Fractions

For those of you like me that rarely use the C++ floating-point types (float, double), it often comes as a bit of surprise when the floating-point representation of a number fails to accurately capture the value. Certainly double, which is usually stored as a 64-bit value, is far better than the old float, which is only 32 bits, but problems do arise. For example: 
float n = 2.0;
float d = 3.0;
cout.precision(17);
cout << n / d << endl;
Produces 0.66666668653488159, which is accurate to 8 decimal places. Not bad, but a bit dirty for a discipline that prides itself on precision.

A solution that is often used when precision is of greatest importance and all of the numbers involved are going to be rational (that is, expressible as a fraction) is to use a custom type that implements fractions / rational numbers. This is what you will do in this assignment.

The Spec

Implement class Fraction. The interface for Fraction should be contained in "fraction.h", and the implementation in "fraction.cc". You must also write a program to demonstrate that you have rigorously tested your Fraction class, which must be in "main.cc". You must submit a Makefile for this assignment.

Fraction must have, at minimum, the following methods: Additionally, bonus credit is available for implementing any or all of the following methods: Extra credit is also available if your fraction is always stored in "lowest terms." You may want to look at the Euclidean Algorithm for help here.

Hints