Question

Simplify the fraction: $ \dfrac{{14}}{{24}} $

Answer 1

Hint: The question asks us to simplify a fraction (proper fraction) which means we are supposed to reduce it to a point from which it cannot be reduced further, which is also the simplest form of the fraction. We check for the highest common factor of the numerator and denominator to reduce the fraction.

Complete step by step answer:
Firstly we write down the fraction and name it for our convenience as
 $ A = \dfrac{{14}}{{24}} $
Now we have to simplify it in a way that it is no longer reducible i.e. numerator and denominator cannot be divided by the same whole number exactly (other than 1). For that, we determine the largest/greatest common divisor known as Highest common factor (HCF) and divide both numerator and denominators by it.
Highest common factor (HCF) of (14, 24) – We write the factors of the two numbers and check for the highest common number in value which divides both the numbers completely.
Factors of 14 = 1, 2,7,14
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factor of the two will be – 2
So we divide 14 and 24 by 2 and write it as
 $
  A = \dfrac{{14}}{{24}} = \dfrac{7}{{12}} \\
  A = \dfrac{7}{{12}} \\
  $
$ A $ is the simplified fraction of the given fraction and hence, it cannot be reduced further.

Note:
Reducing the values does not change the actual value of the fraction but it is written in the simplest form after simplification. Also, the given fraction is a proper fraction because the numerator is smaller in value than the denominator i.e. $ 7 < 12 $.