Question

How do you write $\dfrac{6}{8}$ in simplest form?

Answer 1

Hint:
Find the factors of both the numerator and denominator in the question. Then, select the factors which are common in both numerator and denominator. Divide the factor with numerator and denominator both and we will get our required simplest form.

Complete step by step solution:
When the whole thing is divided into equal parts then each part is known as fraction. We can also say that fraction is the part of whole. The fraction is formed by numerator and denominator. They both are separated by a horizontal bar in which the numerator appears at the top and denominator at the bottom of line.
When the numerator and are not further divisible by a number then that fraction is said to be simplified fractions. To make the fraction a simplified fraction we divide both numerator and denominator by the same number.
The common factor is the number that divides numerator and denominator both and leaves the remainder zero. We divide the fractions till we get 1 as the common factor for both the numerator and denominator.
Now, according to the question, we have to find the simplest form of fraction $\dfrac{6}{8}$.
Therefore, the numerator is 6 and the denominator is 8.
Now, finding the factors of 6 and 8 –
Hence, the factors of 6 are 1, 2 and 3 and factors of 8 are 1, 2 and 4.
So, from the above we get the common factor for 6 and 8 i.e., 2.
Hence, now dividing 2 from numerator and denominator both in the fraction in the question –
$
   \Rightarrow \dfrac{{6 \div 2}}{{8 \div 2}} \\
   \Rightarrow \dfrac{3}{4} \\
 $
Hence, the simplest form of the fraction $\dfrac{6}{8}$ is $\dfrac{3}{4}$.

Note:
The fraction $\dfrac{3}{4}$ is in its simplest form; we cannot further convert it into the simplest form as 2 and 3 have no common factors. When we simplify the fraction it becomes easier to deal with –
1) Addition and subtraction of fractions
2) Comparing one fraction with another
3) Conversion of fraction into decimals and percentages