Converting a Percentage to a Fraction in Simplest Form

Any per cent can be written as a fraction with a denominator of 100 as follows

x% = $\frac{x}{100}$; 50% = $\frac{50}{100}$

Similarly, 8% = $\frac{8}{100}$; 10% = $\frac{10}{100}$; 24% = $\frac{24}{100}$ and so on The fraction can be reduced to simplest form as follows

50% = $\frac{50}{100}$

We divide the numerator and the denominator with their highest common factor (HCF). Here the HCF of 50 and 100 is 50

50% = $\frac{50}{50} \div \frac{100}{50} = \frac{1}{2}$

So, 50% = $\frac{1}{2}$

Rules to convert a percentage into a fraction in simplest form

• The percentage is written as a fraction with 100 as denominator

  For example, 30% = $\frac{30}{100}$

• This fraction is then simplified and reduced to lowest terms

  For example, 30% = $\frac{30}{100} = \frac{3}{10}$

Write the percent as a fraction in the simplest form

24%

Solution

Step 1:

The percent written in fraction form

24% = $\frac{24}{100}$

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 24 and 100 is 4

24% = $\frac{24}{4} \div \frac{100}{4} = \frac{6}{25}$

Step 3:

So, 24% = $\frac{6}{25}$ in simplest form

Write the percent as a fraction in the simplest form

55%

Solution

Step 1:

The percent written in fraction form

55% = $\frac{55}{100}$

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 55 and 100 is 5

55% = $\frac{55}{5} \div \frac{100}{5} = \frac{11}{20}$

Step 3:

So, 55% = $\frac{11}{20}$ in simplest form

Write the percent as a fraction in the simplest form

6%

Solution

Step 1:

The percent written in fraction form

6% = $\frac{6}{100}$

Step 2:

The fraction can be reduced to simplest form as follows

We divide the numerator and the denominator with their highest common factor. Here the HCF of 6 and 100 is 2

6% = $\frac{6}{2} \div \frac{100}{2} = \frac{3}{50}$

Step 3:

So, 6% = $\frac{3}{50}$ in simplest form