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Here is everything you need to know about **percentages **for GCSE maths (Edexcel, AQA and OCR). You’ll learn how to find the percentage of an amount and calculate with percentage multipliers.

You will also work out how to increase and decrease a number by a percentage, percentage change and reverse percentages.

Look out for the percentages worksheets and exam questions at the end.

A **percentage **is a number which is expressed as a fraction of

Percent means “number of parts per hundred” and the symbol we use for percent is the percent sign

E.g.

\[43\%=\frac{43}{100}=0.43\]

\[1\%=\frac{1}{100}=0.01\]

There are different types of percentage questions.

**Percentage of an amount**

This is where we are asked to find a certain percentage of an amount.

E.g. Find

This is the same as finding a

\[32\div4=8\]

The answer is

**Percentage multipliers**

This is where we can find a decimal number and use it as a multiplier to make calculating percentages more efficient.

E.g. Find

We can use

\[41\%=\frac{41}{100}=0.41\]

\[800\times0.41=328\]

The answer is

**Percentage increase**

This is where we are asked to increase (make bigger) a value by a certain amount.

E.g. Increase

We can find

\[40+4=44\]

The answer is

**Percentage decrease**

This is where we are asked to decrease (make smaller) a value by a certain amount.

E.g. Decrease

We can find

\[60-6=54\]

The answer is

**Percentage change**

When values change, we can express this change as a percentage of the original value.

E.g. Work out the percentage change of

The actual change from

\[\frac{1}{25}=\frac{4}{100}=4\%\]

The answer is

**Reverse percentages**

This is where we are given a certain percentage of a number and we have to find the original number.

E.g.

\[20\%=\frac{1}{5}\]

To find the original number we need to find

\[5\times6=30\]

The answer is

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

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

DOWNLOAD FREEIn order to use percentages, you need to be clear about what you have and what you are trying to work out. Percentage questions can vary and there will be links in the other sections with more details.

- Write down what you have and what you are trying to find.
- Work out what you need.
- Write down the final answer.

Find

**Write down what you have and what you are trying to find.**

We need to work out

2 **Work out what you need.**

\[23\% = 20\%+3\%\]

\[10\% = 16, 1\% = 1.6\]

\[(2\times16)+(3\times1.6)=32+4.6=36.8\]

3 **Write down the final answer**.

**£36.80**

Find

**Write down what you have and what you are trying to find.**

We want to find

**Work out what you need**.

We can write the percentage as a decimal number.

\[39\%=0.39\]

This gives the percentage in decimal form which is the percentage multiplier.

\[4700\times0.39=1833\]

**Write down the final answer**.

**£1833**

Increase

**Write down what you have and what you are trying to find.**

We want to find

\[100\%+30\%=130\%\]

**Work out what you need**.

\[200\div10=20\]

\[3\times20=60\]

So

\[200 + 60 = 260\]

**OR**

You could also use the decimal multiplier.

\[100+30=130\]

\[130\%=\frac{130}{100}=1.30\]

\[200\times1.3=260\]

**Write down the final answer**.

**£260**

Decrease

**Write down what you have and what you are trying to find.**

We want to find

\[100\%-20\%=80\%\]

**Work out what you need**.

\[700\div10=70\]

\[2\times70=140\]

So

\[700-140=560\]

**OR**

You could use the decimal multiplier.

\[100-20=80\]

\[80\%=\frac{80}{100}=0.80\]

\[700\times0.80=560\]

**Write down the final answer**.

**560 g.**

The price of a t-shirt increased from

**Write down what you have and what you are trying to find.**

The original amount is

We need to find the change as a percentage of the original amount.

**Work out what you need**.

The actual change is

\[12-10=2\]

The actual change written as a fraction of the original is

\[\frac{2}{10}\]

The actual change is the numerator (top number).

The original number is the denominator (bottom number).

Convert the fraction to an equivalent fraction where the denominator is

\[\frac{2}{10}=\frac{20}{100}=20\%\]

**OR**

Write the actual change as a fraction of the original amount and multiply by

\[\frac{2}{10}\times100=20\]

**Write down the final answer**.

The percentage change of **20%**

The price of a coat is

**Write down what you have and what you are trying to find.**

\[100\%-20\%=80\%\]

£40 represents 80% of the original price.

So

We need the original price which is

**Work out what you need**.

We can work out

\[40\div8=4\]

Then we can work out

\[5\times 10 = 50\]

**OR**

We can make an equation using

\[\begin{aligned}
x\times0.80&=40\\\\
x&=40\div0.80\\\\
x&=50
\end{aligned}
\]

**Write down the final answer**.

The price after the cut is **£50**

**Money needs two digits for the pence**

E.g. Find

\[620\times0.34=210.8\]

The answer is

**The decimal multiplier to work out a percentage increase can be greater than**1

E.g. To increase

\[50\times1.03 =51.5\]

The answer is

**Percentages can be greater than**100%

E.g. Calculate the percentage change from

The actual change is

\[\frac{250}{200}\times100=125\]

So the percentage change from

1. Find 40\% of \pounds 300 .

\pounds 1200

\pounds 120

\pounds 7.50

\pounds 12

10\% of \pounds 300 is \pounds 30 . We can multiply this by 4 to get 40\% .

2. Calculate 12.4\% of \pounds 3000 .

\pounds 3372

\pounds 37200

\pounds 372

\pounds 3720

As a multiplier, 12.4\% is 0.124 . To get the answer we can calculate 0.124\times3000

3. Increase 600m by 30\% .

630m

780m

180m

420m

30\% of 600 is 180 . We can add this on to the original amount to find the quantity after the increase.

4. Decrease 80 kg by 5\% .

75kg

95kg

76kg

84kg

5\% of 80 is 4 . We can subtract this from the original amount to find the quantity after the decrease.

5. Calculate the percentage change from 400 kg to 600 kg .

50\%

200\%

100\%

150\%

The actual increase is given by

600 − 400 = 200The percentage increase is then given by

\frac{200}{400}\times100=50\%6. A book costs \pounds 4 after a price reduction of 20\% . What was the original price?

\pounds 4.20

\pounds 5.00

\pounds 20.00

\pounds 4.25

\pounds 4 represents 80\% of the original amount, which means 10\% of the original amount is \pounds 0.50 .

Multiplying by ten to get 100\% means the original price was \pounds 5 .

1. Work out 90\% of \pounds 70.

**(2 marks)**

Show answer

10\% is 7 , so 90\% is 9 × 7

**(1)**

9\times7 = 63

**(1)**

2. Charlotte invests \pounds 3000 for 4 years.

She gets a simple interest rate of 2\% per year.

Work out the total interest Charlotte gets.

**(3 marks)**

Show answer

3000\times0.02=

**(1)**

4\times60

**(1)**

= \pounds 240

**(1)**

3. Last year Ron paid \pounds 450 for his car insurance.

This year he has to pay \pounds 603 for his car insurance.

Work out the percentage increase in his car insurance.

**(3 marks)**

Show answer

The change is

603-450=

**(1)**

\frac{153}{450}\times 100

**(1)**

= 34\%

**(1)**

You have now learned how to:

- How to work out the percentage of a number
- How to calculate percentage change
- How to work out a percentage increase or decrease

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