How to simplify a fraction in Python?

Question

still learning Python so any help is welcome. I have written a funtion to get a fraction, but more often than not the fraction can be simplified. My code does not do this yet. Any ideas how to simplify the fraction without using any import functions? code:

def add_frac(n1, d1, n2, d2):
    frac = (((n1 * d1) + (n2 * d2)), (d1 * d2))
    return frac

example: add_frac(1, 2, 1, 4) gives (6, 8) in stead of (3, 4)

Any help is welcome!

score 2 · Answer 1 · answered Nov 20 '20 at 14:51

A pretty naive approach to get you started, you can add some checks to make it more efficient.

def simplify_frac(n, d):
    i = 2
    while i < min(n, d) + 1:
        if n % i == 0 and d % i == 0:
            n = n // i
            d = d // i
        else:
            i += 1
    return n, d

# Some examples 
In [105]: simplify_frac(2, 4)
Out[105]: (1, 2)

In [106]: simplify_frac(16, 36)
Out[106]: (4, 9)

In [107]: simplify_frac(7, 3)
Out[107]: (7, 3)

In [108]: simplify_frac(10, 1)
Out[108]: (10, 1)

In [109]: simplify_frac(1, 10)
Out[109]: (1, 10)

In [110]: simplify_frac(102, 10)
Out[110]: (51, 5)

In [111]: simplify_frac(110, 10)
Out[111]: (11, 1)

We use a modulo operator % to check the remainder from integer division by i, if both n and d have a remainder of 0 we know i divides them.

score 1 · Answer 2 · edited Nov 20 '20 at 15:20

1

The naive form of adding two fractions returns a correct answer, just not the most reduced correct answer. For that, you need to divide the numerator and denominator of the result by the greatest common denominator (GCD) of the original denominators. In this case, the GCD of 2 and 4 is 2, so dividing 6 and 8 by 2 gives the desired answer (3,4)

math.gcd can be used:

from math import gcd


def add_frac(n1, d1, n2, d2):
    x = gcd(d1, d2)
    frac = (((n1 * d2) + (n2 * d1)) / x, (d1 * d2) / x)
    return frac

though it sounds like you are expected to define your own implementation of gcd.

edited Nov 20 '20 at 15:20

Edouard Thiel

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answered Nov 20 '20 at 14:42

chepner

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1

He knows `6/8` can be simplified to `3/4`. His question is about the algorithm how to achieve that. How do you get the GCD of the original denominators? It also seems like a homework which is why he is asking not to use imported functions. – Tin Nguyen Nov 20 '20 at 14:45
There are plenty of resources for implementing the GCD algorithm, and if that's the necessary part of the solution, then it's a separate question (and one that's too broad without an initial attempt to write it). – chepner Nov 20 '20 at 14:47
1

I would also suggest making a function that normalizes fractions, otherwise this code will be duplicated in every arithmetic operation on fractions. – Alexander Nov 20 '20 at 14:47

Edouard Thiel · Answer 3 · 2020-11-23T13:39:59.013

1

Here is a solution with a recursive implementation of gcd, using Euclid Algorithm; it also works on negative numbers :

def mygcd(a, b) :
    return gcd_rec(abs(a), abs(b))

def gcd_rec(a,b) :
    if a*b == 0 : return a+b
    if a <= b : return gcd_rec(a, b % a)
    return gcd_rec(a % b, b)

def add_frac(n1, d1, n2, d2):
    n = n1*d2 + n2*d1
    d = d1*d2
    g = mygcd(n, d)
    return n//g, d//g

edited Nov 23 '20 at 13:39

answered Nov 20 '20 at 14:52

Edouard Thiel

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I get `(13, 4)` for `add_frac(1,1,3,4)` (should be `(7,4)`). Maybe you need to catch a special case? – Tom Nov 20 '20 at 14:57
This works great, but it does not work when you could simplify it twice. for example (1, 2, 1, 6). It gives (4, 6), but should give (2, 3). Any way to get this? – David Nov 20 '20 at 15:47
in fact, I've computed gcd before summing; fixed – Edouard Thiel Nov 23 '20 at 13:42

score 1 · Answer 4 · answered Nov 20 '20 at 14:56

In addition to above answers, if you cannot import any other libraries, here's is the implementation of fractions.gcd for python 2.7 (copied from https://stackoverflow.com/a/11175154/10155740)

>>> print inspect.getsource(gcd)
def gcd(a, b):
    """Calculate the Greatest Common Divisor of a and b.

    Unless b==0, the result will have the same sign as b (so that when
    b is divided by it, the result comes out positive).
    """
    while b:
        a, b = b, a%b
    return a

so if you'd incorporate this in your code, you should get something like:

def gcd(a, b):
    while b:
        a, b = b, a%b
    return a

def add_frac(n1, d1, n2, d2):
    frac = (((n1 * d1) + (n2 * d2)), (d1 * d2))
    return tuple(i//gcd(*frac) for i in frac)

print(add_frac(1,2,1,4))
# OUTPUT: (3, 4)

score 0 · Answer 5 · answered Nov 20 '20 at 14:43

0

You need to divide it by GCD.

import math
def add_frac(n1, d1, n2, d2):
    nume = (n1 * d1) + (n2 * d2)
    deno = d1 * d2
    gcd = math.gcd(nume,deno)
    nume /= gcd
    deno /= gcd
    return (nume,deno)

>>> add_frac(1,2,1,4)
>>> (3.0, 4.0)

answered Nov 20 '20 at 14:43

Equinox

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How to simplify a fraction in Python?

5 Answers5