C++ Program 3

rational.cpp

Build an ADT for rational numbers.

A rational number consists of two integer pieces a numerator, say a, and a denominator, say b, representing a fraction a / b.

The rational number is said to be in proper form if the greatest common divisor of both the numerator and denominator is 1 and the denominator is positive.

The result of operations between two rational numbers a / b and c / d follows.

addition (a d + b c) / (b d)
subtraction (a d - b c) / (b d)
multiplication (a c) / (b d)
division (a d) / (b c)
equivalence if ( a d ) == ( b c )
less than a / b < c / d if (a d) < (b c) with rationals in proper form (denominators must always be positive - negative numbers have negative numerators - this has an implication for how you store all rationals)

You should name the class Rational. You should have "four" constructors (perhaps by overloading, or perhaps by default values, or perhaps by both as appropriate): default (initial value zero, 0 / 1), input using a single integer (representing the integer using 1 for the denominator), input using two integers (representing the numerator and denominator respectively), and a copy constructor.

You should have two accessor functions, getNum() for the numerator and getDenom() for the denominator.

You should overload the assignment operators (which should be member functions): =, +=, -=, *=, /=

You should overload binary operators (which should be member functions): +, -, *, /

You should overload the unary operator (which should be a member function): -

You should overload the output operator (which should be a non-member function, but may be a friend): <<

You should overload the comparison operators (which should be member functions): <, <=, >, >=, ==, !=

You should overload the absolute value function (which should be a non-member function, but may be a friend): abs()

In addition to your *.cpp and *.h files turn in a main program that exercises the class Rational. That is, a main program that runs through a selection of arithmetic and logical operations and uses rational input and output.

What to turn in

Provide, as an e-copy in the u:\program3 directory, a pseudocode design of your program.
Be sure your program rational.h, rational.cpp and testRational.exe are saved under your u:\program3 folder

Grading Criteria

80 points maximum
- 70 points – Design and Output Correctness
  - You should name the class Rational. You should have four constructors: default (initial value zero, 0 / 1), input using a single integer (representing the integer using 1 for the denominator), input using two integers (representing the numerator and denominator respectively), and a copy constructor.
  - You should have two accessor functions, getNum() for the numerator and getDenom() for the denominator.
  - You should overload the assignment operators: =, +=, -=, *=, /=
  - You should overload binary operators: +, -, *, /
- 5 points - Comments
  - Complete and correct header comments, declaration, and in-line comments.