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, etc., 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 whole_number and define the constructor so that the object will be initialized to the rational number whole_number/1. Also include a

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

Overload the input and output operators >> and <<. Numbers are to be

input and output in the form 1/2, 15/32, 300/401, and so forth. Note

that the numerator, the denominator, or both may contain a minus sign,

so −1/2, 15/−32, and −300/−401 are also possible inputs. Overload all of

the following operators so that they correctly apply to the type Rational:

==, <, <=, >, >=, +, −, *, and /. 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, a/b is less than c/d provided a*d is less

than c*b. You should include a function to normalize the values stored so

that, after normalization, the denominator is positive and the numerator

and denominator are as small as possible. For example, after

normalization 4/−8 would be represented the same as −1/2. You should also write a test program to test your class.