# Convert percent into ratio

In this chapter we will learn method to convert percentage number into ratio using solved examples.

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

## Steps to convert percent into ratio

To convert the percentage into ratio follow the below steps;

(a) Convert percentage into fraction by dividing percent by 100

(b) Try to simplify the fraction into smallest terms

(c) Change the division sign of fraction into ratio sign ” : “

In the simple three steps, you can convert any given percentage into ratio.

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

## Examples of percent to ratio conversion

Example 01
Convert 16% in ratio form.

Solution

(a) Convert percentage into fraction by dividing it by 100.

\mathtt{\Longrightarrow \ 16\%}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{100}}

(b) Simplify the fraction to lowest terms.

Divide numerator and denominator by 4.

\mathtt{\Longrightarrow \ \frac{16\div 4}{100\div 4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{25}}\

(c) Convert the division into ratio

\mathtt{\Longrightarrow \ \frac{4}{25}}\\\ \\ \mathtt{\Longrightarrow \ 4\ :\ 25}

Hence, 16% is converted into ratio 4 : 25.

Example 02
Convert 93% in the ratio form.

Solution

(a) Convert the percentage into fraction form by dividing it by 100.

\mathtt{\Longrightarrow \ 93\%}\\\ \\ \mathtt{\Longrightarrow \ \frac{93}{100}}

(b) If possible, simplify the fraction.

There is no common factor between numerator and denominator, hence further simplification is not possible.

(c) Convert the fraction into ratio.

\mathtt{\Longrightarrow \ \frac{93}{100}}\\\ \\ \mathtt{\Longrightarrow \ 93\ :\ 100}

Hence 93% is converted into ratio 93 : 100.

Example 03
Convert 22% into ratio form.

Solution

(a) Convert percentage into fraction by dividing it by 100.

\mathtt{\Longrightarrow \ 22\%}\\\ \\ \mathtt{\Longrightarrow \ \frac{22}{100}}

(b) If possible, simplify the fraction to lowest terms.

Dividing numerator and denominator by 2.

\mathtt{\Longrightarrow \frac{22}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{22\div 2}{100\div 2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{11}{50}}

(c) Now convert the fraction into ratio

\mathtt{\Longrightarrow \ \frac{11}{50}}\\\ \\ \mathtt{\Longrightarrow \ 11\ :\ 50}

Hence, 11 : 50 is the ratio form of given percentage.

Example 04
Convert the percentage \mathtt{\ 2\frac{1}{2} \%} into ratio form.

Solution
First convert the mixed number into simple percentage.

\mathtt{\Longrightarrow \ 2\frac{1}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{( 2\times 2) +1}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{2} \%}

(a) Convert the percentage into simple number by dividing it by 100.

\mathtt{\Longrightarrow \ \frac{5}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{2} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{200}}

(b) If possible, simplify the fraction.

Divide numerator and denominator by 5

\mathtt{\Longrightarrow \ \frac{5}{200}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5\div 5}{200\div 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{40}}

(c) Now convert the fraction into ratio.

\mathtt{\Longrightarrow \ \frac{1}{40}}\\\ \\ \mathtt{\Longrightarrow \ 1:40}

Hence, the ratio form of given percentage is 1 : 40.

Example 05
Convert 0.4 % into ratio.

Solution
First convert the decimal into simple percentage.

\mathtt{\Longrightarrow 0.4\ \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{10} \%}

(a) Convert the percentage into number by dividing it by 100.

\mathtt{\Longrightarrow \ \frac{4}{10} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{10} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{1000}}

(b) If possible, simplify the number

Divide numerator and denominator by 4.

\mathtt{\Longrightarrow \ \frac{4}{1000}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4\div 4}{1000\div 4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{250}}

(c) Convert the fraction into ratio.

\mathtt{\Longrightarrow \ \frac{1}{250}}\\\ \\ \mathtt{\Longrightarrow \ 1:\ 250}

Hence, 1: 250 is the required ratio.

## Percent to Ratio – Solved Problems

(01) Convert the following percentage into ratio.

(a) 25%

(b) 1%

(c) 1.5%

(d)1.25 %

(e) \mathtt{3\frac{1}{5} \%}

(f) 101%

(g) \mathtt{10\frac{3}{2} \%}

(h) 0.3%

Solution

(a) 25%

\mathtt{\Longrightarrow \ \frac{25}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{25\div 25}{100\div 25}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{4}}\\\ \\ \mathtt{\Longrightarrow \ 1:4}

Hence, 1 : 4 is the required ratio.

(b) 1%

\mathtt{\Longrightarrow \ \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ 1:100}

Hence, 1 : 100 is the required ratio.

(c) 1.5%

\mathtt{\Longrightarrow \ \frac{15}{10} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{15}{10} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{15}{1000}}

Divide numerator and denominator by 5.

\mathtt{\Longrightarrow \ \frac{15\div 5}{1000\div 5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{200}}\\\ \\ \mathtt{\Longrightarrow \ 3\ :\ 200}

Hence, 3 : 200 is the required ratio.

(d) 1.25 %

\mathtt{\Longrightarrow \ \frac{125}{100} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{125}{100} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{125}{10000}}

Divide numerator and denominator by 125.

\mathtt{\Longrightarrow \ \frac{125\div 125}{10000\div 125}}\\\ \\ \mathtt{\Longrightarrow \ \frac{1}{80}}\\\ \\ \mathtt{\Longrightarrow \ 1:\ 80}

Hence, 1 : 80 is the required ratio.

(e) \mathtt{3\frac{1}{5} \%} \\\ \\

\mathtt{\Longrightarrow \ \frac{( 5\times 3) +1}{5} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{5} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{5} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{16}{500}}

Divide numerator and denominator by 4.

\mathtt{\Longrightarrow \ \frac{16\div 4}{500\div 4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{125}}\\\ \\ \mathtt{\Longrightarrow \ 4\ :\ 125}

Hence, 4 : 125 is the required ratio.

(f) 101%

\mathtt{\Longrightarrow \ \frac{101}{100}}\\\ \\ \mathtt{\Longrightarrow \ 101:100}

Hence, 101 : 100 is the required ratio.

(g) \mathtt{10\frac{3}{2} \%}

Solution
\mathtt{\Longrightarrow \ 10\frac{3}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{( 10\times 2) +3}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{20+3}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{23}{2} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{23}{2} \times \frac{1}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{23}{200}}\\\ \\ \mathtt{\Longrightarrow \ 23:200}

Hence, 23 : 200 is the required ratio.

(h) 0.3 %

Solution
First convert the decimal into simple number.

\mathtt{\Longrightarrow \ 0.3\%}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{10} \%}

Now convert the percentage into ratio.

\mathtt{\Longrightarrow \ \frac{3}{10} \%}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{10} \times \frac{1}{1000}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3}{1000}}\\\ \\ \mathtt{\Longrightarrow \ 3:1000}

Hence, 3 : 1000 is the required ratio.