}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $4\dfrac{6}{10}+3\dfrac{1}{3}=\underline{\hspace{3cm}}$7\dfrac{14}{15}\) \item $\dfrac{9}{15}\div\dfrac{37}{74}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $4\dfrac{4}{9}+7\dfrac{4}{6}=\underline{\hspace{3cm}}$12\dfrac{1}{9}\) \item $8\dfrac{3}{5}-5\dfrac{1}{2}=\underline{\hspace{3cm}}$14\dfrac{1}{10}\) \item $\dfrac{20}{22}\div\dfrac{38}{57}=\underline{\hspace{3cm}}$\dfrac{15}{11}\) \item $6\dfrac{2}{9}+9\dfrac{10}{12}=\underline{\hspace{3cm}}$16\dfrac{1}{18}\) \item $2\dfrac{8}{10}+7\dfrac{8}{12}=\underline{\hspace{3cm}}$10\dfrac{7}{15}\) \item $5\dfrac{8}{10}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$12\dfrac{3}{10}\) \item $4\dfrac{7}{12}+2\dfrac{3}{9}=\underline{\hspace{3cm}}$6\dfrac{11}{12}\) \item $8\dfrac{1}{3}-6\dfrac{9}{12}=\underline{\hspace{3cm}}$15\dfrac{1}{12}\) \item $7\dfrac{2}{8}+6\dfrac{6}{9}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $\dfrac{12}{96}\div\dfrac{9}{84}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $2\dfrac{3}{6}+2\dfrac{6}{8}=\underline{\hspace{3cm}}$5\dfrac{1}{4}\) \item $7\dfrac{3}{10}-9\dfrac{1}{5}=\underline{\hspace{3cm}}$16\dfrac{1}{2}\) \item $\dfrac{24}{90}\div\dfrac{48}{75}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $3\dfrac{1}{2}+2\dfrac{7}{9}=\underline{\hspace{3cm}}$6\dfrac{5}{18}\) \item $\dfrac{12}{14}\times\dfrac{11}{22}=\underline{\hspace{3cm}}$\dfrac{3}{7}\) \item $3\dfrac{7}{12}-2\dfrac{1}{3}=\underline{\hspace{3cm}}$5\dfrac{11}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 8. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $2\dfrac{3}{4}\times\dfrac{45}{55}=\underline{\hspace{3cm}}$\dfrac{9}{4}\) \item $\dfrac{21}{49}\times\dfrac{84}{57}=\underline{\hspace{3cm}}$\dfrac{12}{19}\) \item $\dfrac{38}{19}\div\dfrac{8}{24}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{33}{45}\div\dfrac{33}{63}=\underline{\hspace{3cm}}$\dfrac{7}{5}\) \item $9\dfrac{1}{3}+6\dfrac{4}{9}=\underline{\hspace{3cm}}$15\dfrac{7}{9}\) \item $5\dfrac{7}{12}+2\dfrac{5}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{12}\) \item $\dfrac{4}{6}\div\dfrac{33}{63}=\underline{\hspace{3cm}}$\dfrac{14}{11}\) \item $9\dfrac{1}{2}+5\dfrac{6}{8}=\underline{\hspace{3cm}}$15\dfrac{1}{4}\) \item $\dfrac{50}{85}\times1\dfrac{7}{14}=\underline{\hspace{3cm}}$\dfrac{15}{17}\) \item $\dfrac{63}{98}\times3\dfrac{17}{27}=\underline{\hspace{3cm}}$\dfrac{7}{3}\) \item $6\dfrac{5}{6}+7\dfrac{4}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $\dfrac{11}{62}\times1\dfrac{29}{33}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \item $\dfrac{18}{12}\times\dfrac{24}{99}=\underline{\hspace{3cm}}$\dfrac{4}{11}\) \item $\dfrac{55}{35}\times\dfrac{35}{99}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \item $6\dfrac{2}{9}+4\dfrac{5}{6}=\underline{\hspace{3cm}}$11\dfrac{1}{18}\) \item $9\dfrac{1}{5}+6\dfrac{6}{12}=\underline{\hspace{3cm}}$15\dfrac{7}{10}\) \item $5\dfrac{2}{12}+8\dfrac{5}{6}=\underline{\hspace{3cm}}$-14\) \item $\dfrac{52}{40}\div\dfrac{9}{30}=\underline{\hspace{3cm}}$\dfrac{13}{3}\) \item $6\dfrac{6}{10}+7\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{17}{20}\) \item $9\dfrac{5}{10}-7\dfrac{2}{6}=\underline{\hspace{3cm}}$16\dfrac{5}{6}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 9. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{46}{2}\times\dfrac{6}{46}=\underline{\hspace{3cm}}$\dfrac{3}{1}\) \item $9\dfrac{3}{5}-8\dfrac{2}{10}=\underline{\hspace{3cm}}$17\dfrac{4}{5}\) \item $\dfrac{84}{17}\times\dfrac{17}{35}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{30}{35}\div\dfrac{50}{35}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $\dfrac{45}{33}\div\dfrac{30}{14}=\underline{\hspace{3cm}}$\dfrac{7}{11}\) \item $\dfrac{36}{68}\div\dfrac{81}{45}=\underline{\hspace{3cm}}$\dfrac{5}{17}\) \item $\dfrac{26}{13}\div\dfrac{12}{84}=\underline{\hspace{3cm}}$\dfrac{14}{1}\) \item $\dfrac{20}{24}\div\dfrac{30}{4}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $2\dfrac{2}{6}-4\dfrac{4}{10}=\underline{\hspace{3cm}}$6\dfrac{11}{15}\) \item $\dfrac{54}{15}\times\dfrac{80}{16}=\underline{\hspace{3cm}}$\dfrac{18}{1}\) \item $\dfrac{80}{45}\div\dfrac{24}{36}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $7\dfrac{1}{2}-5\dfrac{4}{7}=\underline{\hspace{3cm}}$13\dfrac{1}{14}\) \item $6\dfrac{3}{4}+9\dfrac{2}{5}=\underline{\hspace{3cm}}$16\dfrac{3}{20}\) \item $6\dfrac{4}{8}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$10\dfrac{5}{6}\) \item $7\dfrac{8}{12}+3\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{11}{12}\) \item $6\dfrac{2}{4}+5\dfrac{3}{10}=\underline{\hspace{3cm}}$11\dfrac{4}{5}\) \item $2\dfrac{22}{28}\times\dfrac{19}{39}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $\dfrac{90}{45}\times\dfrac{56}{42}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $4\dfrac{4}{6}+8\dfrac{10}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{2}\) \item $9\dfrac{2}{3}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$-14\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 10. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $2\dfrac{2}{5}+4\dfrac{3}{12}=\underline{\hspace{3cm}}$6\dfrac{13}{20}\) \item $\dfrac{5}{17}\times\dfrac{34}{55}=\underline{\hspace{3cm}}$\dfrac{2}{11}\) \item $3\dfrac{6}{9}+8\dfrac{2}{3}=\underline{\hspace{3cm}}$12\dfrac{1}{3}\) \item $9\dfrac{1}{2}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$12\dfrac{1}{3}\) \item $2\dfrac{8}{10}-7\dfrac{2}{5}=\underline{\hspace{3cm}}$10\dfrac{1}{5}\) \item $5\dfrac{1}{2}-7\dfrac{7}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \item $2\dfrac{4}{16}\times1\dfrac{6}{90}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $5\dfrac{1}{3}-5\dfrac{4}{12}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $6\dfrac{6}{8}+2\dfrac{1}{5}=\underline{\hspace{3cm}}$8\dfrac{19}{20}\) \item $\dfrac{26}{96}\times\dfrac{96}{32}=\underline{\hspace{3cm}}$\dfrac{13}{16}\) \item $2\dfrac{1}{5}+6\dfrac{8}{12}=\underline{\hspace{3cm}}$8\dfrac{13}{15}\) \item $\dfrac{65}{25}\div\dfrac{26}{10}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{52}{32}\div\dfrac{49}{56}=\underline{\hspace{3cm}}$\dfrac{13}{7}\) \item $\dfrac{24}{2}\div\dfrac{84}{7}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{36}{84}\div\dfrac{10}{42}=\underline{\hspace{3cm}}$\dfrac{9}{5}\) \item $3\dfrac{2}{4}-8\dfrac{1}{5}=\underline{\hspace{3cm}}$11\dfrac{7}{10}\) \item $9\dfrac{1}{6}-6\dfrac{2}{3}=\underline{\hspace{3cm}}$15\dfrac{5}{6}\) \item $7\dfrac{1}{4}+8\dfrac{1}{3}=\underline{\hspace{3cm}}$15\dfrac{7}{12}\) \item $6\dfrac{3}{4}-6\dfrac{8}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \item $\dfrac{38}{54}\div\dfrac{30}{81}=\underline{\hspace{3cm}}$\dfrac{19}{10}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 11. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $2\dfrac{2}{3}+6\dfrac{4}{10}=\underline{\hspace{3cm}}$9\dfrac{1}{15}\) \item $8\dfrac{2}{8}+5\dfrac{5}{6}=\underline{\hspace{3cm}}$14\dfrac{1}{12}\) \item $\dfrac{25}{70}\div\dfrac{15}{6}=\underline{\hspace{3cm}}$\dfrac{1}{7}\) \item $9\dfrac{2}{9}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$11\dfrac{13}{18}\) \item $1\dfrac{2}{4}\times\dfrac{24}{76}=\underline{\hspace{3cm}}$\dfrac{9}{19}\) \item $5\dfrac{4}{5}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{1}{20}\) \item $3\dfrac{4}{5}+8\dfrac{7}{10}=\underline{\hspace{3cm}}$12\dfrac{1}{2}\) \item $\dfrac{10}{18}\div\dfrac{40}{8}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $\dfrac{93}{62}\div\dfrac{99}{30}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $4\dfrac{6}{8}-6\dfrac{3}{5}=\underline{\hspace{3cm}}$11\dfrac{7}{20}\) \item $8\dfrac{7}{9}+3\dfrac{4}{8}=\underline{\hspace{3cm}}$12\dfrac{5}{18}\) \item $8\dfrac{6}{8}-8\dfrac{9}{12}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $6\dfrac{2}{12}+5\dfrac{4}{9}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $5\dfrac{1}{10}+6\dfrac{1}{2}=\underline{\hspace{3cm}}$11\dfrac{3}{5}\) \item $\dfrac{65}{80}\times\dfrac{76}{26}=\underline{\hspace{3cm}}$\dfrac{19}{8}\) \item $3\dfrac{3}{5}-2\dfrac{3}{10}=\underline{\hspace{3cm}}$5\dfrac{9}{10}\) \item $\dfrac{14}{36}\times\dfrac{15}{10}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $6\dfrac{2}{10}+4\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{7}{10}\) \item $\dfrac{12}{72}\div\dfrac{15}{60}=\underline{\hspace{3cm}}$\dfrac{2}{3}\) \item $5\dfrac{3}{9}+8\dfrac{1}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 12. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{87}{29}\div\dfrac{10}{8}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $1\dfrac{3}{44}\times\dfrac{8}{94}=\underline{\hspace{3cm}}$\dfrac{1}{11}\) \item $2\dfrac{2}{5}+5\dfrac{4}{6}=\underline{\hspace{3cm}}$8\dfrac{1}{15}\) \item $7\dfrac{4}{9}-4\dfrac{1}{6}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $\dfrac{70}{45}\div\dfrac{34}{17}=\underline{\hspace{3cm}}$\dfrac{7}{9}\) \item $3\dfrac{3}{12}\times\dfrac{50}{75}=\underline{\hspace{3cm}}$\dfrac{13}{6}\) \item $\dfrac{34}{2}\div\dfrac{56}{8}=\underline{\hspace{3cm}}$\dfrac{17}{7}\) \item $6\dfrac{4}{10}+4\dfrac{2}{5}=\underline{\hspace{3cm}}$10\dfrac{4}{5}\) \item $\dfrac{10}{53}\times1\dfrac{18}{35}=\underline{\hspace{3cm}}$\dfrac{2}{7}\) \item $6\dfrac{8}{9}-8\dfrac{4}{6}=\underline{\hspace{3cm}}$15\dfrac{5}{9}\) \item $\dfrac{10}{28}\div\dfrac{90}{28}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $\dfrac{60}{84}\div\dfrac{25}{85}=\underline{\hspace{3cm}}$\dfrac{17}{7}\) \item $1\dfrac{12}{40}\times1\dfrac{9}{36}=\underline{\hspace{3cm}}$\dfrac{13}{8}\) \item $3\dfrac{1}{10}+6\dfrac{1}{6}=\underline{\hspace{3cm}}$9\dfrac{4}{15}\) \item $2\dfrac{7}{8}-7\dfrac{2}{4}=\underline{\hspace{3cm}}$10\dfrac{3}{8}\) \item $\dfrac{88}{12}\div\dfrac{88}{66}=\underline{\hspace{3cm}}$\dfrac{11}{2}\) \item $1\dfrac{20}{30}\times2\dfrac{21}{30}=\underline{\hspace{3cm}}$\dfrac{9}{2}\) \item $2\dfrac{4}{9}-8\dfrac{1}{2}=\underline{\hspace{3cm}}$10\dfrac{17}{18}\) \item $\dfrac{88}{30}\times\dfrac{2}{88}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $\dfrac{2}{28}\div\dfrac{9}{42}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 13. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $3\dfrac{1}{2}-2\dfrac{5}{6}=\underline{\hspace{3cm}}$6\dfrac{1}{3}\) \item $6\dfrac{5}{10}-6\dfrac{4}{5}=\underline{\hspace{3cm}}$13\dfrac{3}{10}\) \item $\dfrac{77}{42}\div\dfrac{6}{2}=\underline{\hspace{3cm}}$\dfrac{11}{18}\) \item $\dfrac{29}{58}\div\dfrac{57}{19}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $8\dfrac{1}{3}-7\dfrac{2}{12}=\underline{\hspace{3cm}}$15\dfrac{1}{2}\) \item $9\dfrac{10}{12}-7\dfrac{4}{6}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $\dfrac{60}{63}\times\dfrac{84}{60}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{6}{24}\div\dfrac{2}{3}=\underline{\hspace{3cm}}$\dfrac{3}{8}\) \item $\dfrac{12}{48}\times\dfrac{54}{24}=\underline{\hspace{3cm}}$\dfrac{9}{16}\) \item $\dfrac{2}{4}\div\dfrac{60}{75}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $9\dfrac{5}{6}-2\dfrac{1}{9}=\underline{\hspace{3cm}}$11\dfrac{17}{18}\) \item $\dfrac{27}{30}\div\dfrac{54}{78}=\underline{\hspace{3cm}}$\dfrac{13}{10}\) \item $1\dfrac{30}{66}\times1\dfrac{12}{54}=\underline{\hspace{3cm}}$\dfrac{16}{9}\) \item $3\dfrac{5}{10}+9\dfrac{5}{12}=\underline{\hspace{3cm}}$12\dfrac{11}{12}\) \item $4\dfrac{4}{5}+8\dfrac{3}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{20}\) \item $9\dfrac{1}{5}+9\dfrac{3}{12}=\underline{\hspace{3cm}}$18\dfrac{9}{20}\) \item $\dfrac{25}{80}\times\dfrac{9}{15}=\underline{\hspace{3cm}}$\dfrac{3}{16}\) \item $\dfrac{12}{60}\div\dfrac{19}{95}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{36}{54}\times\dfrac{6}{68}=\underline{\hspace{3cm}}$\dfrac{1}{17}\) \item $\dfrac{2}{16}\div\dfrac{38}{32}=\underline{\hspace{3cm}}$\dfrac{2}{19}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 14. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $2\dfrac{3}{9}-5\dfrac{3}{6}=\underline{\hspace{3cm}}$7\dfrac{5}{6}\) \item $\dfrac{16}{25}\times\dfrac{50}{34}=\underline{\hspace{3cm}}$\dfrac{16}{17}\) \item $5\dfrac{2}{12}-9\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{2}\) \item $6\dfrac{4}{6}-7\dfrac{6}{8}=\underline{\hspace{3cm}}$14\dfrac{5}{12}\) \item $2\dfrac{3}{5}+6\dfrac{9}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{20}\) \item $\dfrac{38}{40}\div\dfrac{72}{80}=\underline{\hspace{3cm}}$\dfrac{19}{18}\) \item $3\dfrac{2}{4}-8\dfrac{4}{8}=\underline{\hspace{3cm}}$-12\) \item $\dfrac{38}{12}\div\dfrac{76}{24}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{3}{5}+9\dfrac{3}{10}=\underline{\hspace{3cm}}$14\dfrac{9}{10}\) \item $9\dfrac{8}{12}-9\dfrac{6}{10}=\underline{\hspace{3cm}}$19\dfrac{4}{15}\) \item $1\dfrac{10}{54}\times\dfrac{72}{80}=\underline{\hspace{3cm}}$\dfrac{16}{15}\) \item $\dfrac{46}{45}\div\dfrac{69}{90}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{8}{98}\div\dfrac{72}{63}=\underline{\hspace{3cm}}$\dfrac{1}{14}\) \item $\dfrac{30}{58}\times\dfrac{58}{5}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{14}{4}\times\dfrac{32}{28}=\underline{\hspace{3cm}}$\dfrac{4}{1}\) \item $\dfrac{50}{60}\times\dfrac{76}{10}=\underline{\hspace{3cm}}$\dfrac{19}{3}\) \item $\dfrac{33}{75}\div\dfrac{66}{75}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $\dfrac{95}{20}\div\dfrac{25}{10}=\underline{\hspace{3cm}}$\dfrac{19}{10}\) \item $1\dfrac{13}{65}\times\dfrac{20}{24}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{1}{9}-4\dfrac{8}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{9}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 15. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{48}{86}\times1\dfrac{4}{39}=\underline{\hspace{3cm}}$\dfrac{8}{13}\) \item $\dfrac{48}{10}\div\dfrac{28}{7}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $6\dfrac{6}{8}-6\dfrac{3}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{2}\) \item $7\dfrac{1}{6}+3\dfrac{7}{12}=\underline{\hspace{3cm}}$10\dfrac{3}{4}\) \item $8\dfrac{8}{12}+4\dfrac{2}{3}=\underline{\hspace{3cm}}$13\dfrac{1}{3}\) \item $6\dfrac{1}{4}+7\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{7}{12}\) \item $\dfrac{42}{12}\div\dfrac{98}{70}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $\dfrac{54}{27}\div\dfrac{20}{12}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $8\dfrac{2}{4}+6\dfrac{2}{6}=\underline{\hspace{3cm}}$14\dfrac{5}{6}\) \item $8\dfrac{4}{5}+4\dfrac{5}{10}=\underline{\hspace{3cm}}$13\dfrac{3}{10}\) \item $\dfrac{95}{76}\div\dfrac{55}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $\dfrac{24}{78}\times4\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{54}{72}\div\dfrac{62}{93}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \item $7\dfrac{2}{8}+4\dfrac{3}{6}=\underline{\hspace{3cm}}$11\dfrac{3}{4}\) \item $9\dfrac{5}{8}+3\dfrac{1}{2}=\underline{\hspace{3cm}}$13\dfrac{1}{8}\) \item $4\dfrac{4}{6}-6\dfrac{4}{8}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $2\dfrac{6}{8}+6\dfrac{1}{10}=\underline{\hspace{3cm}}$8\dfrac{17}{20}\) \item $1\dfrac{16}{40}\times\dfrac{15}{28}=\underline{\hspace{3cm}}$\dfrac{3}{4}\) \item $\dfrac{4}{3}\div\dfrac{36}{72}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $8\dfrac{9}{12}-9\dfrac{6}{8}=\underline{\hspace{3cm}}$18\dfrac{1}{2}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 16. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $2\dfrac{2}{12}-3\dfrac{5}{9}=\underline{\hspace{3cm}}$5\dfrac{13}{18}\) \item $\dfrac{99}{11}\div\dfrac{10}{5}=\underline{\hspace{3cm}}$\dfrac{9}{2}\) \item $2\dfrac{3}{10}-6\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{11}{20}\) \item $2\dfrac{5}{10}+5\dfrac{3}{4}=\underline{\hspace{3cm}}$8\dfrac{1}{4}\) \item $6\dfrac{4}{10}+6\dfrac{2}{3}=\underline{\hspace{3cm}}$13\dfrac{1}{15}\) \item $\dfrac{85}{51}\div\dfrac{9}{54}=\underline{\hspace{3cm}}$\dfrac{10}{1}\) \item $6\dfrac{1}{2}-6\dfrac{9}{10}=\underline{\hspace{3cm}}$13\dfrac{2}{5}\) \item $8\dfrac{1}{10}+5\dfrac{3}{5}=\underline{\hspace{3cm}}$13\dfrac{7}{10}\) \item $\dfrac{16}{68}\div\dfrac{19}{38}=\underline{\hspace{3cm}}$\dfrac{8}{17}\) \item $2\dfrac{14}{35}\times\dfrac{4}{6}=\underline{\hspace{3cm}}$\dfrac{8}{5}\) \item $\dfrac{70}{60}\times\dfrac{15}{5}=\underline{\hspace{3cm}}$\dfrac{7}{2}\) \item $\dfrac{90}{98}\div\dfrac{12}{98}=\underline{\hspace{3cm}}$\dfrac{15}{2}\) \item $9\dfrac{5}{9}+6\dfrac{5}{6}=\underline{\hspace{3cm}}$16\dfrac{7}{18}\) \item $\dfrac{78}{57}\div\dfrac{16}{38}=\underline{\hspace{3cm}}$\dfrac{13}{4}\) \item $\dfrac{21}{56}\div\dfrac{5}{80}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $5\dfrac{5}{10}-4\dfrac{2}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{6}\) \item $1\dfrac{28}{42}\times1\dfrac{22}{50}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{60}{32}\times\dfrac{17}{51}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $7\dfrac{2}{4}+6\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{5}{6}\) \item $2\dfrac{2}{4}+3\dfrac{2}{3}=\underline{\hspace{3cm}}$6\dfrac{1}{6}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 17. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $1\dfrac{30}{39}\times\dfrac{12}{69}=\underline{\hspace{3cm}}$\dfrac{4}{13}\) \item $\dfrac{30}{72}\times5\dfrac{2}{10}=\underline{\hspace{3cm}}$\dfrac{13}{6}\) \item $\dfrac{28}{52}\div\dfrac{77}{11}=\underline{\hspace{3cm}}$\dfrac{1}{13}\) \item $1\dfrac{24}{54}\times\dfrac{25}{50}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $\dfrac{42}{63}\div\dfrac{3}{36}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $\dfrac{80}{56}\times\dfrac{11}{44}=\underline{\hspace{3cm}}$\dfrac{5}{14}\) \item $\dfrac{63}{66}\times\dfrac{42}{49}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{14}{21}\div\dfrac{21}{42}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{48}{88}\times\dfrac{85}{51}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{52}{72}\div\dfrac{26}{22}=\underline{\hspace{3cm}}$\dfrac{11}{18}\) \item $\dfrac{14}{63}\div\dfrac{18}{81}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{72}{12}\div\dfrac{88}{4}=\underline{\hspace{3cm}}$\dfrac{3}{11}\) \item $3\dfrac{18}{24}\times\dfrac{8}{30}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $3\dfrac{5}{10}-8\dfrac{1}{9}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $\dfrac{18}{39}\div\dfrac{76}{78}=\underline{\hspace{3cm}}$\dfrac{9}{19}\) \item $5\dfrac{2}{6}+3\dfrac{2}{4}=\underline{\hspace{3cm}}$8\dfrac{5}{6}\) \item $\dfrac{3}{54}\div\dfrac{6}{63}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $9\dfrac{6}{12}-3\dfrac{5}{10}=\underline{\hspace{3cm}}$-13\) \item $2\dfrac{1}{28}\times1\dfrac{6}{18}=\underline{\hspace{3cm}}$\dfrac{19}{7}\) \item $4\dfrac{2}{7}-4\dfrac{3}{6}=\underline{\hspace{3cm}}$8\dfrac{11}{14}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 18. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{70}{35}\div\dfrac{24}{12}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $1\dfrac{15}{20}\times1\dfrac{22}{42}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $\dfrac{10}{48}\times\dfrac{48}{22}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $\dfrac{6}{58}\times1\dfrac{13}{45}=\underline{\hspace{3cm}}$\dfrac{2}{15}\) \item $\dfrac{75}{54}\div\dfrac{60}{18}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $6\dfrac{6}{12}-5\dfrac{6}{10}=\underline{\hspace{3cm}}$12\dfrac{1}{10}\) \item $\dfrac{75}{11}\times\dfrac{22}{70}=\underline{\hspace{3cm}}$\dfrac{15}{7}\) \item $4\dfrac{1}{9}+5\dfrac{4}{12}=\underline{\hspace{3cm}}$9\dfrac{4}{9}\) \item $7\dfrac{3}{4}+2\dfrac{4}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $6\dfrac{6}{9}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{6}\) \item $7\dfrac{5}{9}+7\dfrac{4}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{9}\) \item $\dfrac{80}{57}\times\dfrac{39}{65}=\underline{\hspace{3cm}}$\dfrac{16}{19}\) \item $8\dfrac{8}{12}+3\dfrac{1}{4}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \item $9\dfrac{1}{2}+5\dfrac{1}{9}=\underline{\hspace{3cm}}$14\dfrac{11}{18}\) \item $8\dfrac{2}{10}-3\dfrac{4}{5}=\underline{\hspace{3cm}}$-12\) \item $6\dfrac{8}{12}+2\dfrac{1}{4}=\underline{\hspace{3cm}}$8\dfrac{11}{12}\) \item $\dfrac{60}{28}\div\dfrac{54}{28}=\underline{\hspace{3cm}}$\dfrac{10}{9}\) \item $\dfrac{6}{3}\div\dfrac{27}{24}=\underline{\hspace{3cm}}$\dfrac{16}{9}\) \item $\dfrac{15}{85}\times\dfrac{29}{87}=\underline{\hspace{3cm}}$\dfrac{1}{17}\) \item $9\dfrac{5}{6}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 19. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $9\dfrac{3}{9}+3\dfrac{2}{4}=\underline{\hspace{3cm}}$12\dfrac{5}{6}\) \item $3\dfrac{10}{12}+4\dfrac{8}{9}=\underline{\hspace{3cm}}$8\dfrac{13}{18}\) \item $2\dfrac{2}{18}\times\dfrac{26}{38}=\underline{\hspace{3cm}}$\dfrac{13}{9}\) \item $\dfrac{54}{48}\div\dfrac{9}{80}=\underline{\hspace{3cm}}$\dfrac{10}{1}\) \item $6\dfrac{11}{12}-9\dfrac{3}{9}=\underline{\hspace{3cm}}$16\dfrac{1}{4}\) \item $\dfrac{22}{33}\div\dfrac{60}{95}=\underline{\hspace{3cm}}$\dfrac{19}{18}\) \item $8\dfrac{1}{2}-7\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{1}{10}\) \item $\dfrac{55}{2}\times\dfrac{2}{88}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $\dfrac{52}{26}\times\dfrac{28}{98}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $\dfrac{27}{63}\times\dfrac{63}{33}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{33}{11}\times\dfrac{3}{9}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{3}{10}+3\dfrac{3}{6}=\underline{\hspace{3cm}}$8\dfrac{4}{5}\) \item $\dfrac{27}{30}\times\dfrac{20}{51}=\underline{\hspace{3cm}}$\dfrac{6}{17}\) \item $\dfrac{20}{50}\div\dfrac{39}{15}=\underline{\hspace{3cm}}$\dfrac{2}{13}\) \item $\dfrac{45}{15}\div\dfrac{52}{65}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{10}{5}\div\dfrac{85}{15}=\underline{\hspace{3cm}}$\dfrac{6}{17}\) \item $4\dfrac{5}{10}+3\dfrac{3}{8}=\underline{\hspace{3cm}}$7\dfrac{7}{8}\) \item $\dfrac{8}{10}\times\dfrac{45}{72}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $9\dfrac{6}{10}-3\dfrac{3}{6}=\underline{\hspace{3cm}}$13\dfrac{1}{10}\) \item $\dfrac{66}{33}\times\dfrac{15}{54}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 20. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $9\dfrac{1}{2}-2\dfrac{7}{9}=\underline{\hspace{3cm}}$12\dfrac{5}{18}\) \item $3\dfrac{3}{9}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$7\dfrac{11}{15}\) \item $\dfrac{28}{20}\times\dfrac{40}{28}=\underline{\hspace{3cm}}$\dfrac{2}{1}\) \item $\dfrac{42}{56}\div\dfrac{46}{69}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \item $5\dfrac{3}{12}+8\dfrac{4}{6}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $\dfrac{92}{26}\div\dfrac{46}{12}=\underline{\hspace{3cm}}$\dfrac{12}{13}\) \item $7\dfrac{5}{6}-9\dfrac{4}{8}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $\dfrac{18}{99}\times\dfrac{37}{74}=\underline{\hspace{3cm}}$\dfrac{1}{11}\) \item $5\dfrac{2}{4}-4\dfrac{8}{9}=\underline{\hspace{3cm}}$10\dfrac{7}{18}\) \item $2\dfrac{4}{9}-5\dfrac{3}{6}=\underline{\hspace{3cm}}$7\dfrac{17}{18}\) \item $\dfrac{19}{57}\times\dfrac{36}{90}=\underline{\hspace{3cm}}$\dfrac{2}{15}\) \item $9\dfrac{3}{9}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$13\dfrac{11}{15}\) \item $\dfrac{12}{28}\div\dfrac{20}{70}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $2\dfrac{3}{10}+4\dfrac{1}{2}=\underline{\hspace{3cm}}$6\dfrac{4}{5}\) \item $\dfrac{8}{15}\times4\dfrac{9}{18}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{9}{54}\div\dfrac{26}{91}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $4\dfrac{5}{10}+5\dfrac{1}{7}=\underline{\hspace{3cm}}$9\dfrac{9}{14}\) \item $1\dfrac{3}{17}\times\dfrac{17}{65}=\underline{\hspace{3cm}}$\dfrac{4}{13}\) \item $4\dfrac{6}{10}+4\dfrac{2}{5}=\underline{\hspace{3cm}}$-9\) \item $\dfrac{72}{29}\times\dfrac{58}{24}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 21. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $1\dfrac{8}{72}\times1\dfrac{10}{35}=\underline{\hspace{3cm}}$\dfrac{10}{7}\) \item $\dfrac{46}{8}\div\dfrac{69}{27}=\underline{\hspace{3cm}}$\dfrac{9}{4}\) \item $9\dfrac{3}{5}-4\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{14}{15}\) \item $1\dfrac{17}{39}\times\dfrac{66}{77}=\underline{\hspace{3cm}}$\dfrac{16}{13}\) \item $2\dfrac{4}{20}\times\dfrac{25}{55}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $7\dfrac{2}{12}+4\dfrac{2}{8}=\underline{\hspace{3cm}}$11\dfrac{5}{12}\) \item $7\dfrac{10}{12}-7\dfrac{5}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{3}\) \item $\dfrac{80}{85}\times\dfrac{5}{20}=\underline{\hspace{3cm}}$\dfrac{4}{17}\) \item $\dfrac{28}{60}\div\dfrac{84}{96}=\underline{\hspace{3cm}}$\dfrac{8}{15}\) \item $\dfrac{10}{4}\div\dfrac{69}{23}=\underline{\hspace{3cm}}$\dfrac{5}{6}\) \item $1\dfrac{40}{50}\times\dfrac{55}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $8\dfrac{2}{3}\times1\dfrac{21}{42}=\underline{\hspace{3cm}}$\dfrac{13}{1}\) \item $\dfrac{28}{33}\times1\dfrac{3}{42}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{33}{96}\times\dfrac{96}{48}=\underline{\hspace{3cm}}$\dfrac{11}{16}\) \item $\dfrac{85}{25}\times\dfrac{50}{60}=\underline{\hspace{3cm}}$\dfrac{17}{6}\) \item $6\dfrac{2}{4}+5\dfrac{6}{8}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $8\dfrac{2}{4}-9\dfrac{3}{7}=\underline{\hspace{3cm}}$17\dfrac{13}{14}\) \item $\dfrac{30}{42}\times5\dfrac{2}{8}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $3\dfrac{9}{12}-9\dfrac{5}{8}=\underline{\hspace{3cm}}$13\dfrac{3}{8}\) \item $5\dfrac{9}{12}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$-8\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 22. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{38}{19}\div\dfrac{76}{38}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $3\dfrac{2}{4}+3\dfrac{4}{12}=\underline{\hspace{3cm}}$6\dfrac{5}{6}\) \item $6\dfrac{9}{10}+2\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{2}{5}\) \item $2\dfrac{6}{8}-7\dfrac{3}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $\dfrac{54}{90}\times\dfrac{40}{26}=\underline{\hspace{3cm}}$\dfrac{12}{13}\) \item $\dfrac{16}{20}\times\dfrac{70}{24}=\underline{\hspace{3cm}}$\dfrac{7}{3}\) \item $2\dfrac{6}{8}-9\dfrac{3}{5}=\underline{\hspace{3cm}}$12\dfrac{7}{20}\) \item $7\dfrac{5}{10}+2\dfrac{2}{7}=\underline{\hspace{3cm}}$9\dfrac{11}{14}\) \item $\dfrac{24}{45}\div\dfrac{32}{4}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $2\dfrac{1}{3}+9\dfrac{11}{12}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $5\dfrac{6}{12}-2\dfrac{6}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{10}\) \item $\dfrac{42}{39}\div\dfrac{34}{17}=\underline{\hspace{3cm}}$\dfrac{7}{13}\) \item $\dfrac{51}{18}\div\dfrac{11}{66}=\underline{\hspace{3cm}}$\dfrac{17}{1}\) \item $7\dfrac{4}{6}-2\dfrac{6}{10}=\underline{\hspace{3cm}}$10\dfrac{4}{15}\) \item $7\dfrac{1}{6}-3\dfrac{1}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $9\dfrac{4}{6}+7\dfrac{2}{3}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $2\dfrac{6}{8}-7\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{4}\) \item $4\dfrac{3}{5}-9\dfrac{2}{3}=\underline{\hspace{3cm}}$14\dfrac{4}{15}\) \item $\dfrac{77}{63}\div\dfrac{24}{27}=\underline{\hspace{3cm}}$\dfrac{11}{8}\) \item $\dfrac{98}{28}\times\dfrac{8}{20}=\underline{\hspace{3cm}}$\dfrac{7}{5}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 23. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $8\dfrac{4}{5}-9\dfrac{1}{10}=\underline{\hspace{3cm}}$17\dfrac{9}{10}\) \item $\dfrac{30}{75}\div\dfrac{48}{50}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $1\dfrac{28}{49}\times\dfrac{64}{88}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{26}{52}\div\dfrac{15}{18}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $2\dfrac{11}{20}\times1\dfrac{38}{57}=\underline{\hspace{3cm}}$\dfrac{17}{4}\) \item $\dfrac{33}{55}\times\dfrac{50}{38}=\underline{\hspace{3cm}}$\dfrac{15}{19}\) \item $\dfrac{24}{77}\times3\dfrac{16}{24}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $9\dfrac{2}{5}-6\dfrac{3}{10}=\underline{\hspace{3cm}}$15\dfrac{7}{10}\) \item $4\dfrac{1}{5}-5\dfrac{3}{10}=\underline{\hspace{3cm}}$9\dfrac{1}{2}\) \item $3\dfrac{10}{12}+7\dfrac{5}{9}=\underline{\hspace{3cm}}$11\dfrac{7}{18}\) \item $\dfrac{46}{23}\times\dfrac{9}{81}=\underline{\hspace{3cm}}$\dfrac{2}{9}\) \item $\dfrac{40}{96}\times\dfrac{99}{66}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $\dfrac{65}{78}\times1\dfrac{22}{35}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $\dfrac{36}{57}\times\dfrac{57}{33}=\underline{\hspace{3cm}}$\dfrac{12}{11}\) \item $\dfrac{6}{15}\div\dfrac{4}{80}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $6\dfrac{3}{9}+7\dfrac{7}{12}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $5\dfrac{2}{12}-4\dfrac{6}{9}=\underline{\hspace{3cm}}$9\dfrac{5}{6}\) \item $\dfrac{16}{84}\div\dfrac{29}{87}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $9\dfrac{8}{10}-6\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{2}{5}\) \item $\dfrac{36}{84}\times\dfrac{58}{87}=\underline{\hspace{3cm}}$\dfrac{2}{7}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 24. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{20}{28}\div\dfrac{45}{72}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{69}{81}\times2\dfrac{8}{23}=\underline{\hspace{3cm}}$\dfrac{2}{1}\) \item $8\dfrac{4}{8}-7\dfrac{1}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{3}\) \item $\dfrac{2}{60}\times\dfrac{72}{36}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $\dfrac{75}{81}\div\dfrac{15}{81}=\underline{\hspace{3cm}}$\dfrac{5}{1}\) \item $1\dfrac{28}{32}\times1\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $7\dfrac{4}{8}+5\dfrac{4}{7}=\underline{\hspace{3cm}}$13\dfrac{1}{14}\) \item $\dfrac{70}{77}\times1\dfrac{12}{40}=\underline{\hspace{3cm}}$\dfrac{13}{11}\) \item $2\dfrac{1}{10}-6\dfrac{4}{5}=\underline{\hspace{3cm}}$8\dfrac{9}{10}\) \item $2\dfrac{5}{12}-4\dfrac{4}{8}=\underline{\hspace{3cm}}$6\dfrac{11}{12}\) \item $5\dfrac{1}{2}-4\dfrac{1}{6}=\underline{\hspace{3cm}}$9\dfrac{2}{3}\) \item $6\dfrac{3}{9}-4\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{7}{12}\) \item $\dfrac{21}{6}\times\dfrac{22}{7}=\underline{\hspace{3cm}}$\dfrac{11}{1}\) \item $5\dfrac{1}{8}-8\dfrac{6}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{8}\) \item $\dfrac{11}{2}\times\dfrac{10}{11}=\underline{\hspace{3cm}}$\dfrac{5}{1}\) \item $2\dfrac{3}{6}-9\dfrac{3}{8}=\underline{\hspace{3cm}}$11\dfrac{7}{8}\) \item $\dfrac{16}{10}\div\dfrac{56}{90}=\underline{\hspace{3cm}}$\dfrac{18}{7}\) \item $1\dfrac{11}{17}\times1\dfrac{4}{64}=\underline{\hspace{3cm}}$\dfrac{7}{4}\) \item $\dfrac{11}{88}\div\dfrac{4}{38}=\underline{\hspace{3cm}}$\dfrac{19}{16}\) \item $\dfrac{18}{28}\div\dfrac{24}{42}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 25. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $8\dfrac{2}{3}-5\dfrac{6}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{3}\) \item $7\dfrac{11}{12}-6\dfrac{2}{8}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $4\dfrac{5}{6}+5\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $\dfrac{15}{56}\div\dfrac{60}{48}=\underline{\hspace{3cm}}$\dfrac{3}{14}\) \item $\dfrac{72}{88}\div\dfrac{23}{46}=\underline{\hspace{3cm}}$\dfrac{18}{11}\) \item $\dfrac{72}{86}\times7\dfrac{2}{12}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $2\dfrac{5}{20}\times1\dfrac{18}{27}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{48}{27}\times\dfrac{27}{16}=\underline{\hspace{3cm}}$\dfrac{3}{1}\) \item $6\dfrac{2}{5}-7\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{9}{10}\) \item $9\dfrac{7}{9}+5\dfrac{2}{12}=\underline{\hspace{3cm}}$14\dfrac{17}{18}\) \item $\dfrac{66}{14}\times\dfrac{98}{66}=\underline{\hspace{3cm}}$\dfrac{7}{1}\) \item $1\dfrac{8}{40}\times1\dfrac{25}{30}=\underline{\hspace{3cm}}$\dfrac{11}{5}\) \item $4\dfrac{1}{2}+7\dfrac{2}{7}=\underline{\hspace{3cm}}$11\dfrac{11}{14}\) \item $7\dfrac{6}{7}-6\dfrac{3}{6}=\underline{\hspace{3cm}}$14\dfrac{5}{14}\) \item $3\dfrac{4}{5}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{5}\) \item $6\dfrac{9}{10}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$9\dfrac{11}{15}\) \item $5\dfrac{6}{10}+3\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{1}{10}\) \item $4\dfrac{1}{4}+4\dfrac{7}{10}=\underline{\hspace{3cm}}$8\dfrac{19}{20}\) \item $\dfrac{36}{6}\div\dfrac{33}{2}=\underline{\hspace{3cm}}$\dfrac{4}{11}\) \item $5\dfrac{3}{6}-7\dfrac{5}{7}=\underline{\hspace{3cm}}$13\dfrac{3}{14}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 26. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $7\dfrac{5}{6}+6\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $2\dfrac{10}{12}-8\dfrac{3}{10}=\underline{\hspace{3cm}}$11\dfrac{2}{15}\) \item $\dfrac{9}{78}\div\dfrac{66}{88}=\underline{\hspace{3cm}}$\dfrac{2}{13}\) \item $\dfrac{98}{24}\div\dfrac{14}{6}=\underline{\hspace{3cm}}$\dfrac{7}{4}\) \item $2\dfrac{1}{9}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$4\dfrac{11}{18}\) \item $\dfrac{32}{80}\times2\dfrac{12}{14}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{98}{91}\times\dfrac{13}{63}=\underline{\hspace{3cm}}$\dfrac{2}{9}\) \item $\dfrac{39}{78}\div\dfrac{30}{56}=\underline{\hspace{3cm}}$\dfrac{14}{15}\) \item $5\dfrac{11}{12}-7\dfrac{4}{8}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \item $\dfrac{65}{13}\div\dfrac{70}{22}=\underline{\hspace{3cm}}$\dfrac{11}{7}\) \item $\dfrac{48}{40}\div\dfrac{6}{70}=\underline{\hspace{3cm}}$\dfrac{14}{1}\) \item $3\dfrac{11}{12}-6\dfrac{3}{9}=\underline{\hspace{3cm}}$10\dfrac{1}{4}\) \item $\dfrac{12}{78}\times1\dfrac{19}{38}=\underline{\hspace{3cm}}$\dfrac{3}{13}\) \item $\dfrac{35}{70}\div\dfrac{81}{72}=\underline{\hspace{3cm}}$\dfrac{4}{9}\) \item $7\dfrac{3}{5}-7\dfrac{1}{4}=\underline{\hspace{3cm}}$14\dfrac{17}{20}\) \item $5\dfrac{8}{9}+9\dfrac{1}{3}=\underline{\hspace{3cm}}$15\dfrac{2}{9}\) \item $3\dfrac{3}{4}+8\dfrac{1}{3}=\underline{\hspace{3cm}}$12\dfrac{1}{12}\) \item $\dfrac{48}{8}\times\dfrac{40}{96}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $4\dfrac{3}{6}+6\dfrac{7}{8}=\underline{\hspace{3cm}}$11\dfrac{3}{8}\) \item $3\dfrac{11}{12}+5\dfrac{3}{4}=\underline{\hspace{3cm}}$9\dfrac{2}{3}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 27. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{51}{12}\div\dfrac{85}{20}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $6\dfrac{1}{9}-7\dfrac{4}{12}=\underline{\hspace{3cm}}$13\dfrac{4}{9}\) \item $7\dfrac{5}{6}-8\dfrac{4}{12}=\underline{\hspace{3cm}}$16\dfrac{1}{6}\) \item $4\dfrac{2}{6}-5\dfrac{10}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{6}\) \item $\dfrac{8}{96}\div\dfrac{10}{20}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $1\dfrac{17}{39}\times\dfrac{27}{84}=\underline{\hspace{3cm}}$\dfrac{6}{13}\) \item $2\dfrac{1}{6}-7\dfrac{2}{3}=\underline{\hspace{3cm}}$9\dfrac{5}{6}\) \item $3\dfrac{6}{7}-8\dfrac{5}{10}=\underline{\hspace{3cm}}$12\dfrac{5}{14}\) \item $9\dfrac{2}{8}-9\dfrac{1}{12}=\underline{\hspace{3cm}}$18\dfrac{1}{3}\) \item $2\dfrac{1}{9}+3\dfrac{10}{12}=\underline{\hspace{3cm}}$5\dfrac{17}{18}\) \item $5\dfrac{4}{8}+5\dfrac{2}{7}=\underline{\hspace{3cm}}$10\dfrac{11}{14}\) \item $\dfrac{27}{36}\times\dfrac{2}{18}=\underline{\hspace{3cm}}$\dfrac{1}{12}\) \item $4\dfrac{10}{12}+6\dfrac{3}{6}=\underline{\hspace{3cm}}$11\dfrac{1}{3}\) \item $8\dfrac{3}{6}+5\dfrac{3}{9}=\underline{\hspace{3cm}}$13\dfrac{5}{6}\) \item $\dfrac{57}{99}\div\dfrac{9}{33}=\underline{\hspace{3cm}}$\dfrac{19}{9}\) \item $\dfrac{10}{6}\div\dfrac{77}{21}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $1\dfrac{10}{34}\times\dfrac{16}{22}=\underline{\hspace{3cm}}$\dfrac{16}{17}\) \item $2\dfrac{9}{12}-3\dfrac{3}{5}=\underline{\hspace{3cm}}$6\dfrac{7}{20}\) \item $9\dfrac{7}{9}\times\dfrac{9}{96}=\underline{\hspace{3cm}}$\dfrac{11}{12}\) \item $9\dfrac{1}{3}+9\dfrac{1}{9}=\underline{\hspace{3cm}}$18\dfrac{4}{9}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 28. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{72}{20}\div\dfrac{12}{50}=\underline{\hspace{3cm}}$\dfrac{15}{1}\) \item $4\dfrac{2}{4}+7\dfrac{4}{7}=\underline{\hspace{3cm}}$12\dfrac{1}{14}\) \item $5\dfrac{3}{9}+2\dfrac{4}{5}=\underline{\hspace{3cm}}$8\dfrac{2}{15}\) \item $\dfrac{99}{51}\div\dfrac{75}{85}=\underline{\hspace{3cm}}$\dfrac{11}{5}\) \item $7\dfrac{3}{6}-2\dfrac{7}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $2\dfrac{3}{12}+6\dfrac{5}{8}=\underline{\hspace{3cm}}$8\dfrac{7}{8}\) \item $\dfrac{12}{20}\times\dfrac{68}{24}=\underline{\hspace{3cm}}$\dfrac{17}{10}\) \item $2\dfrac{9}{12}-3\dfrac{3}{10}=\underline{\hspace{3cm}}$6\dfrac{1}{20}\) \item $\dfrac{26}{16}\div\dfrac{29}{58}=\underline{\hspace{3cm}}$\dfrac{13}{4}\) \item $3\dfrac{6}{8}-4\dfrac{6}{9}=\underline{\hspace{3cm}}$8\dfrac{5}{12}\) \item $4\dfrac{6}{8}+4\dfrac{8}{12}=\underline{\hspace{3cm}}$9\dfrac{5}{12}\) \item $3\dfrac{2}{4}-2\dfrac{8}{12}=\underline{\hspace{3cm}}$6\dfrac{1}{6}\) \item $\dfrac{72}{15}\div\dfrac{96}{50}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $6\dfrac{1}{2}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{3}{4}\) \item $6\dfrac{5}{12}-9\dfrac{5}{10}=\underline{\hspace{3cm}}$15\dfrac{11}{12}\) \item $6\dfrac{3}{8}+8\dfrac{1}{2}=\underline{\hspace{3cm}}$14\dfrac{7}{8}\) \item $2\dfrac{6}{10}-2\dfrac{9}{12}=\underline{\hspace{3cm}}$5\dfrac{7}{20}\) \item $1\dfrac{12}{18}\times\dfrac{27}{80}=\underline{\hspace{3cm}}$\dfrac{9}{16}\) \item $9\dfrac{1}{2}+7\dfrac{4}{7}=\underline{\hspace{3cm}}$17\dfrac{1}{14}\) \item $\dfrac{21}{35}\div\dfrac{72}{8}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 29. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{27}{18}\div\dfrac{66}{76}=\underline{\hspace{3cm}}$\dfrac{19}{11}\) \item $\dfrac{10}{68}\times\dfrac{68}{85}=\underline{\hspace{3cm}}$\dfrac{2}{17}\) \item $5\dfrac{1}{3}+5\dfrac{10}{12}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $7\dfrac{3}{4}-4\dfrac{4}{8}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $\dfrac{12}{15}\times1\dfrac{9}{66}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{12}{32}\times\dfrac{52}{12}=\underline{\hspace{3cm}}$\dfrac{13}{8}\) \item $6\dfrac{3}{6}-2\dfrac{3}{12}=\underline{\hspace{3cm}}$8\dfrac{3}{4}\) \item $2\dfrac{4}{7}-2\dfrac{5}{10}=\underline{\hspace{3cm}}$5\dfrac{1}{14}\) \item $\dfrac{51}{27}\div\dfrac{80}{45}=\underline{\hspace{3cm}}$\dfrac{17}{16}\) \item $9\dfrac{3}{6}+7\dfrac{10}{12}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $\dfrac{60}{25}\div\dfrac{38}{10}=\underline{\hspace{3cm}}$\dfrac{12}{19}\) \item $4\dfrac{8}{12}-8\dfrac{2}{6}=\underline{\hspace{3cm}}$-13\) \item $3\dfrac{5}{9}+4\dfrac{2}{12}=\underline{\hspace{3cm}}$7\dfrac{13}{18}\) \item $\dfrac{15}{54}\div\dfrac{40}{12}=\underline{\hspace{3cm}}$\dfrac{1}{12}\) \item $9\dfrac{2}{9}-9\dfrac{3}{6}=\underline{\hspace{3cm}}$18\dfrac{13}{18}\) \item $2\dfrac{16}{28}\times2\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $7\dfrac{8}{12}-3\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{11}{12}\) \item $\dfrac{7}{97}\times2\dfrac{13}{42}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $\dfrac{35}{30}\div\dfrac{95}{30}=\underline{\hspace{3cm}}$\dfrac{7}{19}\) \item $\dfrac{56}{14}\times\dfrac{90}{24}=\underline{\hspace{3cm}}$\dfrac{15}{1}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 30. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} \item $\dfrac{42}{60}\times1\dfrac{6}{14}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $2\dfrac{4}{7}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$9\dfrac{1}{14}\) \item $\dfrac{6}{96}\div\dfrac{45}{90}=\underline{\hspace{3cm}}$\dfrac{1}{8}\) \item $8\dfrac{6}{10}-4\dfrac{9}{12}=\underline{\hspace{3cm}}$13\dfrac{7}{20}\) \item $5\dfrac{7}{12}-3\dfrac{2}{3}=\underline{\hspace{3cm}}$9\dfrac{1}{4}\) \item $6\dfrac{6}{8}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $8\dfrac{1}{4}+9\dfrac{2}{10}=\underline{\hspace{3cm}}$17\dfrac{9}{20}\) \item $1\dfrac{12}{20}\times1\dfrac{6}{84}=\underline{\hspace{3cm}}$\dfrac{12}{7}\) \item $\dfrac{64}{80}\times\dfrac{34}{68}=\underline{\hspace{3cm}}$\dfrac{2}{5}\) \item $\dfrac{49}{21}\div\dfrac{60}{30}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $5\dfrac{5}{8}+4\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{8}\) \item $8\dfrac{5}{10}-4\dfrac{2}{5}=\underline{\hspace{3cm}}$12\dfrac{9}{10}\) \item $\dfrac{29}{58}\times\dfrac{40}{6}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $\dfrac{45}{18}\div\dfrac{90}{12}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \item $\dfrac{76}{98}\div\dfrac{64}{98}=\underline{\hspace{3cm}}$\dfrac{19}{16}\) \item $6\dfrac{3}{9}-3\dfrac{3}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $\dfrac{72}{56}\div\dfrac{60}{28}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $\dfrac{58}{72}\times\dfrac{78}{87}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $\dfrac{88}{72}\times\dfrac{63}{99}=\underline{\hspace{3cm}}$\dfrac{7}{9}\) \item $2\dfrac{1}{4}-8\dfrac{4}{5}=\underline{\hspace{3cm}}$11\dfrac{1}{20}\) \end{enumerate} \end{multicols} \newpage \begin{figure}[ht!] \vspace{-23mm}\hspace*{-23mm}\includegraphics[scale=0.9]{Logo.jpg} \end{figure} \vspace{-15mm}\hspace*{-10mm}\begingroup \centering \LARGE Fraction Arithmetic (General) \\[0.5em] \endgroup \subsection{Exercise 31. Calculate and express the answer in simplest forms.} \begin{multicols}{2} \begin{enumerate}[label=\arabic*)] \setlength\itemsep{2em} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage \newgeometry{ a4paper, total={170mm,257mm}, left=15mm, top=20mm, bottom=20mm, right=15mm } \fontsize{10pt}{10pt}\selectfont \section{Fraction Arithmetic (General) Answer Key} \textbf{p1} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $5\dfrac{7}{13}\times1\dfrac{15}{24}=\underline{\hspace{3cm}}$\dfrac{9}{1}\) \item $1\dfrac{8}{9}\times1\dfrac{13}{17}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $1\dfrac{6}{54}\times\dfrac{9}{85}=\underline{\hspace{3cm}}$\dfrac{2}{17}\) \item $\dfrac{36}{81}\div\dfrac{7}{84}=\underline{\hspace{3cm}}$\dfrac{16}{3}\) \item $6\dfrac{9}{12}+3\dfrac{1}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $5\dfrac{2}{11}\times\dfrac{9}{27}=\underline{\hspace{3cm}}$\dfrac{19}{11}\) \item $\dfrac{21}{45}\div\dfrac{56}{72}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $1\dfrac{1}{15}\times7\dfrac{4}{8}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $\dfrac{10}{52}\times3\dfrac{2}{8}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $8\dfrac{2}{8}-9\dfrac{8}{12}=\underline{\hspace{3cm}}$17\dfrac{11}{12}\) \item $7\dfrac{9}{10}+9\dfrac{2}{8}=\underline{\hspace{3cm}}$17\dfrac{3}{20}\) \item $3\dfrac{4}{6}-9\dfrac{5}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \item $\dfrac{28}{90}\times\dfrac{21}{14}=\underline{\hspace{3cm}}$\dfrac{7}{15}\) \item $2\dfrac{18}{19}\times2\dfrac{25}{35}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $8\dfrac{7}{8}-5\dfrac{3}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{8}\) \item $1\dfrac{2}{6}\times2\dfrac{2}{20}=\underline{\hspace{3cm}}$\dfrac{14}{5}\) \item $\dfrac{10}{72}\times2\dfrac{24}{30}=\underline{\hspace{3cm}}$\dfrac{7}{18}\) \item $\dfrac{23}{34}\times1\dfrac{3}{69}=\underline{\hspace{3cm}}$\dfrac{12}{17}\) \item $\dfrac{45}{36}\div\dfrac{18}{8}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \item $4\dfrac{6}{9}-7\dfrac{1}{4}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \end{enumerate} \end{multicols} \textbf{p2} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $6\dfrac{3}{4}-8\dfrac{1}{10}=\underline{\hspace{3cm}}$14\dfrac{17}{20}\) \item $2\dfrac{4}{8}-8\dfrac{4}{9}=\underline{\hspace{3cm}}$10\dfrac{17}{18}\) \item $\dfrac{45}{20}\div\dfrac{66}{16}=\underline{\hspace{3cm}}$\dfrac{6}{11}\) \item $3\dfrac{8}{10}-2\dfrac{4}{6}=\underline{\hspace{3cm}}$6\dfrac{7}{15}\) \item $9\dfrac{1}{6}-5\dfrac{1}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{4}\) \item $\dfrac{26}{32}\div\dfrac{26}{16}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $5\dfrac{4}{6}+7\dfrac{2}{9}=\underline{\hspace{3cm}}$12\dfrac{8}{9}\) \item $6\dfrac{1}{2}-2\dfrac{3}{5}=\underline{\hspace{3cm}}$9\dfrac{1}{10}\) \item $\dfrac{24}{72}\times\dfrac{40}{30}=\underline{\hspace{3cm}}$\dfrac{4}{9}\) \item $9\dfrac{1}{2}-7\dfrac{1}{7}=\underline{\hspace{3cm}}$16\dfrac{9}{14}\) \item $\dfrac{48}{66}\div\dfrac{56}{88}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $4\dfrac{3}{12}+8\dfrac{1}{10}=\underline{\hspace{3cm}}$12\dfrac{7}{20}\) \item $\dfrac{36}{18}\div\dfrac{28}{8}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $\dfrac{72}{33}\div\dfrac{40}{15}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{36}{48}\div\dfrac{7}{35}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{90}{55}\div\dfrac{72}{44}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $1\dfrac{2}{7}\times1\dfrac{5}{90}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $9\dfrac{9}{12}+4\dfrac{3}{4}=\underline{\hspace{3cm}}$14\dfrac{1}{2}\) \item $6\dfrac{8}{12}-9\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{4}{15}\) \item $5\dfrac{5}{6}-9\dfrac{2}{8}=\underline{\hspace{3cm}}$15\dfrac{1}{12}\) \end{enumerate} \end{multicols} \textbf{p3} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $7\dfrac{1}{4}+2\dfrac{1}{5}=\underline{\hspace{3cm}}$9\dfrac{9}{20}\) \item $9\dfrac{1}{12}-4\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{7}{12}\) \item $\dfrac{8}{64}\div\dfrac{40}{80}=\underline{\hspace{3cm}}$\dfrac{1}{4}\) \item $3\dfrac{5}{10}-8\dfrac{7}{8}=\underline{\hspace{3cm}}$12\dfrac{3}{8}\) \item $5\dfrac{6}{7}-9\dfrac{3}{6}=\underline{\hspace{3cm}}$15\dfrac{5}{14}\) \item $9\dfrac{8}{12}-7\dfrac{5}{6}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $\dfrac{55}{5}\div\dfrac{99}{42}=\underline{\hspace{3cm}}$\dfrac{14}{3}\) \item $9\dfrac{3}{12}+7\dfrac{6}{9}=\underline{\hspace{3cm}}$16\dfrac{11}{12}\) \item $\dfrac{24}{48}\times7\dfrac{1}{3}=\underline{\hspace{3cm}}$\dfrac{11}{3}\) \item $7\dfrac{1}{4}+8\dfrac{5}{6}=\underline{\hspace{3cm}}$16\dfrac{1}{12}\) \item $2\dfrac{6}{9}-6\dfrac{2}{5}=\underline{\hspace{3cm}}$9\dfrac{1}{15}\) \item $\dfrac{66}{46}\div\dfrac{48}{92}=\underline{\hspace{3cm}}$\dfrac{11}{4}\) \item $6\dfrac{11}{12}+4\dfrac{2}{8}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $9\dfrac{6}{12}-4\dfrac{7}{8}=\underline{\hspace{3cm}}$14\dfrac{3}{8}\) \item $7\dfrac{7}{10}-9\dfrac{4}{8}=\underline{\hspace{3cm}}$17\dfrac{1}{5}\) \item $\dfrac{15}{45}\div\dfrac{64}{60}=\underline{\hspace{3cm}}$\dfrac{5}{16}\) \item $3\dfrac{7}{17}\times\dfrac{3}{58}=\underline{\hspace{3cm}}$\dfrac{3}{17}\) \item $1\dfrac{17}{68}\times1\dfrac{5}{7}=\underline{\hspace{3cm}}$\dfrac{15}{7}\) \item $\dfrac{72}{21}\div\dfrac{56}{14}=\underline{\hspace{3cm}}$\dfrac{6}{7}\) \item $4\dfrac{3}{9}-7\dfrac{7}{12}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \end{enumerate} \end{multicols} \textbf{p4} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $4\dfrac{4}{6}+6\dfrac{8}{9}=\underline{\hspace{3cm}}$11\dfrac{5}{9}\) \item $3\dfrac{5}{10}+9\dfrac{1}{5}=\underline{\hspace{3cm}}$12\dfrac{7}{10}\) \item $4\dfrac{2}{10}+4\dfrac{4}{8}=\underline{\hspace{3cm}}$8\dfrac{7}{10}\) \item $5\dfrac{3}{12}-9\dfrac{9}{10}=\underline{\hspace{3cm}}$15\dfrac{3}{20}\) \item $8\dfrac{6}{10}-6\dfrac{3}{4}=\underline{\hspace{3cm}}$15\dfrac{7}{20}\) \item $2\dfrac{1}{4}+8\dfrac{3}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $6\dfrac{8}{9}+8\dfrac{10}{12}=\underline{\hspace{3cm}}$15\dfrac{13}{18}\) \item $\dfrac{27}{24}\times\dfrac{88}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $5\dfrac{4}{12}-9\dfrac{2}{4}=\underline{\hspace{3cm}}$14\dfrac{5}{6}\) \item $7\dfrac{4}{6}-6\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $4\dfrac{10}{12}+5\dfrac{5}{6}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $\dfrac{98}{78}\div\dfrac{21}{18}=\underline{\hspace{3cm}}$\dfrac{14}{13}\) \item $2\dfrac{7}{9}-9\dfrac{5}{6}=\underline{\hspace{3cm}}$12\dfrac{11}{18}\) \item $2\dfrac{4}{8}-8\dfrac{9}{12}=\underline{\hspace{3cm}}$11\dfrac{1}{4}\) \item $9\dfrac{3}{9}+9\dfrac{3}{4}=\underline{\hspace{3cm}}$19\dfrac{1}{12}\) \item $9\dfrac{6}{7}+6\dfrac{6}{12}=\underline{\hspace{3cm}}$16\dfrac{5}{14}\) \item $7\dfrac{3}{6}+6\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{3}{4}\) \item $4\dfrac{2}{8}-6\dfrac{5}{12}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $\dfrac{80}{16}\div\dfrac{25}{60}=\underline{\hspace{3cm}}$\dfrac{12}{1}\) \item $\dfrac{51}{9}\div\dfrac{74}{37}=\underline{\hspace{3cm}}$\dfrac{17}{6}\) \end{enumerate} \end{multicols} \textbf{p5} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $6\dfrac{6}{9}-2\dfrac{3}{4}=\underline{\hspace{3cm}}$9\dfrac{5}{12}\) \item $\dfrac{22}{9}\times\dfrac{35}{77}=\underline{\hspace{3cm}}$\dfrac{10}{9}\) \item $\dfrac{16}{12}\div\dfrac{8}{10}=\underline{\hspace{3cm}}$\dfrac{5}{3}\) \item $3\dfrac{1}{6}+3\dfrac{1}{10}=\underline{\hspace{3cm}}$6\dfrac{4}{15}\) \item $\dfrac{60}{35}\div\dfrac{24}{56}=\underline{\hspace{3cm}}$\dfrac{4}{1}\) \item $5\dfrac{8}{9}+4\dfrac{2}{4}=\underline{\hspace{3cm}}$10\dfrac{7}{18}\) \item $2\dfrac{4}{6}-6\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{1}{6}\) \item $4\dfrac{3}{10}-8\dfrac{3}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{20}\) \item $3\dfrac{5}{10}-5\dfrac{1}{6}=\underline{\hspace{3cm}}$8\dfrac{2}{3}\) \item $9\dfrac{1}{2}+7\dfrac{7}{9}=\underline{\hspace{3cm}}$17\dfrac{5}{18}\) \item $3\dfrac{2}{10}+7\dfrac{4}{8}=\underline{\hspace{3cm}}$10\dfrac{7}{10}\) \item $5\dfrac{6}{12}-6\dfrac{2}{4}=\underline{\hspace{3cm}}$-12\) \item $1\dfrac{20}{32}\times2\dfrac{10}{39}=\underline{\hspace{3cm}}$\dfrac{11}{3}\) \item $\dfrac{77}{99}\div\dfrac{12}{18}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $\dfrac{12}{21}\div\dfrac{32}{76}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $2\dfrac{2}{3}+3\dfrac{8}{10}=\underline{\hspace{3cm}}$6\dfrac{7}{15}\) \item $\dfrac{52}{90}\times\dfrac{80}{64}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $3\dfrac{1}{10}-6\dfrac{6}{12}=\underline{\hspace{3cm}}$9\dfrac{3}{5}\) \item $3\dfrac{4}{8}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$6\dfrac{1}{3}\) \item $7\dfrac{3}{4}-5\dfrac{4}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \end{enumerate} \end{multicols} \newpage \textbf{p6} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $5\dfrac{3}{5}+3\dfrac{9}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{20}\) \item $\dfrac{33}{44}\div\dfrac{72}{66}=\underline{\hspace{3cm}}$\dfrac{11}{16}\) \item $9\dfrac{4}{10}-9\dfrac{3}{12}=\underline{\hspace{3cm}}$18\dfrac{13}{20}\) \item $\dfrac{2}{4}\div\dfrac{21}{6}=\underline{\hspace{3cm}}$\dfrac{1}{7}\) \item $7\dfrac{3}{5}-5\dfrac{1}{2}=\underline{\hspace{3cm}}$13\dfrac{1}{10}\) \item $5\dfrac{1}{12}+6\dfrac{6}{8}=\underline{\hspace{3cm}}$11\dfrac{5}{6}\) \item $\dfrac{90}{45}\div\dfrac{21}{49}=\underline{\hspace{3cm}}$\dfrac{14}{3}\) \item $3\dfrac{5}{15}\times1\dfrac{8}{10}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{10}{33}\times\dfrac{99}{9}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $3\dfrac{5}{12}-3\dfrac{1}{6}=\underline{\hspace{3cm}}$6\dfrac{7}{12}\) \item $\dfrac{60}{50}\div\dfrac{30}{15}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $4\dfrac{2}{8}-6\dfrac{9}{10}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $5\dfrac{2}{8}+7\dfrac{11}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{6}\) \item $8\dfrac{6}{12}-8\dfrac{5}{9}=\underline{\hspace{3cm}}$17\dfrac{1}{18}\) \item $\dfrac{34}{2}\div\dfrac{50}{5}=\underline{\hspace{3cm}}$\dfrac{17}{10}\) \item $5\dfrac{1}{10}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$7\dfrac{3}{5}\) \item $5\dfrac{3}{4}+5\dfrac{2}{5}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $\dfrac{13}{26}\div\dfrac{12}{14}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $3\dfrac{8}{10}-6\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{20}\) \item $\dfrac{57}{96}\times\dfrac{16}{3}=\underline{\hspace{3cm}}$\dfrac{19}{6}\) \end{enumerate} \end{multicols} \textbf{p7} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $4\dfrac{5}{12}+4\dfrac{5}{10}=\underline{\hspace{3cm}}$8\dfrac{11}{12}\) \item $\dfrac{92}{23}\div\dfrac{7}{14}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $4\dfrac{6}{10}+3\dfrac{1}{3}=\underline{\hspace{3cm}}$7\dfrac{14}{15}\) \item $\dfrac{9}{15}\div\dfrac{37}{74}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $4\dfrac{4}{9}+7\dfrac{4}{6}=\underline{\hspace{3cm}}$12\dfrac{1}{9}\) \item $8\dfrac{3}{5}-5\dfrac{1}{2}=\underline{\hspace{3cm}}$14\dfrac{1}{10}\) \item $\dfrac{20}{22}\div\dfrac{38}{57}=\underline{\hspace{3cm}}$\dfrac{15}{11}\) \item $6\dfrac{2}{9}+9\dfrac{10}{12}=\underline{\hspace{3cm}}$16\dfrac{1}{18}\) \item $2\dfrac{8}{10}+7\dfrac{8}{12}=\underline{\hspace{3cm}}$10\dfrac{7}{15}\) \item $5\dfrac{8}{10}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$12\dfrac{3}{10}\) \item $4\dfrac{7}{12}+2\dfrac{3}{9}=\underline{\hspace{3cm}}$6\dfrac{11}{12}\) \item $8\dfrac{1}{3}-6\dfrac{9}{12}=\underline{\hspace{3cm}}$15\dfrac{1}{12}\) \item $7\dfrac{2}{8}+6\dfrac{6}{9}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $\dfrac{12}{96}\div\dfrac{9}{84}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $2\dfrac{3}{6}+2\dfrac{6}{8}=\underline{\hspace{3cm}}$5\dfrac{1}{4}\) \item $7\dfrac{3}{10}-9\dfrac{1}{5}=\underline{\hspace{3cm}}$16\dfrac{1}{2}\) \item $\dfrac{24}{90}\div\dfrac{48}{75}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $3\dfrac{1}{2}+2\dfrac{7}{9}=\underline{\hspace{3cm}}$6\dfrac{5}{18}\) \item $\dfrac{12}{14}\times\dfrac{11}{22}=\underline{\hspace{3cm}}$\dfrac{3}{7}\) \item $3\dfrac{7}{12}-2\dfrac{1}{3}=\underline{\hspace{3cm}}$5\dfrac{11}{12}\) \end{enumerate} \end{multicols} \textbf{p8} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $2\dfrac{3}{4}\times\dfrac{45}{55}=\underline{\hspace{3cm}}$\dfrac{9}{4}\) \item $\dfrac{21}{49}\times\dfrac{84}{57}=\underline{\hspace{3cm}}$\dfrac{12}{19}\) \item $\dfrac{38}{19}\div\dfrac{8}{24}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{33}{45}\div\dfrac{33}{63}=\underline{\hspace{3cm}}$\dfrac{7}{5}\) \item $9\dfrac{1}{3}+6\dfrac{4}{9}=\underline{\hspace{3cm}}$15\dfrac{7}{9}\) \item $5\dfrac{7}{12}+2\dfrac{5}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{12}\) \item $\dfrac{4}{6}\div\dfrac{33}{63}=\underline{\hspace{3cm}}$\dfrac{14}{11}\) \item $9\dfrac{1}{2}+5\dfrac{6}{8}=\underline{\hspace{3cm}}$15\dfrac{1}{4}\) \item $\dfrac{50}{85}\times1\dfrac{7}{14}=\underline{\hspace{3cm}}$\dfrac{15}{17}\) \item $\dfrac{63}{98}\times3\dfrac{17}{27}=\underline{\hspace{3cm}}$\dfrac{7}{3}\) \item $6\dfrac{5}{6}+7\dfrac{4}{12}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $\dfrac{11}{62}\times1\dfrac{29}{33}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \item $\dfrac{18}{12}\times\dfrac{24}{99}=\underline{\hspace{3cm}}$\dfrac{4}{11}\) \item $\dfrac{55}{35}\times\dfrac{35}{99}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \item $6\dfrac{2}{9}+4\dfrac{5}{6}=\underline{\hspace{3cm}}$11\dfrac{1}{18}\) \item $9\dfrac{1}{5}+6\dfrac{6}{12}=\underline{\hspace{3cm}}$15\dfrac{7}{10}\) \item $5\dfrac{2}{12}+8\dfrac{5}{6}=\underline{\hspace{3cm}}$-14\) \item $\dfrac{52}{40}\div\dfrac{9}{30}=\underline{\hspace{3cm}}$\dfrac{13}{3}\) \item $6\dfrac{6}{10}+7\dfrac{1}{4}=\underline{\hspace{3cm}}$13\dfrac{17}{20}\) \item $9\dfrac{5}{10}-7\dfrac{2}{6}=\underline{\hspace{3cm}}$16\dfrac{5}{6}\) \end{enumerate} \end{multicols} \textbf{p9} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{46}{2}\times\dfrac{6}{46}=\underline{\hspace{3cm}}$\dfrac{3}{1}\) \item $9\dfrac{3}{5}-8\dfrac{2}{10}=\underline{\hspace{3cm}}$17\dfrac{4}{5}\) \item $\dfrac{84}{17}\times\dfrac{17}{35}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{30}{35}\div\dfrac{50}{35}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $\dfrac{45}{33}\div\dfrac{30}{14}=\underline{\hspace{3cm}}$\dfrac{7}{11}\) \item $\dfrac{36}{68}\div\dfrac{81}{45}=\underline{\hspace{3cm}}$\dfrac{5}{17}\) \item $\dfrac{26}{13}\div\dfrac{12}{84}=\underline{\hspace{3cm}}$\dfrac{14}{1}\) \item $\dfrac{20}{24}\div\dfrac{30}{4}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $2\dfrac{2}{6}-4\dfrac{4}{10}=\underline{\hspace{3cm}}$6\dfrac{11}{15}\) \item $\dfrac{54}{15}\times\dfrac{80}{16}=\underline{\hspace{3cm}}$\dfrac{18}{1}\) \item $\dfrac{80}{45}\div\dfrac{24}{36}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $7\dfrac{1}{2}-5\dfrac{4}{7}=\underline{\hspace{3cm}}$13\dfrac{1}{14}\) \item $6\dfrac{3}{4}+9\dfrac{2}{5}=\underline{\hspace{3cm}}$16\dfrac{3}{20}\) \item $6\dfrac{4}{8}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$10\dfrac{5}{6}\) \item $7\dfrac{8}{12}+3\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{11}{12}\) \item $6\dfrac{2}{4}+5\dfrac{3}{10}=\underline{\hspace{3cm}}$11\dfrac{4}{5}\) \item $2\dfrac{22}{28}\times\dfrac{19}{39}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $\dfrac{90}{45}\times\dfrac{56}{42}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $4\dfrac{4}{6}+8\dfrac{10}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{2}\) \item $9\dfrac{2}{3}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$-14\) \end{enumerate} \end{multicols} \textbf{p10} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $2\dfrac{2}{5}+4\dfrac{3}{12}=\underline{\hspace{3cm}}$6\dfrac{13}{20}\) \item $\dfrac{5}{17}\times\dfrac{34}{55}=\underline{\hspace{3cm}}$\dfrac{2}{11}\) \item $3\dfrac{6}{9}+8\dfrac{2}{3}=\underline{\hspace{3cm}}$12\dfrac{1}{3}\) \item $9\dfrac{1}{2}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$12\dfrac{1}{3}\) \item $2\dfrac{8}{10}-7\dfrac{2}{5}=\underline{\hspace{3cm}}$10\dfrac{1}{5}\) \item $5\dfrac{1}{2}-7\dfrac{7}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{12}\) \item $2\dfrac{4}{16}\times1\dfrac{6}{90}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $5\dfrac{1}{3}-5\dfrac{4}{12}=\underline{\hspace{3cm}}$10\dfrac{2}{3}\) \item $6\dfrac{6}{8}+2\dfrac{1}{5}=\underline{\hspace{3cm}}$8\dfrac{19}{20}\) \item $\dfrac{26}{96}\times\dfrac{96}{32}=\underline{\hspace{3cm}}$\dfrac{13}{16}\) \item $2\dfrac{1}{5}+6\dfrac{8}{12}=\underline{\hspace{3cm}}$8\dfrac{13}{15}\) \item $\dfrac{65}{25}\div\dfrac{26}{10}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{52}{32}\div\dfrac{49}{56}=\underline{\hspace{3cm}}$\dfrac{13}{7}\) \item $\dfrac{24}{2}\div\dfrac{84}{7}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{36}{84}\div\dfrac{10}{42}=\underline{\hspace{3cm}}$\dfrac{9}{5}\) \item $3\dfrac{2}{4}-8\dfrac{1}{5}=\underline{\hspace{3cm}}$11\dfrac{7}{10}\) \item $9\dfrac{1}{6}-6\dfrac{2}{3}=\underline{\hspace{3cm}}$15\dfrac{5}{6}\) \item $7\dfrac{1}{4}+8\dfrac{1}{3}=\underline{\hspace{3cm}}$15\dfrac{7}{12}\) \item $6\dfrac{3}{4}-6\dfrac{8}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \item $\dfrac{38}{54}\div\dfrac{30}{81}=\underline{\hspace{3cm}}$\dfrac{19}{10}\) \end{enumerate} \end{multicols} \newpage \textbf{p11} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $2\dfrac{2}{3}+6\dfrac{4}{10}=\underline{\hspace{3cm}}$9\dfrac{1}{15}\) \item $8\dfrac{2}{8}+5\dfrac{5}{6}=\underline{\hspace{3cm}}$14\dfrac{1}{12}\) \item $\dfrac{25}{70}\div\dfrac{15}{6}=\underline{\hspace{3cm}}$\dfrac{1}{7}\) \item $9\dfrac{2}{9}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$11\dfrac{13}{18}\) \item $1\dfrac{2}{4}\times\dfrac{24}{76}=\underline{\hspace{3cm}}$\dfrac{9}{19}\) \item $5\dfrac{4}{5}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{1}{20}\) \item $3\dfrac{4}{5}+8\dfrac{7}{10}=\underline{\hspace{3cm}}$12\dfrac{1}{2}\) \item $\dfrac{10}{18}\div\dfrac{40}{8}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $\dfrac{93}{62}\div\dfrac{99}{30}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $4\dfrac{6}{8}-6\dfrac{3}{5}=\underline{\hspace{3cm}}$11\dfrac{7}{20}\) \item $8\dfrac{7}{9}+3\dfrac{4}{8}=\underline{\hspace{3cm}}$12\dfrac{5}{18}\) \item $8\dfrac{6}{8}-8\dfrac{9}{12}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $6\dfrac{2}{12}+5\dfrac{4}{9}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $5\dfrac{1}{10}+6\dfrac{1}{2}=\underline{\hspace{3cm}}$11\dfrac{3}{5}\) \item $\dfrac{65}{80}\times\dfrac{76}{26}=\underline{\hspace{3cm}}$\dfrac{19}{8}\) \item $3\dfrac{3}{5}-2\dfrac{3}{10}=\underline{\hspace{3cm}}$5\dfrac{9}{10}\) \item $\dfrac{14}{36}\times\dfrac{15}{10}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $6\dfrac{2}{10}+4\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{7}{10}\) \item $\dfrac{12}{72}\div\dfrac{15}{60}=\underline{\hspace{3cm}}$\dfrac{2}{3}\) \item $5\dfrac{3}{9}+8\dfrac{1}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \end{enumerate} \end{multicols} \textbf{p12} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{87}{29}\div\dfrac{10}{8}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $1\dfrac{3}{44}\times\dfrac{8}{94}=\underline{\hspace{3cm}}$\dfrac{1}{11}\) \item $2\dfrac{2}{5}+5\dfrac{4}{6}=\underline{\hspace{3cm}}$8\dfrac{1}{15}\) \item $7\dfrac{4}{9}-4\dfrac{1}{6}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $\dfrac{70}{45}\div\dfrac{34}{17}=\underline{\hspace{3cm}}$\dfrac{7}{9}\) \item $3\dfrac{3}{12}\times\dfrac{50}{75}=\underline{\hspace{3cm}}$\dfrac{13}{6}\) \item $\dfrac{34}{2}\div\dfrac{56}{8}=\underline{\hspace{3cm}}$\dfrac{17}{7}\) \item $6\dfrac{4}{10}+4\dfrac{2}{5}=\underline{\hspace{3cm}}$10\dfrac{4}{5}\) \item $\dfrac{10}{53}\times1\dfrac{18}{35}=\underline{\hspace{3cm}}$\dfrac{2}{7}\) \item $6\dfrac{8}{9}-8\dfrac{4}{6}=\underline{\hspace{3cm}}$15\dfrac{5}{9}\) \item $\dfrac{10}{28}\div\dfrac{90}{28}=\underline{\hspace{3cm}}$\dfrac{1}{9}\) \item $\dfrac{60}{84}\div\dfrac{25}{85}=\underline{\hspace{3cm}}$\dfrac{17}{7}\) \item $1\dfrac{12}{40}\times1\dfrac{9}{36}=\underline{\hspace{3cm}}$\dfrac{13}{8}\) \item $3\dfrac{1}{10}+6\dfrac{1}{6}=\underline{\hspace{3cm}}$9\dfrac{4}{15}\) \item $2\dfrac{7}{8}-7\dfrac{2}{4}=\underline{\hspace{3cm}}$10\dfrac{3}{8}\) \item $\dfrac{88}{12}\div\dfrac{88}{66}=\underline{\hspace{3cm}}$\dfrac{11}{2}\) \item $1\dfrac{20}{30}\times2\dfrac{21}{30}=\underline{\hspace{3cm}}$\dfrac{9}{2}\) \item $2\dfrac{4}{9}-8\dfrac{1}{2}=\underline{\hspace{3cm}}$10\dfrac{17}{18}\) \item $\dfrac{88}{30}\times\dfrac{2}{88}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $\dfrac{2}{28}\div\dfrac{9}{42}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \end{enumerate} \end{multicols} \textbf{p13} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $3\dfrac{1}{2}-2\dfrac{5}{6}=\underline{\hspace{3cm}}$6\dfrac{1}{3}\) \item $6\dfrac{5}{10}-6\dfrac{4}{5}=\underline{\hspace{3cm}}$13\dfrac{3}{10}\) \item $\dfrac{77}{42}\div\dfrac{6}{2}=\underline{\hspace{3cm}}$\dfrac{11}{18}\) \item $\dfrac{29}{58}\div\dfrac{57}{19}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $8\dfrac{1}{3}-7\dfrac{2}{12}=\underline{\hspace{3cm}}$15\dfrac{1}{2}\) \item $9\dfrac{10}{12}-7\dfrac{4}{6}=\underline{\hspace{3cm}}$17\dfrac{1}{2}\) \item $\dfrac{60}{63}\times\dfrac{84}{60}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{6}{24}\div\dfrac{2}{3}=\underline{\hspace{3cm}}$\dfrac{3}{8}\) \item $\dfrac{12}{48}\times\dfrac{54}{24}=\underline{\hspace{3cm}}$\dfrac{9}{16}\) \item $\dfrac{2}{4}\div\dfrac{60}{75}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $9\dfrac{5}{6}-2\dfrac{1}{9}=\underline{\hspace{3cm}}$11\dfrac{17}{18}\) \item $\dfrac{27}{30}\div\dfrac{54}{78}=\underline{\hspace{3cm}}$\dfrac{13}{10}\) \item $1\dfrac{30}{66}\times1\dfrac{12}{54}=\underline{\hspace{3cm}}$\dfrac{16}{9}\) \item $3\dfrac{5}{10}+9\dfrac{5}{12}=\underline{\hspace{3cm}}$12\dfrac{11}{12}\) \item $4\dfrac{4}{5}+8\dfrac{3}{12}=\underline{\hspace{3cm}}$13\dfrac{1}{20}\) \item $9\dfrac{1}{5}+9\dfrac{3}{12}=\underline{\hspace{3cm}}$18\dfrac{9}{20}\) \item $\dfrac{25}{80}\times\dfrac{9}{15}=\underline{\hspace{3cm}}$\dfrac{3}{16}\) \item $\dfrac{12}{60}\div\dfrac{19}{95}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{36}{54}\times\dfrac{6}{68}=\underline{\hspace{3cm}}$\dfrac{1}{17}\) \item $\dfrac{2}{16}\div\dfrac{38}{32}=\underline{\hspace{3cm}}$\dfrac{2}{19}\) \end{enumerate} \end{multicols} \textbf{p14} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $2\dfrac{3}{9}-5\dfrac{3}{6}=\underline{\hspace{3cm}}$7\dfrac{5}{6}\) \item $\dfrac{16}{25}\times\dfrac{50}{34}=\underline{\hspace{3cm}}$\dfrac{16}{17}\) \item $5\dfrac{2}{12}-9\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{2}\) \item $6\dfrac{4}{6}-7\dfrac{6}{8}=\underline{\hspace{3cm}}$14\dfrac{5}{12}\) \item $2\dfrac{3}{5}+6\dfrac{9}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{20}\) \item $\dfrac{38}{40}\div\dfrac{72}{80}=\underline{\hspace{3cm}}$\dfrac{19}{18}\) \item $3\dfrac{2}{4}-8\dfrac{4}{8}=\underline{\hspace{3cm}}$-12\) \item $\dfrac{38}{12}\div\dfrac{76}{24}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{3}{5}+9\dfrac{3}{10}=\underline{\hspace{3cm}}$14\dfrac{9}{10}\) \item $9\dfrac{8}{12}-9\dfrac{6}{10}=\underline{\hspace{3cm}}$19\dfrac{4}{15}\) \item $1\dfrac{10}{54}\times\dfrac{72}{80}=\underline{\hspace{3cm}}$\dfrac{16}{15}\) \item $\dfrac{46}{45}\div\dfrac{69}{90}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{8}{98}\div\dfrac{72}{63}=\underline{\hspace{3cm}}$\dfrac{1}{14}\) \item $\dfrac{30}{58}\times\dfrac{58}{5}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $\dfrac{14}{4}\times\dfrac{32}{28}=\underline{\hspace{3cm}}$\dfrac{4}{1}\) \item $\dfrac{50}{60}\times\dfrac{76}{10}=\underline{\hspace{3cm}}$\dfrac{19}{3}\) \item $\dfrac{33}{75}\div\dfrac{66}{75}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $\dfrac{95}{20}\div\dfrac{25}{10}=\underline{\hspace{3cm}}$\dfrac{19}{10}\) \item $1\dfrac{13}{65}\times\dfrac{20}{24}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{1}{9}-4\dfrac{8}{12}=\underline{\hspace{3cm}}$9\dfrac{7}{9}\) \end{enumerate} \end{multicols} \textbf{p15} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{48}{86}\times1\dfrac{4}{39}=\underline{\hspace{3cm}}$\dfrac{8}{13}\) \item $\dfrac{48}{10}\div\dfrac{28}{7}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $6\dfrac{6}{8}-6\dfrac{3}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{2}\) \item $7\dfrac{1}{6}+3\dfrac{7}{12}=\underline{\hspace{3cm}}$10\dfrac{3}{4}\) \item $8\dfrac{8}{12}+4\dfrac{2}{3}=\underline{\hspace{3cm}}$13\dfrac{1}{3}\) \item $6\dfrac{1}{4}+7\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{7}{12}\) \item $\dfrac{42}{12}\div\dfrac{98}{70}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $\dfrac{54}{27}\div\dfrac{20}{12}=\underline{\hspace{3cm}}$\dfrac{6}{5}\) \item $8\dfrac{2}{4}+6\dfrac{2}{6}=\underline{\hspace{3cm}}$14\dfrac{5}{6}\) \item $8\dfrac{4}{5}+4\dfrac{5}{10}=\underline{\hspace{3cm}}$13\dfrac{3}{10}\) \item $\dfrac{95}{76}\div\dfrac{55}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $\dfrac{24}{78}\times4\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{54}{72}\div\dfrac{62}{93}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \item $7\dfrac{2}{8}+4\dfrac{3}{6}=\underline{\hspace{3cm}}$11\dfrac{3}{4}\) \item $9\dfrac{5}{8}+3\dfrac{1}{2}=\underline{\hspace{3cm}}$13\dfrac{1}{8}\) \item $4\dfrac{4}{6}-6\dfrac{4}{8}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $2\dfrac{6}{8}+6\dfrac{1}{10}=\underline{\hspace{3cm}}$8\dfrac{17}{20}\) \item $1\dfrac{16}{40}\times\dfrac{15}{28}=\underline{\hspace{3cm}}$\dfrac{3}{4}\) \item $\dfrac{4}{3}\div\dfrac{36}{72}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $8\dfrac{9}{12}-9\dfrac{6}{8}=\underline{\hspace{3cm}}$18\dfrac{1}{2}\) \end{enumerate} \end{multicols} \newpage \textbf{p16} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $2\dfrac{2}{12}-3\dfrac{5}{9}=\underline{\hspace{3cm}}$5\dfrac{13}{18}\) \item $\dfrac{99}{11}\div\dfrac{10}{5}=\underline{\hspace{3cm}}$\dfrac{9}{2}\) \item $2\dfrac{3}{10}-6\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{11}{20}\) \item $2\dfrac{5}{10}+5\dfrac{3}{4}=\underline{\hspace{3cm}}$8\dfrac{1}{4}\) \item $6\dfrac{4}{10}+6\dfrac{2}{3}=\underline{\hspace{3cm}}$13\dfrac{1}{15}\) \item $\dfrac{85}{51}\div\dfrac{9}{54}=\underline{\hspace{3cm}}$\dfrac{10}{1}\) \item $6\dfrac{1}{2}-6\dfrac{9}{10}=\underline{\hspace{3cm}}$13\dfrac{2}{5}\) \item $8\dfrac{1}{10}+5\dfrac{3}{5}=\underline{\hspace{3cm}}$13\dfrac{7}{10}\) \item $\dfrac{16}{68}\div\dfrac{19}{38}=\underline{\hspace{3cm}}$\dfrac{8}{17}\) \item $2\dfrac{14}{35}\times\dfrac{4}{6}=\underline{\hspace{3cm}}$\dfrac{8}{5}\) \item $\dfrac{70}{60}\times\dfrac{15}{5}=\underline{\hspace{3cm}}$\dfrac{7}{2}\) \item $\dfrac{90}{98}\div\dfrac{12}{98}=\underline{\hspace{3cm}}$\dfrac{15}{2}\) \item $9\dfrac{5}{9}+6\dfrac{5}{6}=\underline{\hspace{3cm}}$16\dfrac{7}{18}\) \item $\dfrac{78}{57}\div\dfrac{16}{38}=\underline{\hspace{3cm}}$\dfrac{13}{4}\) \item $\dfrac{21}{56}\div\dfrac{5}{80}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $5\dfrac{5}{10}-4\dfrac{2}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{6}\) \item $1\dfrac{28}{42}\times1\dfrac{22}{50}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{60}{32}\times\dfrac{17}{51}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $7\dfrac{2}{4}+6\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{5}{6}\) \item $2\dfrac{2}{4}+3\dfrac{2}{3}=\underline{\hspace{3cm}}$6\dfrac{1}{6}\) \end{enumerate} \end{multicols} \textbf{p17} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $1\dfrac{30}{39}\times\dfrac{12}{69}=\underline{\hspace{3cm}}$\dfrac{4}{13}\) \item $\dfrac{30}{72}\times5\dfrac{2}{10}=\underline{\hspace{3cm}}$\dfrac{13}{6}\) \item $\dfrac{28}{52}\div\dfrac{77}{11}=\underline{\hspace{3cm}}$\dfrac{1}{13}\) \item $1\dfrac{24}{54}\times\dfrac{25}{50}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $\dfrac{42}{63}\div\dfrac{3}{36}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $\dfrac{80}{56}\times\dfrac{11}{44}=\underline{\hspace{3cm}}$\dfrac{5}{14}\) \item $\dfrac{63}{66}\times\dfrac{42}{49}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{14}{21}\div\dfrac{21}{42}=\underline{\hspace{3cm}}$\dfrac{4}{3}\) \item $\dfrac{48}{88}\times\dfrac{85}{51}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{52}{72}\div\dfrac{26}{22}=\underline{\hspace{3cm}}$\dfrac{11}{18}\) \item $\dfrac{14}{63}\div\dfrac{18}{81}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $\dfrac{72}{12}\div\dfrac{88}{4}=\underline{\hspace{3cm}}$\dfrac{3}{11}\) \item $3\dfrac{18}{24}\times\dfrac{8}{30}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $3\dfrac{5}{10}-8\dfrac{1}{9}=\underline{\hspace{3cm}}$11\dfrac{11}{18}\) \item $\dfrac{18}{39}\div\dfrac{76}{78}=\underline{\hspace{3cm}}$\dfrac{9}{19}\) \item $5\dfrac{2}{6}+3\dfrac{2}{4}=\underline{\hspace{3cm}}$8\dfrac{5}{6}\) \item $\dfrac{3}{54}\div\dfrac{6}{63}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $9\dfrac{6}{12}-3\dfrac{5}{10}=\underline{\hspace{3cm}}$-13\) \item $2\dfrac{1}{28}\times1\dfrac{6}{18}=\underline{\hspace{3cm}}$\dfrac{19}{7}\) \item $4\dfrac{2}{7}-4\dfrac{3}{6}=\underline{\hspace{3cm}}$8\dfrac{11}{14}\) \end{enumerate} \end{multicols} \textbf{p18} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{70}{35}\div\dfrac{24}{12}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $1\dfrac{15}{20}\times1\dfrac{22}{42}=\underline{\hspace{3cm}}$\dfrac{8}{3}\) \item $\dfrac{10}{48}\times\dfrac{48}{22}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $\dfrac{6}{58}\times1\dfrac{13}{45}=\underline{\hspace{3cm}}$\dfrac{2}{15}\) \item $\dfrac{75}{54}\div\dfrac{60}{18}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $6\dfrac{6}{12}-5\dfrac{6}{10}=\underline{\hspace{3cm}}$12\dfrac{1}{10}\) \item $\dfrac{75}{11}\times\dfrac{22}{70}=\underline{\hspace{3cm}}$\dfrac{15}{7}\) \item $4\dfrac{1}{9}+5\dfrac{4}{12}=\underline{\hspace{3cm}}$9\dfrac{4}{9}\) \item $7\dfrac{3}{4}+2\dfrac{4}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $6\dfrac{6}{9}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{1}{6}\) \item $7\dfrac{5}{9}+7\dfrac{4}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{9}\) \item $\dfrac{80}{57}\times\dfrac{39}{65}=\underline{\hspace{3cm}}$\dfrac{16}{19}\) \item $8\dfrac{8}{12}+3\dfrac{1}{4}=\underline{\hspace{3cm}}$11\dfrac{11}{12}\) \item $9\dfrac{1}{2}+5\dfrac{1}{9}=\underline{\hspace{3cm}}$14\dfrac{11}{18}\) \item $8\dfrac{2}{10}-3\dfrac{4}{5}=\underline{\hspace{3cm}}$-12\) \item $6\dfrac{8}{12}+2\dfrac{1}{4}=\underline{\hspace{3cm}}$8\dfrac{11}{12}\) \item $\dfrac{60}{28}\div\dfrac{54}{28}=\underline{\hspace{3cm}}$\dfrac{10}{9}\) \item $\dfrac{6}{3}\div\dfrac{27}{24}=\underline{\hspace{3cm}}$\dfrac{16}{9}\) \item $\dfrac{15}{85}\times\dfrac{29}{87}=\underline{\hspace{3cm}}$\dfrac{1}{17}\) \item $9\dfrac{5}{6}-4\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \end{enumerate} \end{multicols} \textbf{p19} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $9\dfrac{3}{9}+3\dfrac{2}{4}=\underline{\hspace{3cm}}$12\dfrac{5}{6}\) \item $3\dfrac{10}{12}+4\dfrac{8}{9}=\underline{\hspace{3cm}}$8\dfrac{13}{18}\) \item $2\dfrac{2}{18}\times\dfrac{26}{38}=\underline{\hspace{3cm}}$\dfrac{13}{9}\) \item $\dfrac{54}{48}\div\dfrac{9}{80}=\underline{\hspace{3cm}}$\dfrac{10}{1}\) \item $6\dfrac{11}{12}-9\dfrac{3}{9}=\underline{\hspace{3cm}}$16\dfrac{1}{4}\) \item $\dfrac{22}{33}\div\dfrac{60}{95}=\underline{\hspace{3cm}}$\dfrac{19}{18}\) \item $8\dfrac{1}{2}-7\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{1}{10}\) \item $\dfrac{55}{2}\times\dfrac{2}{88}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $\dfrac{52}{26}\times\dfrac{28}{98}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $\dfrac{27}{63}\times\dfrac{63}{33}=\underline{\hspace{3cm}}$\dfrac{9}{11}\) \item $\dfrac{33}{11}\times\dfrac{3}{9}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $5\dfrac{3}{10}+3\dfrac{3}{6}=\underline{\hspace{3cm}}$8\dfrac{4}{5}\) \item $\dfrac{27}{30}\times\dfrac{20}{51}=\underline{\hspace{3cm}}$\dfrac{6}{17}\) \item $\dfrac{20}{50}\div\dfrac{39}{15}=\underline{\hspace{3cm}}$\dfrac{2}{13}\) \item $\dfrac{45}{15}\div\dfrac{52}{65}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{10}{5}\div\dfrac{85}{15}=\underline{\hspace{3cm}}$\dfrac{6}{17}\) \item $4\dfrac{5}{10}+3\dfrac{3}{8}=\underline{\hspace{3cm}}$7\dfrac{7}{8}\) \item $\dfrac{8}{10}\times\dfrac{45}{72}=\underline{\hspace{3cm}}$\dfrac{1}{2}\) \item $9\dfrac{6}{10}-3\dfrac{3}{6}=\underline{\hspace{3cm}}$13\dfrac{1}{10}\) \item $\dfrac{66}{33}\times\dfrac{15}{54}=\underline{\hspace{3cm}}$\dfrac{5}{9}\) \end{enumerate} \end{multicols} \textbf{p20} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $9\dfrac{1}{2}-2\dfrac{7}{9}=\underline{\hspace{3cm}}$12\dfrac{5}{18}\) \item $3\dfrac{3}{9}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$7\dfrac{11}{15}\) \item $\dfrac{28}{20}\times\dfrac{40}{28}=\underline{\hspace{3cm}}$\dfrac{2}{1}\) \item $\dfrac{42}{56}\div\dfrac{46}{69}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \item $5\dfrac{3}{12}+8\dfrac{4}{6}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $\dfrac{92}{26}\div\dfrac{46}{12}=\underline{\hspace{3cm}}$\dfrac{12}{13}\) \item $7\dfrac{5}{6}-9\dfrac{4}{8}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $\dfrac{18}{99}\times\dfrac{37}{74}=\underline{\hspace{3cm}}$\dfrac{1}{11}\) \item $5\dfrac{2}{4}-4\dfrac{8}{9}=\underline{\hspace{3cm}}$10\dfrac{7}{18}\) \item $2\dfrac{4}{9}-5\dfrac{3}{6}=\underline{\hspace{3cm}}$7\dfrac{17}{18}\) \item $\dfrac{19}{57}\times\dfrac{36}{90}=\underline{\hspace{3cm}}$\dfrac{2}{15}\) \item $9\dfrac{3}{9}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$13\dfrac{11}{15}\) \item $\dfrac{12}{28}\div\dfrac{20}{70}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $2\dfrac{3}{10}+4\dfrac{1}{2}=\underline{\hspace{3cm}}$6\dfrac{4}{5}\) \item $\dfrac{8}{15}\times4\dfrac{9}{18}=\underline{\hspace{3cm}}$\dfrac{12}{5}\) \item $\dfrac{9}{54}\div\dfrac{26}{91}=\underline{\hspace{3cm}}$\dfrac{7}{12}\) \item $4\dfrac{5}{10}+5\dfrac{1}{7}=\underline{\hspace{3cm}}$9\dfrac{9}{14}\) \item $1\dfrac{3}{17}\times\dfrac{17}{65}=\underline{\hspace{3cm}}$\dfrac{4}{13}\) \item $4\dfrac{6}{10}+4\dfrac{2}{5}=\underline{\hspace{3cm}}$-9\) \item $\dfrac{72}{29}\times\dfrac{58}{24}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \end{enumerate} \end{multicols} \newpage \textbf{p21} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $1\dfrac{8}{72}\times1\dfrac{10}{35}=\underline{\hspace{3cm}}$\dfrac{10}{7}\) \item $\dfrac{46}{8}\div\dfrac{69}{27}=\underline{\hspace{3cm}}$\dfrac{9}{4}\) \item $9\dfrac{3}{5}-4\dfrac{2}{6}=\underline{\hspace{3cm}}$13\dfrac{14}{15}\) \item $1\dfrac{17}{39}\times\dfrac{66}{77}=\underline{\hspace{3cm}}$\dfrac{16}{13}\) \item $2\dfrac{4}{20}\times\dfrac{25}{55}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $7\dfrac{2}{12}+4\dfrac{2}{8}=\underline{\hspace{3cm}}$11\dfrac{5}{12}\) \item $7\dfrac{10}{12}-7\dfrac{5}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{3}\) \item $\dfrac{80}{85}\times\dfrac{5}{20}=\underline{\hspace{3cm}}$\dfrac{4}{17}\) \item $\dfrac{28}{60}\div\dfrac{84}{96}=\underline{\hspace{3cm}}$\dfrac{8}{15}\) \item $\dfrac{10}{4}\div\dfrac{69}{23}=\underline{\hspace{3cm}}$\dfrac{5}{6}\) \item $1\dfrac{40}{50}\times\dfrac{55}{66}=\underline{\hspace{3cm}}$\dfrac{3}{2}\) \item $8\dfrac{2}{3}\times1\dfrac{21}{42}=\underline{\hspace{3cm}}$\dfrac{13}{1}\) \item $\dfrac{28}{33}\times1\dfrac{3}{42}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{33}{96}\times\dfrac{96}{48}=\underline{\hspace{3cm}}$\dfrac{11}{16}\) \item $\dfrac{85}{25}\times\dfrac{50}{60}=\underline{\hspace{3cm}}$\dfrac{17}{6}\) \item $6\dfrac{2}{4}+5\dfrac{6}{8}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $8\dfrac{2}{4}-9\dfrac{3}{7}=\underline{\hspace{3cm}}$17\dfrac{13}{14}\) \item $\dfrac{30}{42}\times5\dfrac{2}{8}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $3\dfrac{9}{12}-9\dfrac{5}{8}=\underline{\hspace{3cm}}$13\dfrac{3}{8}\) \item $5\dfrac{9}{12}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$-8\) \end{enumerate} \end{multicols} \textbf{p22} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{38}{19}\div\dfrac{76}{38}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $3\dfrac{2}{4}+3\dfrac{4}{12}=\underline{\hspace{3cm}}$6\dfrac{5}{6}\) \item $6\dfrac{9}{10}+2\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{2}{5}\) \item $2\dfrac{6}{8}-7\dfrac{3}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $\dfrac{54}{90}\times\dfrac{40}{26}=\underline{\hspace{3cm}}$\dfrac{12}{13}\) \item $\dfrac{16}{20}\times\dfrac{70}{24}=\underline{\hspace{3cm}}$\dfrac{7}{3}\) \item $2\dfrac{6}{8}-9\dfrac{3}{5}=\underline{\hspace{3cm}}$12\dfrac{7}{20}\) \item $7\dfrac{5}{10}+2\dfrac{2}{7}=\underline{\hspace{3cm}}$9\dfrac{11}{14}\) \item $\dfrac{24}{45}\div\dfrac{32}{4}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $2\dfrac{1}{3}+9\dfrac{11}{12}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $5\dfrac{6}{12}-2\dfrac{6}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{10}\) \item $\dfrac{42}{39}\div\dfrac{34}{17}=\underline{\hspace{3cm}}$\dfrac{7}{13}\) \item $\dfrac{51}{18}\div\dfrac{11}{66}=\underline{\hspace{3cm}}$\dfrac{17}{1}\) \item $7\dfrac{4}{6}-2\dfrac{6}{10}=\underline{\hspace{3cm}}$10\dfrac{4}{15}\) \item $7\dfrac{1}{6}-3\dfrac{1}{3}=\underline{\hspace{3cm}}$10\dfrac{1}{2}\) \item $9\dfrac{4}{6}+7\dfrac{2}{3}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $2\dfrac{6}{8}-7\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{4}\) \item $4\dfrac{3}{5}-9\dfrac{2}{3}=\underline{\hspace{3cm}}$14\dfrac{4}{15}\) \item $\dfrac{77}{63}\div\dfrac{24}{27}=\underline{\hspace{3cm}}$\dfrac{11}{8}\) \item $\dfrac{98}{28}\times\dfrac{8}{20}=\underline{\hspace{3cm}}$\dfrac{7}{5}\) \end{enumerate} \end{multicols} \textbf{p23} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $8\dfrac{4}{5}-9\dfrac{1}{10}=\underline{\hspace{3cm}}$17\dfrac{9}{10}\) \item $\dfrac{30}{75}\div\dfrac{48}{50}=\underline{\hspace{3cm}}$\dfrac{5}{12}\) \item $1\dfrac{28}{49}\times\dfrac{64}{88}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{26}{52}\div\dfrac{15}{18}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $2\dfrac{11}{20}\times1\dfrac{38}{57}=\underline{\hspace{3cm}}$\dfrac{17}{4}\) \item $\dfrac{33}{55}\times\dfrac{50}{38}=\underline{\hspace{3cm}}$\dfrac{15}{19}\) \item $\dfrac{24}{77}\times3\dfrac{16}{24}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $9\dfrac{2}{5}-6\dfrac{3}{10}=\underline{\hspace{3cm}}$15\dfrac{7}{10}\) \item $4\dfrac{1}{5}-5\dfrac{3}{10}=\underline{\hspace{3cm}}$9\dfrac{1}{2}\) \item $3\dfrac{10}{12}+7\dfrac{5}{9}=\underline{\hspace{3cm}}$11\dfrac{7}{18}\) \item $\dfrac{46}{23}\times\dfrac{9}{81}=\underline{\hspace{3cm}}$\dfrac{2}{9}\) \item $\dfrac{40}{96}\times\dfrac{99}{66}=\underline{\hspace{3cm}}$\dfrac{5}{8}\) \item $\dfrac{65}{78}\times1\dfrac{22}{35}=\underline{\hspace{3cm}}$\dfrac{19}{14}\) \item $\dfrac{36}{57}\times\dfrac{57}{33}=\underline{\hspace{3cm}}$\dfrac{12}{11}\) \item $\dfrac{6}{15}\div\dfrac{4}{80}=\underline{\hspace{3cm}}$\dfrac{8}{1}\) \item $6\dfrac{3}{9}+7\dfrac{7}{12}=\underline{\hspace{3cm}}$13\dfrac{11}{12}\) \item $5\dfrac{2}{12}-4\dfrac{6}{9}=\underline{\hspace{3cm}}$9\dfrac{5}{6}\) \item $\dfrac{16}{84}\div\dfrac{29}{87}=\underline{\hspace{3cm}}$\dfrac{4}{7}\) \item $9\dfrac{8}{10}-6\dfrac{3}{5}=\underline{\hspace{3cm}}$16\dfrac{2}{5}\) \item $\dfrac{36}{84}\times\dfrac{58}{87}=\underline{\hspace{3cm}}$\dfrac{2}{7}\) \end{enumerate} \end{multicols} \textbf{p24} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{20}{28}\div\dfrac{45}{72}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{69}{81}\times2\dfrac{8}{23}=\underline{\hspace{3cm}}$\dfrac{2}{1}\) \item $8\dfrac{4}{8}-7\dfrac{1}{6}=\underline{\hspace{3cm}}$15\dfrac{2}{3}\) \item $\dfrac{2}{60}\times\dfrac{72}{36}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \item $\dfrac{75}{81}\div\dfrac{15}{81}=\underline{\hspace{3cm}}$\dfrac{5}{1}\) \item $1\dfrac{28}{32}\times1\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $7\dfrac{4}{8}+5\dfrac{4}{7}=\underline{\hspace{3cm}}$13\dfrac{1}{14}\) \item $\dfrac{70}{77}\times1\dfrac{12}{40}=\underline{\hspace{3cm}}$\dfrac{13}{11}\) \item $2\dfrac{1}{10}-6\dfrac{4}{5}=\underline{\hspace{3cm}}$8\dfrac{9}{10}\) \item $2\dfrac{5}{12}-4\dfrac{4}{8}=\underline{\hspace{3cm}}$6\dfrac{11}{12}\) \item $5\dfrac{1}{2}-4\dfrac{1}{6}=\underline{\hspace{3cm}}$9\dfrac{2}{3}\) \item $6\dfrac{3}{9}-4\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{7}{12}\) \item $\dfrac{21}{6}\times\dfrac{22}{7}=\underline{\hspace{3cm}}$\dfrac{11}{1}\) \item $5\dfrac{1}{8}-8\dfrac{6}{12}=\underline{\hspace{3cm}}$13\dfrac{5}{8}\) \item $\dfrac{11}{2}\times\dfrac{10}{11}=\underline{\hspace{3cm}}$\dfrac{5}{1}\) \item $2\dfrac{3}{6}-9\dfrac{3}{8}=\underline{\hspace{3cm}}$11\dfrac{7}{8}\) \item $\dfrac{16}{10}\div\dfrac{56}{90}=\underline{\hspace{3cm}}$\dfrac{18}{7}\) \item $1\dfrac{11}{17}\times1\dfrac{4}{64}=\underline{\hspace{3cm}}$\dfrac{7}{4}\) \item $\dfrac{11}{88}\div\dfrac{4}{38}=\underline{\hspace{3cm}}$\dfrac{19}{16}\) \item $\dfrac{18}{28}\div\dfrac{24}{42}=\underline{\hspace{3cm}}$\dfrac{9}{8}\) \end{enumerate} \end{multicols} \textbf{p25} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $8\dfrac{2}{3}-5\dfrac{6}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{3}\) \item $7\dfrac{11}{12}-6\dfrac{2}{8}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $4\dfrac{5}{6}+5\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $\dfrac{15}{56}\div\dfrac{60}{48}=\underline{\hspace{3cm}}$\dfrac{3}{14}\) \item $\dfrac{72}{88}\div\dfrac{23}{46}=\underline{\hspace{3cm}}$\dfrac{18}{11}\) \item $\dfrac{72}{86}\times7\dfrac{2}{12}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $2\dfrac{5}{20}\times1\dfrac{18}{27}=\underline{\hspace{3cm}}$\dfrac{15}{4}\) \item $\dfrac{48}{27}\times\dfrac{27}{16}=\underline{\hspace{3cm}}$\dfrac{3}{1}\) \item $6\dfrac{2}{5}-7\dfrac{2}{4}=\underline{\hspace{3cm}}$13\dfrac{9}{10}\) \item $9\dfrac{7}{9}+5\dfrac{2}{12}=\underline{\hspace{3cm}}$14\dfrac{17}{18}\) \item $\dfrac{66}{14}\times\dfrac{98}{66}=\underline{\hspace{3cm}}$\dfrac{7}{1}\) \item $1\dfrac{8}{40}\times1\dfrac{25}{30}=\underline{\hspace{3cm}}$\dfrac{11}{5}\) \item $4\dfrac{1}{2}+7\dfrac{2}{7}=\underline{\hspace{3cm}}$11\dfrac{11}{14}\) \item $7\dfrac{6}{7}-6\dfrac{3}{6}=\underline{\hspace{3cm}}$14\dfrac{5}{14}\) \item $3\dfrac{4}{5}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$8\dfrac{1}{5}\) \item $6\dfrac{9}{10}+2\dfrac{10}{12}=\underline{\hspace{3cm}}$9\dfrac{11}{15}\) \item $5\dfrac{6}{10}+3\dfrac{4}{8}=\underline{\hspace{3cm}}$9\dfrac{1}{10}\) \item $4\dfrac{1}{4}+4\dfrac{7}{10}=\underline{\hspace{3cm}}$8\dfrac{19}{20}\) \item $\dfrac{36}{6}\div\dfrac{33}{2}=\underline{\hspace{3cm}}$\dfrac{4}{11}\) \item $5\dfrac{3}{6}-7\dfrac{5}{7}=\underline{\hspace{3cm}}$13\dfrac{3}{14}\) \end{enumerate} \end{multicols} \newpage \textbf{p26} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $7\dfrac{5}{6}+6\dfrac{3}{9}=\underline{\hspace{3cm}}$14\dfrac{1}{6}\) \item $2\dfrac{10}{12}-8\dfrac{3}{10}=\underline{\hspace{3cm}}$11\dfrac{2}{15}\) \item $\dfrac{9}{78}\div\dfrac{66}{88}=\underline{\hspace{3cm}}$\dfrac{2}{13}\) \item $\dfrac{98}{24}\div\dfrac{14}{6}=\underline{\hspace{3cm}}$\dfrac{7}{4}\) \item $2\dfrac{1}{9}+2\dfrac{1}{2}=\underline{\hspace{3cm}}$4\dfrac{11}{18}\) \item $\dfrac{32}{80}\times2\dfrac{12}{14}=\underline{\hspace{3cm}}$\dfrac{8}{7}\) \item $\dfrac{98}{91}\times\dfrac{13}{63}=\underline{\hspace{3cm}}$\dfrac{2}{9}\) \item $\dfrac{39}{78}\div\dfrac{30}{56}=\underline{\hspace{3cm}}$\dfrac{14}{15}\) \item $5\dfrac{11}{12}-7\dfrac{4}{8}=\underline{\hspace{3cm}}$13\dfrac{5}{12}\) \item $\dfrac{65}{13}\div\dfrac{70}{22}=\underline{\hspace{3cm}}$\dfrac{11}{7}\) \item $\dfrac{48}{40}\div\dfrac{6}{70}=\underline{\hspace{3cm}}$\dfrac{14}{1}\) \item $3\dfrac{11}{12}-6\dfrac{3}{9}=\underline{\hspace{3cm}}$10\dfrac{1}{4}\) \item $\dfrac{12}{78}\times1\dfrac{19}{38}=\underline{\hspace{3cm}}$\dfrac{3}{13}\) \item $\dfrac{35}{70}\div\dfrac{81}{72}=\underline{\hspace{3cm}}$\dfrac{4}{9}\) \item $7\dfrac{3}{5}-7\dfrac{1}{4}=\underline{\hspace{3cm}}$14\dfrac{17}{20}\) \item $5\dfrac{8}{9}+9\dfrac{1}{3}=\underline{\hspace{3cm}}$15\dfrac{2}{9}\) \item $3\dfrac{3}{4}+8\dfrac{1}{3}=\underline{\hspace{3cm}}$12\dfrac{1}{12}\) \item $\dfrac{48}{8}\times\dfrac{40}{96}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $4\dfrac{3}{6}+6\dfrac{7}{8}=\underline{\hspace{3cm}}$11\dfrac{3}{8}\) \item $3\dfrac{11}{12}+5\dfrac{3}{4}=\underline{\hspace{3cm}}$9\dfrac{2}{3}\) \end{enumerate} \end{multicols} \textbf{p27} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{51}{12}\div\dfrac{85}{20}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $6\dfrac{1}{9}-7\dfrac{4}{12}=\underline{\hspace{3cm}}$13\dfrac{4}{9}\) \item $7\dfrac{5}{6}-8\dfrac{4}{12}=\underline{\hspace{3cm}}$16\dfrac{1}{6}\) \item $4\dfrac{2}{6}-5\dfrac{10}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{6}\) \item $\dfrac{8}{96}\div\dfrac{10}{20}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $1\dfrac{17}{39}\times\dfrac{27}{84}=\underline{\hspace{3cm}}$\dfrac{6}{13}\) \item $2\dfrac{1}{6}-7\dfrac{2}{3}=\underline{\hspace{3cm}}$9\dfrac{5}{6}\) \item $3\dfrac{6}{7}-8\dfrac{5}{10}=\underline{\hspace{3cm}}$12\dfrac{5}{14}\) \item $9\dfrac{2}{8}-9\dfrac{1}{12}=\underline{\hspace{3cm}}$18\dfrac{1}{3}\) \item $2\dfrac{1}{9}+3\dfrac{10}{12}=\underline{\hspace{3cm}}$5\dfrac{17}{18}\) \item $5\dfrac{4}{8}+5\dfrac{2}{7}=\underline{\hspace{3cm}}$10\dfrac{11}{14}\) \item $\dfrac{27}{36}\times\dfrac{2}{18}=\underline{\hspace{3cm}}$\dfrac{1}{12}\) \item $4\dfrac{10}{12}+6\dfrac{3}{6}=\underline{\hspace{3cm}}$11\dfrac{1}{3}\) \item $8\dfrac{3}{6}+5\dfrac{3}{9}=\underline{\hspace{3cm}}$13\dfrac{5}{6}\) \item $\dfrac{57}{99}\div\dfrac{9}{33}=\underline{\hspace{3cm}}$\dfrac{19}{9}\) \item $\dfrac{10}{6}\div\dfrac{77}{21}=\underline{\hspace{3cm}}$\dfrac{5}{11}\) \item $1\dfrac{10}{34}\times\dfrac{16}{22}=\underline{\hspace{3cm}}$\dfrac{16}{17}\) \item $2\dfrac{9}{12}-3\dfrac{3}{5}=\underline{\hspace{3cm}}$6\dfrac{7}{20}\) \item $9\dfrac{7}{9}\times\dfrac{9}{96}=\underline{\hspace{3cm}}$\dfrac{11}{12}\) \item $9\dfrac{1}{3}+9\dfrac{1}{9}=\underline{\hspace{3cm}}$18\dfrac{4}{9}\) \end{enumerate} \end{multicols} \textbf{p28} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{72}{20}\div\dfrac{12}{50}=\underline{\hspace{3cm}}$\dfrac{15}{1}\) \item $4\dfrac{2}{4}+7\dfrac{4}{7}=\underline{\hspace{3cm}}$12\dfrac{1}{14}\) \item $5\dfrac{3}{9}+2\dfrac{4}{5}=\underline{\hspace{3cm}}$8\dfrac{2}{15}\) \item $\dfrac{99}{51}\div\dfrac{75}{85}=\underline{\hspace{3cm}}$\dfrac{11}{5}\) \item $7\dfrac{3}{6}-2\dfrac{7}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $2\dfrac{3}{12}+6\dfrac{5}{8}=\underline{\hspace{3cm}}$8\dfrac{7}{8}\) \item $\dfrac{12}{20}\times\dfrac{68}{24}=\underline{\hspace{3cm}}$\dfrac{17}{10}\) \item $2\dfrac{9}{12}-3\dfrac{3}{10}=\underline{\hspace{3cm}}$6\dfrac{1}{20}\) \item $\dfrac{26}{16}\div\dfrac{29}{58}=\underline{\hspace{3cm}}$\dfrac{13}{4}\) \item $3\dfrac{6}{8}-4\dfrac{6}{9}=\underline{\hspace{3cm}}$8\dfrac{5}{12}\) \item $4\dfrac{6}{8}+4\dfrac{8}{12}=\underline{\hspace{3cm}}$9\dfrac{5}{12}\) \item $3\dfrac{2}{4}-2\dfrac{8}{12}=\underline{\hspace{3cm}}$6\dfrac{1}{6}\) \item $\dfrac{72}{15}\div\dfrac{96}{50}=\underline{\hspace{3cm}}$\dfrac{5}{2}\) \item $6\dfrac{1}{2}+2\dfrac{2}{8}=\underline{\hspace{3cm}}$8\dfrac{3}{4}\) \item $6\dfrac{5}{12}-9\dfrac{5}{10}=\underline{\hspace{3cm}}$15\dfrac{11}{12}\) \item $6\dfrac{3}{8}+8\dfrac{1}{2}=\underline{\hspace{3cm}}$14\dfrac{7}{8}\) \item $2\dfrac{6}{10}-2\dfrac{9}{12}=\underline{\hspace{3cm}}$5\dfrac{7}{20}\) \item $1\dfrac{12}{18}\times\dfrac{27}{80}=\underline{\hspace{3cm}}$\dfrac{9}{16}\) \item $9\dfrac{1}{2}+7\dfrac{4}{7}=\underline{\hspace{3cm}}$17\dfrac{1}{14}\) \item $\dfrac{21}{35}\div\dfrac{72}{8}=\underline{\hspace{3cm}}$\dfrac{1}{15}\) \end{enumerate} \end{multicols} \textbf{p29} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{27}{18}\div\dfrac{66}{76}=\underline{\hspace{3cm}}$\dfrac{19}{11}\) \item $\dfrac{10}{68}\times\dfrac{68}{85}=\underline{\hspace{3cm}}$\dfrac{2}{17}\) \item $5\dfrac{1}{3}+5\dfrac{10}{12}=\underline{\hspace{3cm}}$11\dfrac{1}{6}\) \item $7\dfrac{3}{4}-4\dfrac{4}{8}=\underline{\hspace{3cm}}$12\dfrac{1}{4}\) \item $\dfrac{12}{15}\times1\dfrac{9}{66}=\underline{\hspace{3cm}}$\dfrac{10}{11}\) \item $\dfrac{12}{32}\times\dfrac{52}{12}=\underline{\hspace{3cm}}$\dfrac{13}{8}\) \item $6\dfrac{3}{6}-2\dfrac{3}{12}=\underline{\hspace{3cm}}$8\dfrac{3}{4}\) \item $2\dfrac{4}{7}-2\dfrac{5}{10}=\underline{\hspace{3cm}}$5\dfrac{1}{14}\) \item $\dfrac{51}{27}\div\dfrac{80}{45}=\underline{\hspace{3cm}}$\dfrac{17}{16}\) \item $9\dfrac{3}{6}+7\dfrac{10}{12}=\underline{\hspace{3cm}}$17\dfrac{1}{3}\) \item $\dfrac{60}{25}\div\dfrac{38}{10}=\underline{\hspace{3cm}}$\dfrac{12}{19}\) \item $4\dfrac{8}{12}-8\dfrac{2}{6}=\underline{\hspace{3cm}}$-13\) \item $3\dfrac{5}{9}+4\dfrac{2}{12}=\underline{\hspace{3cm}}$7\dfrac{13}{18}\) \item $\dfrac{15}{54}\div\dfrac{40}{12}=\underline{\hspace{3cm}}$\dfrac{1}{12}\) \item $9\dfrac{2}{9}-9\dfrac{3}{6}=\underline{\hspace{3cm}}$18\dfrac{13}{18}\) \item $2\dfrac{16}{28}\times2\dfrac{7}{21}=\underline{\hspace{3cm}}$\dfrac{6}{1}\) \item $7\dfrac{8}{12}-3\dfrac{1}{4}=\underline{\hspace{3cm}}$10\dfrac{11}{12}\) \item $\dfrac{7}{97}\times2\dfrac{13}{42}=\underline{\hspace{3cm}}$\dfrac{1}{6}\) \item $\dfrac{35}{30}\div\dfrac{95}{30}=\underline{\hspace{3cm}}$\dfrac{7}{19}\) \item $\dfrac{56}{14}\times\dfrac{90}{24}=\underline{\hspace{3cm}}$\dfrac{15}{1}\) \end{enumerate} \end{multicols} \textbf{p30} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)] \item $\dfrac{42}{60}\times1\dfrac{6}{14}=\underline{\hspace{3cm}}$\dfrac{1}{1}\) \item $2\dfrac{4}{7}+6\dfrac{2}{4}=\underline{\hspace{3cm}}$9\dfrac{1}{14}\) \item $\dfrac{6}{96}\div\dfrac{45}{90}=\underline{\hspace{3cm}}$\dfrac{1}{8}\) \item $8\dfrac{6}{10}-4\dfrac{9}{12}=\underline{\hspace{3cm}}$13\dfrac{7}{20}\) \item $5\dfrac{7}{12}-3\dfrac{2}{3}=\underline{\hspace{3cm}}$9\dfrac{1}{4}\) \item $6\dfrac{6}{8}+4\dfrac{4}{10}=\underline{\hspace{3cm}}$11\dfrac{3}{20}\) \item $8\dfrac{1}{4}+9\dfrac{2}{10}=\underline{\hspace{3cm}}$17\dfrac{9}{20}\) \item $1\dfrac{12}{20}\times1\dfrac{6}{84}=\underline{\hspace{3cm}}$\dfrac{12}{7}\) \item $\dfrac{64}{80}\times\dfrac{34}{68}=\underline{\hspace{3cm}}$\dfrac{2}{5}\) \item $\dfrac{49}{21}\div\dfrac{60}{30}=\underline{\hspace{3cm}}$\dfrac{7}{6}\) \item $5\dfrac{5}{8}+4\dfrac{6}{12}=\underline{\hspace{3cm}}$10\dfrac{1}{8}\) \item $8\dfrac{5}{10}-4\dfrac{2}{5}=\underline{\hspace{3cm}}$12\dfrac{9}{10}\) \item $\dfrac{29}{58}\times\dfrac{40}{6}=\underline{\hspace{3cm}}$\dfrac{10}{3}\) \item $\dfrac{45}{18}\div\dfrac{90}{12}=\underline{\hspace{3cm}}$\dfrac{1}{3}\) \item $\dfrac{76}{98}\div\dfrac{64}{98}=\underline{\hspace{3cm}}$\dfrac{19}{16}\) \item $6\dfrac{3}{9}-3\dfrac{3}{4}=\underline{\hspace{3cm}}$10\dfrac{1}{12}\) \item $\dfrac{72}{56}\div\dfrac{60}{28}=\underline{\hspace{3cm}}$\dfrac{3}{5}\) \item $\dfrac{58}{72}\times\dfrac{78}{87}=\underline{\hspace{3cm}}$\dfrac{13}{18}\) \item $\dfrac{88}{72}\times\dfrac{63}{99}=\underline{\hspace{3cm}}$\dfrac{7}{9}\) \item $2\dfrac{1}{4}-8\dfrac{4}{5}=\underline{\hspace{3cm}}$11\dfrac{1}{20}\) \end{enumerate} \end{multicols} \newpage \textbf{p31} \begin{multicols}{5} \begin{enumerate}[label=\arabic*)]