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Place value Arithmetic Simplifying fractions Improper fractions and mixed numbersThis topic is relevant for:

Here we will learn about **converting percentages to fractions**.

There are also percentages to fractions worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.

Converting **percentages to fractions** is representing the percentages as a fraction without changing its value to achieve equivalence.

E.g.

\[25\% =\frac{1}{4} \\
45\% =\frac{9}{20} \\
33.\dot{3}\% =\frac{1}{3} \\
80\% =\frac{4}{5}\]

In order to convert a percentage to a fraction:

**Divide the percentage by a hundred (because percent means out of \pmb{100}).****Write in fraction form i.e with a numerator and \pmb{100} as the denominator.****If required, convert the numerator to an integer by multiplying by a power of \pmb{10}**

E.g. \pmb{10}, \pmb{100}, \pmb{1000}. You need to do the same to the denominator to create an equivalent fraction.**Simplify the fraction (where possible).****Clearly state the answer showing the βpercentageβ = βfractionβ.**

Get your free percentages to fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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**Divide the percentage by a hundred.**

\[7\div100\]

**2Write in fraction form.**

\[7\div100=\frac{7}{100}\]

**3If required, convert the numerator to an integer by multiplying by a multiple of \pmb{10} . You need to do the same to the denominator to create an equivalent fraction.**

The numerator is already an integer so you do not need to multiply the numerator and denominator by a multiple of 10.

**4Simplify the fraction.**

This fraction cannot be simplified because the only factor 7 and 100 share is 1.

**5Clearly state the answer showing βpercentageβ = βfractionβ.**

\[7\%=\frac{7}{100}\]

We can read this as β7 hundredthsβ or β7 out of 100β.

This is a decimal fraction as the denominator is a power of 10.

Convert 40% to a fraction, give your answer in its simplest form.

**Divide the percentage by a hundred.**

\[40\div100\]

**Write in fraction form.**

\[40\div100=\frac{40}{100}\]

**If required, convert the numerator to an integer by multiplying by a multiple of 10. You need to do the same to the denominator to create an equivalent fraction.**

The numerator is already an integer so you do not need to multiply the numerator and denominator by a multiple of 10.

**Simplify the fraction.**

\[\frac{40}{100}\]

can be simplified by dividing the numerator and denominator by 20 (the highest common factor of 20 and 100):

\[\frac{40\div20}{100\div20}=\frac{2}{5}\]

**Clearly state the answer showing βpercentageβ = βfractionβ.**

\[40\%=\frac{2}{5}\]

Convert 60.2% to a fraction.

**Divide the percentage by a hundred.**

\[60.2\div100\]

**Write in fraction form.**

\[60.2\div100=\frac{60.2}{100}\]

The lowest value in the number 60.2 is the 2 βtenthsβ in the first decimal place. This means if we multiply 60.2 by 10 we will get the integer value 602.

We need to multiply the numerator and the denominator by the same value.

\[\frac{60.2}{100}=\frac{60.2\times10}{100\times10}=\frac{602}{1000}\]

**Simplify the fraction.**

\[\frac{62}{1000}\]

can be simplified by dividing the numerator and denominator by 2 (the highest common factor of 602 and 1000):

\[\frac{602\div2}{1000\div2}=\frac{301}{500}\]

**Clearly state the answer showing βpercentageβ = βfractionβ.**

\[60.2\%=\frac{301}{500}\]

Convert 120% to a fraction. Give you answer as a improper fraction.

**Divide the percentage by a hundred.**

\[120\div100\]

**Write in fraction form.**

\[120\div100=\frac{120}{100}\]

**Simplify the fraction.**

\[\frac{120}{100}\]

can be simplified by dividing the numerator and denominator by

\[\frac{120\div20}{100\div20}=\frac{6}{5}\]

**Clearly state the answer showing βpercentageβ = βfractionβ.**

\[120\%=\frac{6}{5}\]

This is an improper fraction as the numerator is greater than the denominator.

Convert 150% to a fraction. Give you answer as mixed number.

**Divide the percentage by a hundred.**

\[150\div100\]

**Write in fraction form.**

\[150\div100=\frac{150}{100}\]

**Simplify the fraction.**

\[\frac{150}{100}\]

can be simplified by dividing the numerator and denominator by 50 (the highest common factor of 150 and 100):

\[\frac{150\div50}{100\div50}=\frac{3}{2}\]

**Clearly state the answer showing βpercentageβ = βfractionβ**.

\[150\%=\frac{3}{2}\]

\[\frac{3}{2}\]

This is an improper fraction, we need to give the answer as a mixed number.

\[\frac{3}{2}=1\frac{1}{2}\]

Therefore,

\[150\%=1\frac{1}{2}\]

**Step by step guide**: Improper Fractions and Mixed Numbers

Convert 0.008% to a fraction, give your answer in its simplest form.

**Divide the percentage by a hundred.**

\[0.008\div100\]

**Write in fraction form**.

\[0.008\div100=\frac{0.008}{100}\]

The lowest value in the number 0.008 is the third digit after the decimal point, 8 βthousandthsβ. This means if we multiply 0.008 by 1000 we will get the integer value 8.

We need to multiply the numerator and the denominator by the same value.

\[\frac{0.008\times1000}{100\times1000}=\frac{8}{100000}\]

**Simplify the fraction.**

\[\frac{8}{100000}\]

can be simplified by dividing the numerator and denominator by 8 (the highest common factor of 8 and 100000):

\[\frac{8\div8}{100000\div8}=\frac{1}{12500}\]

**Clearly state the answer showing βpercentageβ = βfractionβ.**

\[0.008\%=\frac{1}{12500}\]

**Multiplying by an incorrect multiple of \pmb{10}**

You must multiply by a power 10 (e.g 10, 100 or 1000) that results in the numerator being an integer (a whole number). Use your knowledge of place value to help decide which multiple of 10 to multiple by.

E.g.

0.003 Γ 10 = 0.03. This is not an integer.

0.003 Γ 1000 = 3. This is an integer.

**Simplifying the fraction**

Often questions will say βgive your answer in the simplest formβ so we need to check whether the fraction can be simplified. To simplify a fraction we need to divide the numerator and the denominator by a common factor.

**Not multiplying the denominator by the same number as the numerator**

When you multiply the numerator by a multiple of 10 you must do the same for the denominator, otherwise you are changing the value of the fraction.

**Converting between a mixed number and an improper fraction**

A common error is to incorrectly convert between numbers in different forms

E.g. mixed numbers and improper fractions.

Percentages to fractions is part of our series of lessons to support revision on comparing fractions, decimals and percentages. You may find it helpful to start with the main comparing fractions, decimals and percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Convert 10 % to a fraction in its simplest form

\frac{10}{100}

\frac{1}{10}

\frac{0.1}{1}

\frac{0.01}{100}

10 % can be written as \frac{10}{100} . We can simplify this by dividing both the numerator and denominator by 10 .

2. Convert 20 % to a fraction in its simplest form

\frac{20}{100}

\frac{2}{10}

\frac{1}{5}

\frac{0.4}{1}

20% can be written as \frac{20}{100} . We can simplify this by dividing both the numerator and denominator by 5 .

3. Convert 130% to a fraction in its simplest form

\frac{1.3}{1}

\frac{13}{10}

\frac{130}{100}

\frac{3}{10}

130 % can be written as \frac{130}{100} . We can simplify this by dividing both the numerator and denominator by 10 .

4. Convert 0.6 % to a fraction in its simplest form

\frac{0.006}{1}

\frac{6}{1}

\frac{6}{1000}

\frac{3}{500}

0.6% can be written as \frac{0.6}{100} . We then need to multiply both the numerator and denominator by 10 to make the numerator an integer. We can simplify this by dividing both the numerator and denominator by 2 .

5. Convert 3005 % to a fraction in its simplest form

\frac{601}{20}

\frac{1}{20}

3005

\frac{3005}{1000}

3005 % can be written as \frac{3005}{100} . We can simplify this by dividing both the numerator and denominator by 5 .

6. Which of the below is the fractional equivalent of 12 %

\frac{3}{25}

\frac{12}{100}

\frac{6}{50}

\frac{12}{10}

12 % can be written as \frac{12}{100} . We can simplify this by dividing both the numerator and denominator by 4 .

1. Convert each of the following percentages to fractions:

a) 90%

b) 25%

c) 9%

d) 0.9%

e) 990%

All answers must be given in their simplest form.

**(5 marks)**

Show answer

a) \frac{9}{10}

**(1)**

b) \frac{1}{4}

**(1)**

c) \frac{9}{100}

**(1)**

d) \frac{9}{1000}

**(1)**

e) \frac{99}{10}

**(1)**

2. Convert each of the following percentages to fractions:

a) 54%

b) 114%

c) 18.2%

All answers must be given in their simplest form.

**(6 marks)**

Show answer

a) \frac{54}{100}

**(1)**

\frac{27}{50}

**(1)**

b) \frac{114}{100}

**(1)**

\frac{57}{50}

**(1)**

c) \frac{182}{100}

**(1)**

\frac{91}{500}

**(1)**

3. Match the percentages to the fractions:

Show answer

a) 50\%=\frac{1}{2}

**(1)**

b) 140\%=\frac{7}{5}

**(1)**

c) 80\%=\frac{4}{5}

**(1)**

d) 3\%=\frac{3}{100}

**(1)**

e) 0.52\%=\frac{13}{2500}

**(1)**

4. Write 88.8 % as a fraction in its simplest form.

**(2 marks)**

Show answer

\frac{88.8}{100}

**(1)**

\frac{111}{125}

**(1)**

You have now learned how to:

- Convert a percentage to a fraction

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