Question

(Rational Numbers) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private instance variables of the class- the numerator and the denominator. Provide a constructor that enables an object of this class to be initialized when it's declared. The constructor should store the fraction in reduced form. The fraction 2/4 is equivalent to h and would be stored in the object as 1 in the numerator and 2 in the denominator. Provide a no-argument constructor with default values in case no initializers are provided. Provide public methods that perform each of the following operations: a) Add two Rational numbers: The result of the addition should be stored in reduced form. b) Subtract two Rational numbers: The result of the subtraction should be stored in reduced form. c) Multiply two Rational numbers: The result of the multiplication should be stored in reduced form. d) Divide two Rational numbers: The result of the division should be stored in reduced form. e) Return a String representation of a Rational number in the form a/b where a is the numerator and b is the denominator. f) Return a String representation of a Rational number in a floating-point format. (Consider providing formatting capabilities that enable the user of the class to specify the number of digits of precision to the right of the decimal point.)

Answer 1

C++ CODE:

#include<iostream>
#include<string>
#include<sstream>
using namespace std;
class Rational
{
private:
int num;
int denom;
int gcd(int a, int b)
{
if (a == 0)
return b;
if (b == 0)
return a;
if (a == b)
return a;
if (a > b)
return gcd(a-b, b);
return gcd(a, b-a);
}
void reduce()
{
int d;
d=gcd(num, denom);
num=num/d;
denom=denom/d;
}
string to_string(int num)
{
ostringstream str1;
str1 << num;
return str1.str();
}
string to_string(float num)
{
ostringstream str1;
str1 << num;
return str1.str();
}
public:
void set(int x,int y)
{
num=x;
denom=y;
if(y==0)
denom=1;
reduce();
}
int getNum()
{
return num;
}
int getDenom()
{
return denom;
}
Rational(int x,int y)
{
num=x;
denom=y;
if(y==0)
denom=1;
reduce();
}
Rational()
{
num=1;
denom=2;
}
Rational operator +(Rational r)
{
Rational sum;
int x=num*r.getDenom()+denom*r.getNum();
int y=denom*r.getDenom();
sum.set(x,y);
return sum;
}
Rational operator -(Rational r)
{
Rational sub;
int x=num*r.getDenom()-denom*r.getNum();
int y=denom*r.getDenom();
sub.set(x,y);
return sub;
}
Rational operator *(Rational r)
{
Rational mul;
int x=num*r.getNum();
int y=denom*r.getDenom();
mul.set(x,y);
return mul;
}
Rational operator /(Rational r)
{
Rational div;
int x=num*r.getDenom();
int y=denom*r.getNum();
div.set(x,y);
return div;
}
string fraction()
{
string x=to_string(num);
string y=to_string(denom);
return x+"/"+y;
}
string decimal(int place)
{
float no=(float)num/(float)denom;
string str=to_string(no);
int dotindex=0;
for(int i=0;i<str.size();i++)
{
if(str[i]=='.')
{
dotindex=i;
break;
}
}
if(str.size()-dotindex-1<place)
{
int s=str.size();
for(int i=0;i<place-s+dotindex+1;i++)
str+="0";
}
else if(str.size()-dotindex>place)
{
str=str.substr(0,dotindex+place+1);
}
return str;
}
};
int main()
{
Rational r1(3,6);
Rational r2(4,10);
cout<<"r1="<<r1.fraction()<<"="<<r1.decimal(2)<<endl;
cout<<"r2="<<r2.fraction()<<"="<<r2.decimal(2)<<endl;
Rational r3=r1+r2;
cout<<"r1+r2="<<r3.fraction()<<"="<<r3.decimal(2)<<endl;
Rational r4=r1-r2;
cout<<"r1-r2="<<r4.fraction()<<"="<<r4.decimal(2)<<endl;
Rational r5=r1*r2;
cout<<"r1*r2="<<r5.fraction()<<"="<<r5.decimal(2)<<endl;
Rational r6=r1/r2;
cout<<"r1/r2="<<r6.fraction()<<"="<<r6.decimal(2)<<endl;
return 0;
}

Output:

"CAUsers Ashish Shrivastav Desktoplc,C++ Programs\rational.exe" r1-1/2=0.50 r 2-2/5=0.40 r1+r2-9/10-0.90 r1-r2- 1/10-0.10 r1r2-1/5-0.20 r1/r2-5/4-1.25 Process returned 0 (0x0) Press any key to continue execution time: 0.452 s