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Place value Arithmetic Simplifying fractions Mixed numbers and improper fractionsThis topic is relevant for:

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

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

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

E.g.

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

In order to convert from a fraction to a percentage there are two methods which are used depending on whether the denominator is a factor or a multiple of

**Determine if the denominator is a factor or multiple of**100

If** it is **follow these steps:

2**Convert the fraction so the denominator is 100**

3**Write the numerator as a percentage because it is now ‘out of 100’**

4**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

If the denominator **is not **a factor or multiple of

**2Divide the numerator by the denominator**

3**Multiply by 100 to convert to a percentage**

**4Clearly state the answer showing the ‘fraction’ = ‘percentage’**

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

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

DOWNLOAD FREEConvert \frac{3}{4} to a percentage

**See if the denominator is a factor or multiple of**100

2 **Convert the fraction so the denominator is 100**

\[\begin{aligned}
&\frac{3}{4} \\\\
&=\frac{3\times25}{4\times25} \\\\
&=\frac{75}{100} \\\\
\end{aligned}\]

3**Write the numerator as a percentage **

\frac{75}{100}=75\% \quad \quad *because % means out of 100*

4**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{3}{4}=75\%\]

Convert \frac{60}{200} to a percentage

**See if the denominator is a factor or multiple of 100**

**Convert the fraction so the denominator is 100**

**and numerator** by

\[\begin{aligned}
&\frac{60}{200}\\\\
&=\frac{60\div2}{200\div2}\\\\
&=\frac{30}{100}
\end{aligned}\]

Because we are converting to a percentage we only need to simplify the fraction so that the denominator is **not **in its simplest form.

**Write the numerator as a percentage**

\frac{30}{100}=30\% \quad \quad * because % means out of 100*

**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{60}{200}=30\%\]

Convert \frac{5}{8} to a percentage

**Determine if the denominator is a factor or multiple of 100**

**Divide the numerator by the denominator **

\[\begin{aligned}
&\frac{5}{8} = 5\div8 \\\\
\end{aligned}\]

Therefore,

\[\frac{5}{8}=0.625\]

**Multiply by 100 to convert to a percentage**

\[\begin{aligned}
&0.625\times100 \\\\
&62.5\%
\end{aligned}\]

**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{5}{8}=62.5\%\]

Convert \frac{2}{9} to a percentage

**Determine if the denominator is a factor or multiple of 100**

**Divide the numerator by the denominator **

\[\begin{aligned}
&\frac{2}{9}=2\div9\\\\
\end{aligned}\]

Therefore,

\[\frac{2}{9}=0.22222…=0.\dot{2}\]

**Multiply by 100 to convert to a percentage**

\[0.\dot{2}\times100 = 22.\dot{2}\%\]

**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{2}{9}=22.\dot{2}\%\]

Convert \frac{25}{20} to a percentage

**See if the denominator is a factor or multiple of 100**

**Convert the fraction so the denominator is 100**

**denominator and numerator by 5**

\[\begin{aligned}
&\frac{25}{20}\\\\
&=\frac{25\times5}{20\times5}\\\\
&=\frac{125}{100}
\end{aligned}\]

**Write the numerator as a percentage**

\frac{125}{100}=125\% \quad \quad *because % means out of 100*

**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{25}{20}=125\%\]

Convert 4\frac{5}{16} to a percentage

** Added step- convert to an improper fraction first**:

\[4\frac{5}{16}=\frac{69}{16}\]

**Determine if the denominator is a factor or multiple of 100**

**Divide the numerator by the denominator **

\[\begin{aligned}
&\frac{69}{16} = 69\div16 \\\\
\end{aligned}\]

Therefore

\[\frac{69}{16}=4.3125\]

**Multiply by 100 to convert to a percentage**

\[\begin{aligned}
&4.3125\times100 \\\\
&431.25\%
\end{aligned}\]

**Clearly state the answer showing the ‘fraction’ = ‘percentage’**

\[\frac{69}{16}=431.25\%\]

If you are allowed to use a calculator you can perform the operation in one calculation.

E.g.

Convert \frac{25}{20} to a percentage

- Enter the fraction on the calculator and multiply by
100 - Press =
- This means 125\%

**Mistakes with written division**

Often mistakes are made when implementing a form of written division. For example a common mistake with the ‘bus stop’ method is mixing up the number being divided (dividend) by the number you are dividing by (divisor).

The numerator is the dividend and therefore goes inside the ‘bus stop’.

**Not multiplying by**100 to make a percentage

The percent sign means the number is given out of

E.g

\[\frac{3}{4}=0.75=75\%\]

**Not noticing a recurring decimal**

Sometimes a recurring decimal is not immediately obvious. For example

\[\frac{1}{7}=0.142857142857142857..\]

Therefore

\[\frac{1}{7}= 0.\dot{1}4285\dot{7}\]

Fractions to percentages 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 \frac{1}{10} to a percentage

1\%

10\%

0.1\%

0.01\%

\begin{aligned}
1\div10=0.1\\\\
0.1\times100=10\\\\
10\%\\
\end{aligned}

2. Convert \frac{4}{10} to a percentage

40\%

4\%

0.4\%

2.5\%

\begin{aligned}
4\div10=0.4\\\\
0.4\times100=40\\\\
40\%
\end{aligned}

3. Convert \frac{11}{10} to a percentage

90.9\%

1.1\%

\frac{11}{10}\%

110\%

\begin{aligned}
110\div10=1.1\\\\
1.1\times100=110\\\\
110\%
\end{aligned}

4. Convert \frac{6}{1000} to a percentage

0.6

166.6\%

6\%

0.6\%

\begin{aligned}
6\div1000=0.006\\\\
0.006\times100=0.6\\\\
0.6\%
\end{aligned}

5. Convert \frac{601}{20} to a percentage

30.05

3005\%

3.327787\%

601\%

\begin{aligned}
601\div20=30.05\\\\
30.05\times100=3005\\\\
3005\%
\end{aligned}

6. Convert \frac{15}{16} to a percentage

0.9375\%

93.75\%

1.06\%

937.5\%

\begin{aligned}
15\div16=0.9375\\\\
0.9375\times100=93.75\\\\
93.75\%
\end{aligned}

1. Convert each of the following fractions to percentages

a) \frac{9}{10}

b) \frac{1}{4}

c) \frac{9}{100}

d) \frac{9}{1000}

e) \frac{99}{10}

**(5 Marks)**

Show answer

a) 90\%

**(1)**

b) 25\%

**(1)**

c) 9\%

**(1)**

d) 0.9\%

**(1)**

e) 990\%

**(1)**

2. Convert each of the following fractions to percentages

a) \frac{16}{50}

b) \frac{7}{25}

c) \frac{4}{75}

**(4 Marks)**

Show answer

a) 32\%

**(1)**

b) 28\%

**(1)**

c) 1 mark for correct method but not showing the recurring decimals e.g 5.3\%

**(1)**

5.33333…\% or 5.\dot{3}\%

**(1)**

3. Match the fractions to the percentage

\begin{aligned} &\frac{2}{5} \quad \quad \quad \quad \quad 75\% \\\\ &\frac{3}{4} \quad \quad \quad \quad \quad 120\% \\\\ &\frac{6}{5} \quad \quad \quad \quad \quad 40\% \\\\ &\frac{26}{10} \quad \quad \quad \quad \quad 3\% \\\\ &\frac{3}{100} \quad \quad \quad \quad 260\% \end{aligned}

**(5 Marks)**

Show answer

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

**(1)**

\frac{3}{4}=75\%

**(1)**

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

**(1)**

\frac{26}{10}=260\%

**(1)**

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

**(1)**

4. Represent \frac{113}{125} as a percentage.

**(2 Marks)**

Show answer

113\div125=0.904

**(1)**

0.904\times100=90.4

90.4\%

**(1)**

You have now learned how to:

- Convert a fraction to a percentage

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