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.
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