Converting Percentages (%) to Fractions

A percentage is a number or ratio expressed as a fraction of 100. It is denoted using the percent sign “%“.

To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100.

Example 10.1.1: 

Express each of the following as a fraction in its simplest form.

i. 40%
ii. 65%
iii. 12¾ %

Solution

(i) 40% = \( \frac{40}{100} \\ = \frac{4}{10} \\ = \frac{2}{5} \)

(ii) 65% = \( \frac{65}{100} \\ = \frac{13}{20} \)

(iii) 12¾ %   

Change the fraction to improper fraction 

\(\scriptsize 12 \frac{3}{4} \% \\ = \frac{51}{4}\scriptsize \%\)

\( \frac{\large \frac{51}{4}}{100} \\ = \frac{51 \: \times \: 1}{4 \: \times \: 100} = \frac{51}{400}\)