Question

How do you simplify the fraction $\dfrac{{10}}{{12}}?$

Answer 1

Hint: Simplest form of a fraction is expressed when the numerator and denominator do not have a common factor which can divide both numerator and the denominator. As well the common factor should only be a whole number, because dividing with decimal number or fraction will make it more complex instead of converting in simplest form.

Complete step by step solution:
Simplifying a fraction means to find the simplest form of the fraction. Simplest form of a fraction is the fraction in which it consists of a numerator and denominator having no common factor except unity.
To simplify a fraction we have to find the Highest Common Factor (HCF) of numerator and the denominator, and divide them with that number (HCF) to get the simplest form.
So let us find the highest common factor a between the numerator $(10)$ and the denominator $(12)$
$
10 = 2 \times 5 \\
12 = 2 \times 2 \times 3 \\
$
We can see that the highest common factor of $(12)\;{\text{and}}\;(36)$ comes out to be $2$
Now dividing both the numerator and the denominator by $2$,
\[\dfrac{{10 \div 2}}{{12 \div 2}} = \dfrac{5}{6}\]
\[\therefore \dfrac{5}{6}\] is the simplest form of the fraction $\dfrac{{10}}{{12}}$

Note: Also if a fraction, contains prime numbers in its numerator and denominator then it is already in its simplest form because prime numbers are unique numbers which cannot be divided by a number except $1$
You can convert a fraction into its simplest form by one more method that is by continue division of the numerator and the denominator with prime numbers $(2,\;3,\;5,\;7,\;13.....)$ until they does not have any common factor left except $1,$ try it by yourself and check the answer.