# :mod:fractions --- Rational numbers

Source code: :source:Lib/fractions.py

The :mod:fractions module provides support for rational number arithmetic.

A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string.

The first version requires that numerator and denominator are instances of :class:numbers.Rational and returns a new :class:Fraction instance with value numerator/denominator. If denominator is :const:0, it raises a :exc:ZeroDivisionError. The second version requires that other_fraction is an instance of :class:numbers.Rational and returns a :class:Fraction instance with the same value. The next two versions accept either a :class:float or a :class:decimal.Decimal instance, and return a :class:Fraction instance with exactly the same value. Note that due to the usual issues with binary floating-point (see :ref:tut-fp-issues), the argument to Fraction(1.1) is not exactly equal to 11/10, and so Fraction(1.1) does not return Fraction(11, 10) as one might expect. (But see the documentation for the :meth:limit_denominator method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:

[sign] numerator ['/' denominator]


where the optional sign may be either '+' or '-' and numerator and denominator (if present) are strings of decimal digits. In addition, any string that represents a finite value and is accepted by the :class:float constructor is also accepted by the :class:Fraction constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:

>>> from fractions import Fraction
>>> Fraction(16, -10)
Fraction(-8, 5)
>>> Fraction(123)
Fraction(123, 1)
>>> Fraction()
Fraction(0, 1)
>>> Fraction('3/7')
Fraction(3, 7)
>>> Fraction(' -3/7 ')
Fraction(-3, 7)
>>> Fraction('1.414213 \t\n')
Fraction(1414213, 1000000)
>>> Fraction('-.125')
Fraction(-1, 8)
>>> Fraction('7e-6')
Fraction(7, 1000000)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(1.1)
Fraction(2476979795053773, 2251799813685248)
>>> from decimal import Decimal
>>> Fraction(Decimal('1.1'))
Fraction(11, 10)


The :class:Fraction class inherits from the abstract base class :class:numbers.Rational, and implements all of the methods and operations from that class. :class:Fraction instances are hashable, and should be treated as immutable. In addition, :class:Fraction has the following methods: