Converting a Fraction to a Percentage Denominator of 20, 25, or 50

Consider any fraction with a denominator of 20, 25 or 50. 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 20, 25 or 50 as denominator

• If the fraction has a denominator 20, we multiply and divide the fraction with 5. For example: $\frac{3}{20} = \frac{(3 \times 5)}{(20 \times 5)} = \frac{15}{100}$

• If the fraction has a denominator 25, we multiply and divide the fraction with 4. For example: $\frac{2}{25} = \frac{(2 \times 4)}{(25 \times 4)} = \frac{8}{100}$

• If the fraction has a denominator 50, we multiply and divide the fraction with 2. For example: $\frac{7}{50} = \frac{(7 \times 2)}{(50 \times 2)} = \frac{14}{100}$

• 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

$\mathbf{\frac{11}{20}}$

Solution

Step 1:

The given fraction $\frac{11}{20}$ has a denominator 20.

We multiply and divide the fraction by 5

$\frac{11}{20} = \frac{(11 \times 5)}{(20 \times 5)} = \frac{55}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{55}{100}$ = 55%

Step 3:

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

Write the following fraction as a percentage

$\mathbf{\frac{9}{25}}$

Solution

Step 1:

The given fraction $\frac{9}{25}$ has a denominator 25.

We multiply and divide the fraction by 4

$\frac{9}{25} = (9 \times 4) \div (25 \times 4) = \frac{36}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{36}{100}$ = 36%

Step 3:

So, $\frac{9}{25}$ = 36%

Write the following fraction as a percentage

$\mathbf{\frac{13}{50}}$

Solution

Step 1:

The given fraction $\frac{13}{50}$ has a denominator 50.

We multiply and divide the fraction by 2

$\frac{13}{50} = (13 \times 2) \div (50 \times 2) = \frac{26}{100}$

Step 2:

Writing this fraction as a percentage

By definition, $\frac{26}{100}$ = 26%

Step 3:

So, $\frac{13}{50}$ = 26%