Hướng dẫn python simplify fraction

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!

Tom

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asked Nov 20, 2020 at 14:38

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.

answered Nov 20, 2020 at 14:51

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 //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]

answered Nov 20, 2020 at 14:56

QuadUQuadU

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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 >> add_frac[1,2,1,4]
>>> [3.0, 4.0]

answered Nov 20, 2020 at 14:43

EquinoxEquinox

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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.

answered Nov 20, 2020 at 14:42

chepnerchepner

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3

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