Does Python have a function to reduce fractions?

Question

For example, when I calculate 98/42 I want to get 7/3, not 2.3333333, is there a function for that using Python or Numpy?

score 64 · Accepted Answer · edited May 23 '17 at 11:53

64

The fractions module can do that

>>> from fractions import Fraction
>>> Fraction(98, 42)
Fraction(7, 3)

There's a recipe over here for a numpy gcd. Which you could then use to divide your fraction

>>> def numpy_gcd(a, b):
...     a, b = np.broadcast_arrays(a, b)
...     a = a.copy()
...     b = b.copy()
...     pos = np.nonzero(b)[0]
...     while len(pos) > 0:
...         b2 = b[pos]
...         a[pos], b[pos] = b2, a[pos] % b2
...         pos = pos[b[pos]!=0]
...     return a
... 
>>> numpy_gcd(np.array([98]), np.array([42]))
array([14])
>>> 98/14, 42/14
(7, 3)

edited May 23 '17 at 11:53

Community

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answered Jul 08 '13 at 23:31

John La Rooy

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Thanks! Works great! The input value has to be integers, cannot be float. – LWZ Jul 08 '13 at 23:35
@LWZ You should be able to use floats as other fractions – Nathan majicvr.com Jan 25 '20 at 09:16

score 9 · Answer 2 · answered Feb 27 '21 at 02:58

9

Addition to John's answer:

To get simplified fraction from a decimal number (say 2.0372856077554062)

Using Fraction gives the following output:

Fraction(2.0372856077554062)
#> Fraction(4587559351967261, 2251799813685248)

To get simplified answer :

Fraction(2.0372856077554062).limit_denominator()
#> Fraction(2732, 1341)

answered Feb 27 '21 at 02:58

rahul-ahuja

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Thanks, I now use this by default: even in simple cases, `Fraction` sometimes fails to provide simple answers (1.8 yields 8106479329266893/4503599627370496 instead of 9/5). – Anthony Labarre May 09 '21 at 21:58
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@AnthonyLabarre This might look like a "simple case", but 1.8 cannot be expressed exactly as a binary number; ie, an integer divided by a power of 2. Hence it cannot be represented exactly as a float. A workaround is to use a string instead of a float: compare `Fraction(1.8) --> Fraction(8106479329266893, 4503599627370496)` with `Fraction("1.8") --> Fraction(9, 5)`. Note that the denominator 4503599627370496 is 2**52. – Stef Jan 20 '22 at 18:47

Jadon Jung · Answer 3 · 2023-06-24T22:09:23.130

Using the math gcd from the math module

    import math
    def simplify_fraction(numerator, denominator):
        if math.gcd(numerator, denominator) == denominator:
            return int(numerator/denominator)
        elif math.gcd(numerator, denominator) == 1:
            return str(numerator) + "/" + str(denominator)
        else:
            top = numerator / math.gcd(numerator, denominator)
            bottom = denominator / math.gcd(numerator, denominator)
            return str(top) + "/" + str(bottom)
    print(fractions(46,23))
    print(fractions(34,25))
    print(fractions(24, 28))

mins · Answer 4 · 2023-03-16T10:52:30.733

Does Python have a function to reduce fractions?

No there is no built-in or external function, still you have two solutions.

1. Using fractions module

You can use Fraction objects from fractions module. From the documentation:

from fractions import Fraction
Fraction(16, -10)

>>> Fraction(-8, 5)

In this module a fraction is implicitly reduced, you can get the numerator and the denominator:

a = 16
b = -10
q = Fraction(a, b)
a = q.numerator
b = q.denominator
print (f'{q} == {a}/{b}')

>>> -8/5 == -8/5

2. Reduction using the GCD

Any fraction can be reduced using the GCD, greatest common factor, of numerator and denominator: a/b == (a/gcd)/(b/gcd).

GCD function is available both from numpy and math modules:

import numpy as np
a = 98
b = 42
gcd = np.gcd(a, b)
print(f'{a}/{b} == {int(a/gcd)}/{int(b/gcd)}')

`>>> 98/42 == 7/3

There is an alternative, but I do not consider it as valid for common needs: Use symbolic math with module sympy.

This allows to work with exact numbers at the cost of a loss of efficiency. sympy is it's own world and some learning time is required.

Does Python have a function to reduce fractions?

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