(Rational Class) Create a class called Rational for performing arithmetic with fractions. Write a program to test your class. Use integer variables to represent the private data of the class—the numerator and the denom- inator. Provide a constructor that enables an object of this class to be initialized when it is declared. The constructor should contain default values in case no initializers

Question

are provided and should store the fraction in reduced form. For example, the fraction 2/4 would be stored in the object as 1 in the numerator and 2 in the denominator. Provide public member functions that perform each of the following tasks:

a) Adding two Rational numbers. The result should be stored in reduced form.
b) Subtracting two Rational numbers. The result should be stored in reduced form.
c) Multiplying two Rational numbers. The result should be stored in reduced form.
d) Dividing two Rational numbers. The result should be stored in reduced form.
e) Printing Rational numbers in the form a/b, where a is the numerator and b is the denominator.
f) Printing Rational numbers in floating-point format.

Answer 1

```
#ifndef RATIONAL_H
#define RATIONAL_H

class Rational
{
public:
Rational( int = 0, int = 1 ); // default constructor
Rational addition( const Rational & ); // function addition
Rational subtraction( const Rational & ); // function subtraction
Rational multiplication( const Rational & ); // function multi.
Rational division( const Rational & ); // function division
void printRational (); // print rational format
void printRationalAsDouble(); // print rational as double format
private:
int numerator; // integer numerator
int denominator; // integer denominator
void reduction(); // utility function
}; // end class Rational

#endif
```
```
// Member-function definitions for class Rational.
#include
#include "Rational.h" // include definition of class Rational
using namespace std;

Rational::Rational( int n, int d )
{
numerator = n; // sets numerator
denominator = d; // sets denominator
reduction(); // store the fraction in reduced form
} // end Rational constructor

Rational Rational::addition( const Rational &a )
{
Rational t; // creates Rational object

t.numerator = a.numerator * denominator;
t.numerator += a.denominator * numerator;
t.denominator = a.denominator * denominator;
t.reduction(); // store the fraction in reduced form
return t;
} // end function addition

Rational Rational::subtraction( const Rational &s )
{
Rational t; // creates Rational object

t.numerator = s.denominator * numerator;
t.numerator -= denominator * s.numerator;
t.denominator = s.denominator * denominator;
t.reduction(); // store the fraction in reduced form
return t;
} // end function subtraction

Rational Rational::multiplication( const Rational &m )
{
Rational t; // creates Rational object

t.numerator = m.numerator * numerator;
t.denominator = m.denominator * denominator;
t.reduction(); // store the fraction in reduced form
return t;
} // end function multiplication

Rational Rational::division( const Rational &v )
{
Rational t; // creates Rational object

t.numerator = v.denominator * numerator;
t.denominator = denominator * v.numerator;
t.reduction(); // store the fraction in reduced form
return t;
} // end function division

void Rational::printRational ()
{
if ( denominator == 0 ) // validates denominator
cout << "\nDIVIDE BY ZERO ERROR!!!" << '\n';
else if ( numerator == 0 ) // validates numerator
cout << 0;
else
cout << numerator << '/' << denominator;
} // end function printRational

void Rational::printRationalAsDouble()
{
cout << static_cast< double >( numerator ) / denominator;
} // end function printRationalAsDouble

void Rational::reduction()
{
int largest;
largest = numerator > denominator ? numerator : denominator;

int gcd = 0; // greatest common divisor

for ( int loop = 2; loop <= largest; loop++ )

if ( numerator % loop == 0 && denominator % loop == 0 )
gcd = loop;

if (gcd != 0)
{
numerator /= gcd;
denominator /= gcd;
} // end if
} // end function reduction
```
```
#include
#include "Rational.h" // include definition of class Rational
using namespace std;

int main()
{
Rational c( 2, 6 ), d( 7, 8 ), x; // creates three rational objects

c.printRational(); // prints rational object c
cout << " + ";
d.printRational(); // prints rational object d
x = c.addition( d ); // adds object c and d; sets the value to x

cout << " = ";
x.printRational(); // prints rational object x
cout << '\n';
x.printRational(); // prints rational object x
cout << " = ";
x.printRationalAsDouble(); // prints rational object x as double
cout << "\n\n";

c.printRational(); // prints rational object c
cout << " - ";
d.printRational(); // prints rational object d
x = c.subtraction( d ); // subtracts object c and d

cout << " = ";
x.printRational(); // prints rational object x
cout << '\n';
x.printRational(); // prints rational object x
cout << " = ";
x.printRationalAsDouble(); // prints rational object x as double
cout << "\n\n";

c.printRational(); // prints rational object c
cout << " x ";
d.printRational(); // prints rational object d
x = c.multiplication( d ); // multiplies object c and d

cout << " = ";
x.printRational(); // prints rational object x
cout << '\n';
x.printRational(); // prints rational object x
cout << " = ";
x.printRationalAsDouble(); // prints rational object x as double
cout << "\n\n";

c.printRational(); // prints rational object c
cout << " / ";
d.printRational(); // prints rational object d
x = c.division( d ); // divides object c and d

cout << " = ";
x.printRational(); // prints rational object x
cout << '\n';
x.printRational(); // prints rational object x
cout << " = ";
x.printRationalAsDouble(); // prints rational object x as double
cout << endl;
} // end main
```
1/3 + 7/8 = 29/24
29/24 = 1.20833
1/3 - 7/8 = -13/24
-13/24 = -0.541667
1/3 x 7/8 = 7/24
7/24 = 0.291667
1/3 / 7/8 = 8/21
8/21 = 0.380952