Now that I've learned about the existence of the Python built-in fractions package that handles fractions, let's take a quick look at how it behaves.

Environment used in the article

Use Python 3.8.6. For the rest, we'll just use the built-in fractions package.

Basic usage

First of all, you need to import the fractions package to handle it. In particular, the Fraction class is the main usage, so import that.

from fractions import Fraction

The Fraction class accepts a first argument, the numerator, and a second argument, the denominator.

f = Fraction(numerator=3, denominator=4)

If you try to display an instance of the Fraction class on an interactive shell or Jupyter, it will be displayed as a repr, including the values of the numerator and denominator.

>>> f

Fraction(3, 4)

If you look through the print function, it will be displayed as 3/4.

>>> print(f)

3/4

Can be compared with int and float

It seems that Fraction instances can be compared with ints and floats as they are.

`Comparison with int`


>>> f = Fraction(numerator=4, denominator=4)
>>> f == 1

True

`Comparison with float`


>>> f = Fraction(numerator=3, denominator=4)
>>> f == 3 / 4

True

If it is an int value, Fraction is returned even if four arithmetic operations are performed.

If you perform four arithmetic operations on a Fraction instance with int etc., the Fraction instance will be returned as it is.

>>> Fraction(3, 4) + 1

Fraction(7, 4)

>>> Fraction(5, 4) - 1

Fraction(1, 4)

>>> Fraction(3, 4) * 2

Fraction(3, 2)

Fraction also returns four arithmetic operations between Fractions

If you add Fractions together, the result will also be an instance of Fractions.

>>> Fraction(1, 4) + Fraction(1, 4)

Fraction(1, 2)

Fraction + Fraction + int will return Fraction as it is.

>>> Fraction(1, 4) + Fraction(1, 4) + 1

Fraction(3, 2)

Float is returned when four arithmetic operations are performed with the value of float.

If you perform four arithmetic operations with the values of Fraction and float, the result will be float.

>>> Fraction(3, 4) + 1.5

2.25

The denominator argument can be omitted

By specifying float as the argument of the numerator (numerator) of the first argument, you can create a Fraction instance even if you omit the denominator argument of the denominator.

>>> Fraction(numerator=0.25)

Fraction(1, 4)

>>> Fraction(numerator=0.26)

Fraction(1170935903116329, 4503599627370496)

>>> 1170935903116329 / 4503599627370496

0.26

You can also specify a string in the numerator argument

You can also specify a character string using a half-width slash, such as 1/4, in the numerator argument.

>>> Fraction(numerator='1/4')

Fraction(1, 4)

Automatically reduced

If you can reduce the amount when you create an instance of Fraction or perform a calculation, the reduction will be executed automatically.

>>> Fraction(2, 4)

Fraction(1, 2)

>>> Fraction(1, 6) + Fraction(1, 6)

Fraction(1, 3)

You can get the approximate value of an irrational number with the limit_denominator method

If you specify an irrational number, you can specify the maximum denominator value (max_denominator argument) to get an approximate value within the range of that value or less.

>>> Fraction(3.14159265359)

Fraction(3537118876014453, 1125899906842624)

`Setting the denominator is limited to 10 or less`


>>> Fraction(3.14159265359).limit_denominator(max_denominator=10)
Fraction(22, 7)

>>> 22 / 7
3.142857142857143

`Setting the denominator is limited to 150 or less`


>>> Fraction(3.14159265359).limit_denominator(max_denominator=150)
Fraction(3.14159265359).limit_denominator(max_denominator=150)

>>> 355 / 113
3.1415929203539825

References / Reference Sites

Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! -fractions --- Rational Numbers (Official Document) -Calculation of fractions (rational numbers) with Python, fractions

I took a quick look at the fractions package that handles Python built-in fractions.