# Simplify a Fraction

Calculator to simplify ONE fraction with steps. For an expression with more than a fraction, use this Fraction Calculator.

The fraction is already in its simpliest form

= 41/15

\approx2.73333333333333

Steps

• Input : 41/15

• Factor the numerator : 41 (41 is a prime number, that is, it can be divisible only by itself and 1)

• Factor the denominator : 15 = 3 * 5

• Rewrite the fraction : (41)/(3 * 5)

• Simplify by cancelling common factors out of the numerator and denimninator :
numerator and denominator have no common factors.
Result : 41/15

## How to simplify a fraction?

There are two methods to simplify (or reduce) a fraction.

The method of successive simplifications
This method consists in making successive simplifications by dividing by "small" numbers (2, 3, 5, etc.) until obtaining the irreducible form of the fraction.
Example: how to reduce the fraction 210/378 by the method of successive simplifications?
We start by dividing 210 and 378 by 2.
We get 105 and 189.
So we have 210/378 = 105/189
We repeat the operation with 105 and 189.
The latter are divisible by 3 because 105/3 = 35 and 189/3 = 63.
So we have,
210/378 = 35/63
35 and 63 are divisible by 7, 35/7 = 5 and 63/7 = 9
210/378 = 5/9
We get to the end of the process because 5 and 9 have no common divisor other than 1!
The reduced form of fraction 210/378 is 5/9.

GCD Method
This method is based on GCD (Greatest Common Divisor) i.e. find the GCD of the numerator and denominator and divide them by this GCD.
Example: how to reduce the fraction 210/378 using the GCD method ?
GCD (210,378) = 42. More details on this page How to calculate the GCD of 210 and 378 ?.
To get the reduced fraction, simply divide the numerator and denominator by the GCD ie 42 !
The numerator of the reduced fraction is equal to 210/42 i.e. 5.
The denominator of the reduced fraction is equal to 378/42 i.e. 9.
The same result is obtained as by the first method: 5/9.

## Python

Here is a python function that simplifies a fraction. The input variables "num" and "denom" represent the numerator and denominator of the fraction. For the gcd function, we can either import the python gcd function of the math module or rewrite it as here: Calculate gcd with python.


from math import gcd
def ReduceFraction (num, denom):
d = gcd (num, denom);
num = num//d;
denom = denom//d;

return (num, denom)