Kata

This kata is part one of precise fractions series (see pt. 2: http://www.codewars.com/kata/precise-fractions-pt-2-conversion).

When dealing with fractional values, there's always a problem with the precision of arithmetical operations. So lets fix it!

Your task is to implement class Fraction that takes care of simple fraction arithmetics. Requirements:

• class must have two-parameter constructor Fraction(numerator, denominator); passed values will be non-zero integers, and may be positive or negative.

• two conversion methods must be supported:

• toDecimal() returns decimal representation of fraction

• toString() returns string with fractional representation of stored value in format:

  [ SIGN ] [ WHOLES ] [ NUMERATOR / DENOMINATOR ]

  • Note: each part is returned only if it is available and non-zero, with the only possible space character going between WHOLES and fraction. Examples: '-1/2', '3', '-5 3/4'

• The fractional part must always be normalized (ie. the numerator and denominators must not have any common divisors).

• Four operations need to be implemented: add, subtract, multiply and divide. Each of them may take integers as well as another Fraction instance as an argument, and must return a new Fraction instance.

• Instances must be immutable, hence none of the operations may modify either of the objects it is called upon, nor the passed argument.

Python Notes

• If one integer is passed into the initialiser, then the fraction should be assumed to represent an integer not a fraction.
• You must implement the standard operator overrides __add__, __sub__, __mul__, __div__, in each case you should support other being an int or another instance of Fraction.
• Implement __str__ and to_decimal in place of toString and toDecimal as described above.