Chapter 8, Problem 2PP

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. ( $C++$

By 1/2 and so on we mean the everyday fraction, not the integer division this expression would produce in a 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/l. 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, IS/ 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 the following operators so that they correctly apply to the type Rational: $==,<,<=,>,>=,+,-,*,$ and /. Write a test program to test your class. Hints: Two rational numbers a/b and c/d are equal if a equals c *b. If b and d are positive rational numbers, a/b is less than c/d provided is less than c 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 $-1/2.$