# How to convert percent to fraction

In this post we will learn method to convert percent to fraction.

Before getting into the method understand what percent number means.

Percent basically tells you the unit value out of the number 100.

Thus 4% means there are 4 unit present per 100 value.
so 4% can be expressed as \frac{4}{100}

## Converting Percent to fraction

Suppose you have to convert 4.5% into fraction
For conversion do the following steps:

(01) Remove % sign from the number and insert 100 in the denominator
Now the percentage is expressed in fraction form

(02) If number is simple whole number, move to step 03
If number is decimal, convert it into whole number by:
⟹ First removing the decimal point
⟹ Insert zero (as much as decimal place value) in the denominator

(03) Simplify the fraction as much as possible

Hence 9/200 is the required fraction

These are the exact steps for percentage to fraction conversion.
Let us see some examples for conceptual understanding.

Example 01
Convert 25% into fraction

Solution
(a) Remove % sign and insert 100 in denominator
25\%\Longrightarrow \frac{25}{100}

(b) Number is whole number, so move to step 03

(c) Reduce fraction to its lowest terms
Divide numerator and denominator by 25
\frac{25\ \div \ 25}{100\ \div \ 25} \ =\frac{1}{4}

Hence \frac{1}{4} is the solution.

You can see that we have converted 25% into fraction \frac{1}{4}

Example 02
Convert 42% into fraction

Solution
Do the following steps:

(a) Remove % sign and insert 100 in denominator
42\%\Longrightarrow \frac{42}{100}

(c) Reduce fraction to its lowest terms
Divide numerator and denominator by 2
\frac{42\ \div \ 2}{100\ \div \ 2} \ =\frac{21}{50}

Hence \frac{21}{50} is the solution

Example 03
Convert 55.5%

Solution
Do the following steps:
(a) Remove % sign and insert 100 as denominator
55.5\%\Longrightarrow \frac{55.5}{100}

(b) Convert the numerator, from decimal to whole number
Remove the decimal point and multiply 10 in denominator (as 55.5 contain one decimal place)

(c) Reduce the fraction to its lowest terms
Divide numerator and denominator by 5

\frac{555\ \div \ 5}{1000\ \div \ 5} \ =\frac{111}{200}\\\ \\

Hence, \frac{111}{200} is the required fraction

Example 04
Convert 103% into fraction

Solution
Do the following steps:
(a) Remove % symbol and insert 100 in denominator
103\%\Longrightarrow \frac{103}{100}

(c) Reduce fraction to lowest terms
Further simplification is not possible.

hence \frac{103}{100} is the required answer

Example 05
Convert 12.25% into fraction

Solution
(a) Remove % symbol and insert 100 in denominator
12.25\%\Longrightarrow \frac{12.25}{100}

(b) Convert the decimal into whole number
Remove the decimal point and multiply 100 in denominator (since 12.25 contain two decimal places)

(c) Reduce the fraction to its lowest terms
Divide numerator and denominator by 25
\frac{1225\ \div \ 25}{10000\ \div \ 25} \ =\frac{49}{400}

Hence \frac{49}{400} is the solution

Example 06
Find fraction for 215%

Solution
(a) Remove % symbol and insert 100 in denominator
215\%\Longrightarrow \frac{215}{100}

(c) Reduce the fraction to its lowest term
Divide numerator and denominator by 5
\frac{215\ \div \ 5}{100\ \div \ 5} \ =\frac{43}{20}

Hence, \frac{43}{20} is the solution

I hope the steps are clear to you.
Let us solve some practice questions on this topic.

## Important Percentage to Fraction Values

Given below are table of values which i think you should remember for higher classes.

Try to remember the values such as:
⟹ 50% is 1/2
⟹ 75% is 3/4

so that you can find answer quickly without any calculation.
This memorization will give you edge in math competition exams.

## Percentage into Fractions Problems

Given below are set of Percentage into Fraction Problems.
All the questions are to the standard of Grade 5 Math

(01) Convert 40% into fraction

(a) 1/5
(b) 2/5
(c) 3/5
(d) 2/7

40\%\Longrightarrow \frac{40}{100}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 20\\\ \\ \frac{40\ \div \ 20}{100\ \div \ 20} \ =\frac{2}{5} \\\ \\

Hence, \frac{2}{5} is the solution

Option (b) is the right answer

(02) Represent 160% in fraction

(a) 6/5
(b) 13/5
(c) 11/5
(d) 8/5

160\%\Longrightarrow \frac{160}{100}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 20\\\ \\ \frac{160\ \div \ 20}{100\ \div \ 20} \ =\frac{8}{5} \\\ \\

Hence, \frac{8}{5} is the solution

Option (d) is the right answer

(03) Represent 65% in fraction

(a) 13/20
(b) 13/10
(c) 17/20
(d) 17/10

65\%\Longrightarrow \frac{65}{100}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 5\\\ \\ \frac{65\ \div \ 5}{100\ \div \ 5} \ =\frac{13}{20} \\\ \\

Hence, \frac{13}{20} is the solution

Option (a) is the right answer

(04) Represent 1000% in fraction

(a) 100
(b) 1
(c) 10
(d) 50

1000\%\Longrightarrow \frac{1000}{100}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 100\\\ \\ \frac{1000\ \div \ 100}{100\ \div \ 100} \ =\frac{10}{1} \\\ \\

Hence, 10 is the solution
Option (c) is the right answer

(05) Convert 250% to fraction

(a) 20/3
(b) 10/3
(c) 5/2
(d) 5/3

250\%\Longrightarrow \frac{250}{100}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 50\\\ \\ \frac{250\ \div \ 50}{100\ \div \ 50} \ =\frac{5}{2} \\\ \\

Hence, 5/2 is the solution
Option (c) is the right answer

(06) Convert 83% into fraction

(a) 83/100
(b) 83/50
(c) 45/50
(d) 89/100

83\%\Longrightarrow \frac{83}{100}

The number is not divisible further.
Hence 83/100 is the solution

option (a) is the right answer

(07) Convert 16.5% into fraction

(a) 21/200
(b) 19/200
(c) 15/200
(d) 33/200

16.5\%\Longrightarrow \frac{16.5}{100}\\\ \\ Convert\ decimal\ into\ whole\ number\\ \\ Remove\ decimal\ point\ and\ multiply\ 10\ in\ denominator\\\ \\ \frac{16.5}{100} \Longrightarrow \frac{165}{100\times 10} \Longrightarrow \ \frac{165}{1000}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 5\\\ \\ \frac{165\ \div \ 5}{1000\ \div \ 5} \ =\frac{33}{200}\\\ \\

Option (d) is the right answer

(08) Convert 10.25% into fraction

(a) 41/200
(b) 41/400
(c) 21/200
(d) 21/400

10.25\%\Longrightarrow \frac{10.25}{100}\\\ \\ Convert\ decimal\ into\ whole\ number\\\ \\ Remove\ decimal\ point\ and\ multiply\ 100\ in\ denominator\\\ \\ \frac{10.25}{100} \Longrightarrow \frac{1025}{100\times 100} \Longrightarrow \ \frac{1025}{10000}\\\ \\ Divide\ numerator\ and\ denominator\ by\ 25\\\ \\ \frac{1025\ \div \ 25}{10000\ \div \ 25} \ =\frac{41}{400}

Option (b) is the right answer

(09) Convert 113% into fraction

(a) 113/1000
(b) 109/100
(c) 113/100
(d) 113/10

113\%\Longrightarrow \frac{113}{100}

The number is not divisible further.
Hence 113/100 is the solution

option (c) is the right answer

(10) Convert 1.33% into fraction

(a) 133/1000
(b) 133/10000
(c) 133/10
(d) 133/1