Write a rational number class. This problem will be revisited in Chapter

11, where operator overloading will make the problem much easier. For

now we will use member functions add, sub, mul, div, and less that each

carry out the operations +, -, *, /, and <. For example, a + b will be written

a.add(b), and a < b will be written a.less(b).

Define a class for rational numbers. A rational number is a “ratio-nal”

number, composed of two integers with division indicated. The division is

not carried out, it is only indicated, as in 1/2, 2/3, 15/32, 65/4, 16/5. You

should represent rational numbers by two int values, numerator and

denominator.

A principle of abstract data type construction is that constructors must be

present to create objects with any legal values. You should provide

constructors to make objects out of pairs of int values; this is a constructor

with two int parameters. Since every int is also a rational number, as in

2/1 or 17/1, you should provide a constructor with a single int parameter.

Provide member functions input and output that take an istream and

ostream argument, respectively, and fetch or write rational numbers in

the form 2/3 or 37/51 to or from the keyboard (and to or from a file).

Provide member functions add, sub, mul, and div that return a rational value.

Provide a function less that returns a bool value. These functions should do the operation suggested by the name. Provide a member function neg that has no parameters and returns the negative of the calling object.

Provide a main function that thoroughly tests your class implementation.

The following formulas will be useful in defining functions.

a/b + c/d = (a*d + b*c) / (b*d)

a/b - c/d = (a*d - b*c) / (b*d)

(a/b) * (c/d) = (a*c) / (b*d)

(a/b) / (c/d) = (a*d) / (c*b)

-(a/b) = (-a/b)

(a/b) < (c/d) means (a*d) < (c*b)

(a/b) == (c/d) means (a*d) == (c*b)

Let any sign be carried by the numerator; keep the denominator positive.