Converting a Fraction to a Percentage Denominator of 4, 5, or 10

Consider any fraction with a denominator of 4, 5 or 10. Such fractions can be converted to fractions with a denominator of 100. Then it would be easy to write those fractions as percentages as shown below in examples

Rules to convert a fraction into a percentage with 4, 5 or 10 as denominator

• If the fraction has a denominator 4, we multiply and divide the fraction with 25. For example: $\frac{3}{4} = \frac{(3 \times 25)}{(4 \times 25)} = \frac{75}{100}$

• If the fraction has a denominator 5, we multiply and divide the fraction with 20. For example: $\frac{2}{5} = \frac{(2 \times 20)}{(5 \times 20)} = \frac{40}{100}$

• If the fraction has a denominator 10, we multiply and divide the fraction with 10. For example: $\frac{7}{10} = \frac{(7 \times 10)}{(10 \times 10)} = \frac{70}{100}$

• The fractions with 100 as denominator are converted to percentages. For example: $\frac{75}{100}$ = 75%; $\frac{40}{100}$ = 40%; $\frac{70}{100}$ = 70%

Write the following fraction as a percentage

$\mathbf {\frac{1}{4}}$

Solution

Step 1:

The given fraction $\frac{1}{4}$ has a denominator 4.

We multiply and divide the fraction by 25

$\frac{1}{4} = \frac{(1 \times 25)}{(4 \times 25)} = \frac{25}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{25}{100}$ = 25%

Step 3:

So, $\frac{1}{4}$ = 25%

Write the following fraction as a percentage

$\mathbf{\frac{4}{5}}$

Solution

Step 1:

The given fraction $\frac{4}{5}$ has a denominator 5.

We multiply and divide the fraction by 20

$\frac{4}{5} = \frac{(4 \times 20)}{(5 \times 20)} = \frac{80}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{80}{100}$ = 80%

Step 3:

So, $\frac{4}{5}$ = 80%

Write the following fraction as a percentage

$\mathbf{\frac{9}{10}}$

Solution

Step 1:

The given fraction $\frac{9}{10}$ has a denominator 10.

We multiply and divide the fraction by 10

$\frac{9}{10} = \frac{(9 \times 10)} {(10 \times 10)} = \frac{90}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{90}{100}$ = 90%

Step 3:

So, $\frac{9}{10}$ = 90%