Converting Percentages to Fractions

To change a percentage to a fraction, divide it by 100 and then reduce the fraction to its lowest term.

Worked Example 9.2.1:

Express the following as fractions in their simplest form.

a. 25%
b. 56%
c. 45 ¼ %
d. 25.25%

Solution

a. 25% = \( \frac{25}{100}\\ = \frac{5}{20}\\ = \frac{1}{4} \)

b. 56% = \( \frac{56}{100}\\ = \frac{28}{50} \\ = \frac{14}{25} \)

c. 45 ¼ % = \( \frac{45 \frac{1}{4}}{\normalsize \frac{100}{1}} \\ = \large \frac{ \frac{181}{4}}{\frac{100}{1}} \\= \frac{181}{4} \: \times \: \frac{1}{100} \\ = \frac{181}{4 \: \times \: 100} \\ = \frac{181}{400} \)

d. 25.25% = \( \large \frac{\frac{2525}{100}}{\frac{100}{1}} \\ = \frac{2525}{100} \: \times \: \frac{1}{100} \\ = \frac{2525}{100 \: \times \: 100} \\ = \frac{2525}{10000} \\ = \frac{505}{2000} \\ = \frac{101}{400} \)