Modify the class Rational of Programming Challenge 8 (Refer to Rational Arithmetic I below) to add overloaded operators +, -, *, and / to be used for addition, subtraction, multiplication, and division. Test the class by reading and processing from the keyboard (or from a file) a series of rational expressions such as 2 / 3 + 2 / 8
2 / 3 * –2 / 8
2 / 3 – 2 / 8
2 / 3 / 2 / 8
To facilitate parsing of the input, you may assume that numbers and arithmetic operators are separated by whitespace.
Rational Arithmetic I
A rational number is a quotient of two integers. For example, 12/5, 12/–4, –3/4, and 4/6 are all rational numbers. A rational number is said to be in reduced form if its denominator is positive and its numerator and denominator have no common divisor other than 1. For example, the reduced forms of the rational numbers given above are 12/5, –3/1, –3/4, and 2/3.
Write a class called Rational with a constructor Rational(int, int) that takes two integers, a numerator and a denominator, and stores those two values in reduced form in corresponding private members. The class should have a private member function void reduce() that is used to accomplish the transformation to reduced form. The class should have an overloaded insertion operator << that will be used for output of objects of the class.