Define a class for rational numbers. A rational number is a number that can be represented as the quotient of two integers. For example, 1/2, 3/4, 64/2, and so forth are all rational numbers.

(By 1/2 we mean the everyday meaning of the fraction, not the integer division this expression would produce in a C++ program.) Represent rational numbers as two values of type int, one for the numerator and one for the denominator. Call the class Rational.

Include a constructor with two arguments that can be used to set the member variables of an object to any legitimate values. Also include a constructor that has only a single parameter of type int; call this single parameter wholeNumber and define the constructor so that the object will be initialized to the rational number wholeNumber/1.

Also include a default constructor that initializes an object to 0 (that is, 0/1).

Overload the relational operators ==, <, <=, >, >=, and != so that they correctly apply to type Rational.

Also write a test program to test your class.

Hints: Two rational numbers a/b and c/d are equal if a*d equals c*b. If b and d are positive rational numbers then a/b is less than c/d provided a*d is less than c*b.

use the header file Rational.h as a starting point

A function to standardize the values stored so that the denominator is always positive should be included. (An additional exercise would be to include a function to reduce the rational number so the numerator and denominator are as small as possible.)

Rational.h:

#ifndef RATIONAL_H

#define RATIONAL_H

#include

using namespace std;

class Rational

{

public:

Rational();

// Initializes the rational number to 0

Rational(int wholeNumber);

// Initializes the rational number to wholeNumber/1

Rational(int m, int n);

// Initializes the rational number to m/n if n is not 0;

// the sign of the rational is stored in the numerator

// (the denominator is always positive);

// exits if n = 0 (invalid rational number)

void output();

// Precondition: The rational number is defined.

// Postcondition: The rational number has been displayed on

// the screen in the form m/n.

friend bool operator ==(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 equals r2; false otherwise.

friend bool operator <(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 is less than r2; false otherwise.

friend bool operator >(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 is greater than r2; false otherwise.

friend bool operator <=(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 is less than or equal to r2; false otherwise.

friend bool operator >=(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 is greater than or equal to r2; false otherwise.

friend bool operator !=(const Rational& r1, const Rational& r2);

// Precondition: r1 and r2 are valid rational numbers

// Returns true if r1 is not equal to r2; false otherwise.

private:

int num; // the numerator of the number

int denom; // the denominator of the number

void standardize();

// Precondition: num and denom have values

// Postcondition: if denom is 0 the program is terminated;

// otherwise the rational number is standardized so that

// denom is positive.

};

#endif