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

50% = $frac{50}{50} span frac{100}{50} = frac{1}{2}$

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

24% = $frac{24}{4} span frac{100}{4} = frac{6}{25}$

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

55% = $frac{55}{5} span frac{100}{5} = frac{11}{20}$

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

6% = $frac{6}{2} span frac{100}{2} = frac{3}{50}$

Step 3:

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