# Convert ratio into percentage

In this post we will learn methods to convert ratio into percentage with solved examples.

At the end of the chapter, some problems are also given for your practice.

## Converting ratio into percent

To convert the given ratio into percentage, follow the below steps;

(a) Write the given ratio into fraction form

(b) If possible, simplify the fraction

(c) Multiply the fraction by 100 to convert into percentage

In the above three steps, you can convert any ratio in percent form.

I hope you understood the above process. Let us see some solved examples for further clarity.

### Ratio into percent – Solved examples

Example 01
Convert 2 : 5 into percentage.

Solution

(a) Write the ratio in fraction form.

\mathtt{\Longrightarrow \ 2:\ 5}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{5}}

(b) Multiply the fraction by 100 to convert into percentage.

\mathtt{\Longrightarrow \ \frac{2}{5} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{2}{\cancel{5}} \times \cancel{100} \ 20}\\\ \\ \mathtt{\Longrightarrow \ 40\%}

Hence, the ratio is converted into 40%.

Example 02
Convert 3 : 18 into percentage.

Solution

(a) Convert ratio into fraction.

\mathtt{\Longrightarrow \ 3:\ 18}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{18}}

(b) If possible, simplify the fraction.

\mathtt{\Longrightarrow \ \frac{3}{18}}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{3}}{\cancel{18} \ \mathbf{6}}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{6}}

(c) Multiply the fraction with 100

\mathtt{\Longrightarrow \ \frac{1}{6} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{\cancel{6} \ \mathbf{3}} \times \cancel{100} \ 50}\\\ \\ \mathtt{\Longrightarrow \ \frac{50}{3} \%}

Hence, 50/3 % is the required solution.

Example 03
Convert 9 : 25 into percentage.

Solution

(a) Convert the ratio into fraction.

\mathtt{\Longrightarrow \ 9:\ 25}\\\ \\ \mathtt{\Longrightarrow \ \frac{9}{25}}

(b) Multiply the fraction by 100

\mathtt{\Longrightarrow \ \frac{9}{25} \times 100}\\\ \\ \mathtt{\Longrightarrow \frac{9}{\cancel{25}} \times \cancel{100} \ 4}\\\ \\ \mathtt{\Longrightarrow \ 36\%}

Hence, 36% is the required solution.

Example 04
Convert 5 : 35 into percentage.

Solution

(a) Convert the ratio into fraction

\mathtt{\Longrightarrow \ 5:\ 35}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{35}}

(b) If possible, simplify the fraction

\mathtt{\Longrightarrow \ \frac{5}{35}}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{5}}{\cancel{35} \ 7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{7}}

(c) Multiply the fraction by 100.

\mathtt{\Longrightarrow \ \frac{1}{7} \times 100}\\\ \\ \mathtt{\Longrightarrow \frac{100}{7} \ \%}\\\ \\ \mathtt{\Longrightarrow \ 14.28\ \%}

Hence, the given ratio is converted into 14.28%.

Example 05
Convert 22 : 105 into percentage.

Solution

(a) Convert the ratio into fraction.

\mathtt{\Longrightarrow 22:\ 105}\\\ \\ \mathtt{\Longrightarrow \ \frac{22}{105}}

(b) Multiply the fraction by 100.

\mathtt{\Longrightarrow \ \frac{22}{105} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{22}{\cancel{105\ }\mathbf{21}} \times \cancel{100} \ 20}\\\ \\ \mathtt{\Longrightarrow \ \frac{440}{21} \%}

Hence, 440 / 21% is the solution.

I hope you understood all the above examples. Given below are some math problems for your practice.

## Ratio into percentage – Practice problems

(01) Convert the below ratios into percentage.

(a) 81 : 10

(b) 9 : 54

(c) 4 : 7

(d) 11 : 13

(e) 21 : 5

(f) 16 : 3

(g) 81 : 100

(h) 200 : 15

(i) 1: 25

(j) 50 : 75

Solution

(a) 81 : 10

\mathtt{\Longrightarrow \ \frac{81}{10} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{81}{\cancel{10}} \times 10\cancel{0}}\\\ \\ \mathtt{\Longrightarrow \ 810\%}

Hence, 810% is the solution.

(b) 9 : 54

\mathtt{\Longrightarrow \ \frac{9}{54} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{9}}{\cancel{54} \ \mathbf{6}} \times 100}\\\ \\ \mathtt{\Longrightarrow \ 16.67\%}

Hence, 16.67% is the solution.

(c) 4 : 7

\mathtt{\Longrightarrow \ \frac{4}{7} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{400}{7} \%}\\\ \\ \mathtt{\Longrightarrow \ 57.14\%}

Hence, 57.14% is the solution.

(d) 11 : 13

\mathtt{\Longrightarrow \ \frac{11}{13} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{1100}{13} \%}

Hence, 1100 / 13 % is the solution

(e) 21 : 5

\mathtt{\Longrightarrow \ \frac{21}{5} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{21}{\cancel{5}} \times \cancel{100} \ 20}\\\ \\ \mathtt{\Longrightarrow \ 420\%}

Hence, the given ratio is converted into 420%

(f) 16 : 3

\mathtt{\Longrightarrow \ \frac{16}{3} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{1600}{3} \%}\\\ \\ \mathtt{\Longrightarrow \ 533.33\%}

Hence, 533.33% is the solution.

(g) 81 : 100

\mathtt{\Longrightarrow \ \frac{81}{100} \times 100}\\\ \\ \mathtt{\Longrightarrow \frac{81}{\cancel{100}} \times \cancel{100}}\\\ \\ \mathtt{\Longrightarrow \ 81\%}

Hence, 81% is the solution.

(h) 200 : 15

\mathtt{\Longrightarrow \ \frac{200}{15} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{200}{\cancel{15} \ \mathbf{3}} \times \cancel{100\ } 20}\\\ \\ \mathtt{\Longrightarrow \ \frac{4000}{3} \%}

Hence, 4000/3 % is the solution.

(i) 1: 25

\mathtt{\Longrightarrow \ \frac{1}{25} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{100}{25} \%}\\\ \\ \mathtt{\Longrightarrow \ 4\%}

Hence, 4% is the required solution.

(j) 50 : 75

\mathtt{\Longrightarrow \ \frac{50}{75} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{\cancel{50}}{\cancel{75} \ 3} \times 100}\\\ \\ \mathtt{\Longrightarrow \ \frac{100}{3} \%}\\\ \\ \mathtt{\Longrightarrow \ 33.33\%}

Hence, 33.33% is the solution.