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Introduction

The fractions module allows us to create and work with rational numbers: fractions with an integer numerator divided by an integer denominator. For example, we can store 2/3 as an exact fraction instead of the approximate float value 0.6666....

Unlike int, float, and complex numbers, fractions do not have a literal form. However, the fraction constructor is quite flexible.

Most obviously, it can take two integers as arguments. Common factors are automatically removed, converting the fraction to its "lowest form" (the smallest integers that accurately represent the fraction):

>>> from fractions import Fraction

>>> f1 = Fraction(2, 3) # 2/3
>>> f1
Fraction(2, 3)

>>> f2 = Fraction(6, 9)
>>> f2
Fraction(2, 3)  # automatically simplified

>>> f1 == f2
True

The fraction constructor can also parse a string representation:

>>> f3 = Fraction('2/3')
>>> f3
Fraction(2, 3)

Fractions can also work with float parameters, but this may run into problems with the approximate nature of representing the decimal value internally as binary. For more on this representation issue, see the 0.30000000000000004 website, and Floating Point Arithmetic: Issues and Limitations in the Python documentation.

For a more reliable result when using floats with fractions, there is the <fraction>.limit_denominator() method.

Arithmetic with Fractions

The usual arithmetic operators + - * / ** will work with fractions, as with other numeric types.

Integers and other Fractions can be included in the equation and give a Fraction result. Including a float in the expression results in float output, with a consequent (possible) loss in precision:

>>> Fraction(2, 3) + Fraction(1, 4) # addition
Fraction(11, 12)

>>> Fraction(2, 3) * Fraction(6, 5) # multiply fractions
Fraction(4, 5)

>>> Fraction(2, 3) * 6 / 5 # fraction with integers
Fraction(4, 5)

>>> Fraction(2, 3) * 1.2  # fraction with float -> float
0.7999999999999999

>>> Fraction(2, 3) ** 2  # exponentiation with integer
Fraction(4, 9)

Various standard Python numeric functions also give the result you might expect from working with int and float types:

>>> round(Fraction(11, 3))
4

>>> from math import floor, ceil
>>> floor(Fraction(11, 3))
3
>>> ceil(Fraction(11, 3))
4

>>> float(Fraction(11, 3))
3.6666666666666665