Fractions with the Python Fraction Type

Today we’ll be talking about fractions. Sometimes decimal fractions are not exactly what you want. You may want to operate on fractions like 1/3 or 3/4 for example. If this is the case, you can easily do it in Python using the Fraction type from the fractions module.

We’ll make use of the fractions module, so let’s import it now:

from fractions import *

As I just mentioned, we use the Fraction type from the fractions module to create fractions.

Let’s say we want to create the fraction ¾. We can do it in a couple of ways using the Fraction method:

>>> Fraction(3, 4) # we can pass the numerator and denominator
Fraction(3, 4)

>>> Fraction(0.75) # we can pass the decimal value
Fraction(3, 4)

>>> Fraction('3/4') # we can pass a string 
Fraction(3, 4)

Learn how to make beautiful GUI apps

in Python using the Kivy framework.

Comprehensive, for Kivy beginners, easy to follow.

Get the book here (PDF) or on Amazon:

ebook / paperback (black and white) / paperback (full color)

We can also use the built-in float method as_integer_ratio, which returns a tuple. Then we have to add an asterisk which expands the tuple into its individual elements:

>>> Fraction(*(0.75).as_integer_ratio())
Fraction(3, 4)

The default value of the denominator is 1, so:

>>> Fraction(4) == Fraction(4, 1)
True

The default value of the numerator is 0, so:

>>> Fraction() == Fraction(0, 1) == Fraction(0, 3) == 0
True

You can use fractions in arithmetic operations:

>>> Fraction(3, 5) + Fraction(1, 5) # 3/5 + 1/5
Fraction(4, 5)

>>> Fraction(2, 7) * Fraction(7, 2) # 2/7 * 7/2
Fraction(1, 1)

>>> 49 ** Fraction(1, 2) # 49 ** (1/2)
7.0

>>> a = Fraction(2, 3)
>>> b = Fraction(5, 6)
>>> a + b, a - b, a * b, a / b, a // b
(Fraction(3, 2), Fraction(-1, 6), Fraction(5, 9), Fraction(4, 5), 0)

Your Panda3D Magazine

Make Awesome Games and Other 3D Apps

with Panda3D and Blender using Python.

Cool stuff, easy to follow articles.

Get the magazine here (PDF).

We can also pass a fraction as a numerator or denominator:

>>> Fraction(Fraction(3, 5), 2) # same as (3/5) / 2
Fraction(3, 10)

>>> Fraction(5, Fraction(1, 5)) # same as 5 / (1/5)
Fraction(25, 1)

>>> Fraction(Fraction(2, 3), Fraction(8, 5)) # same as (2/3) / (8/5)
Fraction(5, 12)

If either the numerator or the denominator is a negative number, in the resulting fraction the numerator is negative:

>>> Fraction(-1, 5)
Fraction(-1, 5)
>>> Fraction(1, -5)
Fraction(-1, 5)

Python Jumpstart Course

Learn the basics of Python, including OOP.

with lots of exercises, easy to follow

The course is available on Udemy.

It’s also possible to use scientific notation in a string passed as the argument:

>>> Fraction('-5e3')  # same as -5 * 10 ** 3
Fraction(-5000, 1)

>>> Fraction('3e-2')  # same as 3 * 10 ** (-2)
Fraction(3, 100)

We can use the limit_denominator method to obtain the closest fractional representation of a given float number where the denominator is not greater than the max_denominator passed as an argument to the function:

# the denominator can be no more than 5, so 3/2 is the closest to 1.54657
>>> Fraction(1.54657).limit_denominator(5) 
Fraction(3, 2)

# the denominator can be no more than 10, so 14/9 is the closest to 1.54657
>>> Fraction(1.54657).limit_denominator(10)
Fraction(14, 9)

# the denominator can be no more than 100000, so 154657/100000 is the closest to 1.54657, actually this is the exact same thing
>>> Fraction(1.54657).limit_denominator(100000)
Fraction(154657, 100000)

Feel free to explore the fractions module even further.

Blender Jumpstart Course

Learn the basics of 3D modeling in Blender.

step-by-step, easy to follow, visually rich

The course is available on Udemy and on Skillshare.

Here’s the video version: