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In order to access this I need to be confident with:

Calculating percentages of amounts with and without a calculator

Converting between percentages and decimals

This topic is relevant for:

Here is everything you need to know about **percentage increase** for GCSE maths (Edexcel, AQA and OCR). You’ll learn how to increase a value by a given percentage, use multipliers to calculate percentage increase and work out percentage change.

Look out for the percentage increase and decrease worksheets and exam questions at the end.

**Percentage increase** means adding a given percentage of a value on to the original value. To do this we can either calculate the given percentage of the value and then add it on to the original value or use a percentage multiplier.

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

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

DOWNLOAD FREEIn order to increase a value by a percentage:

- Calculate the given percentage of the value.
- Add it on to the original number.

Increase

- Calculate
40% of£50

To do this without a calculator, the easiest way is to calculate

2 Add

Increase

Calculate 65% of 400

Add 260 on to the original value

Increase

Calculate 27% of 350m

When using a calculator to calculate a percentage, we divide the value by

\begin{array}{l}
350 \div 100=3.5 \\
1\%=3.5\\\\
3.5 \times 27=94.5 \mathrm{~m}\\
27\%=94.5
\end{array}

Add 94.5m on to the original value

The price of Katrina’s train ticket last year was

Calculate 17.5% of £72

\[\begin{array}{l}
72 \div 100=0.72 \\
1\%=0.72\\\\
0.72 \times 17.5= £ \hspace{1mm} 12.60\\
17.5\%= £ \hspace{1mm} 12.60
\end{array}\]

Add £12.60 on to the original value

We can increase a value by a percentage using a **percentage multiplier**. A percentage multiplier is a decimal that is related to the percentage you are trying to find.

- Add the percentage we are increasing by to
100%

We add it on to

2Convert to a decimal

3Multiply the original amount by the decimal

Increase

Here we are calculating a 24 percent increase so add 24% on to 100%

\[100\% + 24\% = 124\%\]

Convert to a decimal. To do this we divide the percentage by 100.

\[124\% = 1.24\]

Multiply 3200 by 1.24

\[3200\times 1.24=3968ml\]

In

This is a 12.5 percent increase so we add 12.5% on to 100%

\[100\% + 12.5\% = 112.5\%\]

Convert to a decimal.

\[112.5\% = 1.125\]

Multiply £620 by 1.125

Remember to always write money using two decimal places.

Given two values, we can calculate the percentage change. This may also be called percentage difference, percentage increase, percentage gain or percentage profit.

We can calculate percentage change using the percentage change formula:

\[\text { Percentage change }=\frac{\text { Change }}{\text { Original }} \times 100\]

The same formula can be used to calculate percentage decrease

- Work out how much the value has changed by subtracting the old number from the new number.
- Apply the percentage change formula

The weight of a lamb has increased from

The weight of the lamb has changed from 4kg to 5.2kg. Work out the actual change:

\[5.2 − 4 = 1.2kg\]

Apply the percentage change formula. The change is 1.2kg and the original amount is 4kg.

\begin{array}{l}
\text { Percentage change }&=\frac{\text { Change }}{\text { Original }} \times 100 \\\\
\text { Percentage change}&=\frac{1.2}{4} \times 100\end{array}

Percentage change

The lamb’s weight has increased by

Lucy buys an antique table for

Work out the change in value by subtracting the original price from the new price:

Apply the percentage change formula. The change is £35 and the original price is £150.

\[\text { Percentage change }=\frac{35}{150} \times 100\]

Percentage change

The percentage profit is

**Percentages greater than**100%

Believing that percentages cannot be greater than

**Converting between percentages and decimals**

Incorrectly converting percentages to decimals. The most common mistakes are with single digit percentages (e.g.

Remember to divide the percentage by

E.g.

**Using an incorrect value for the denominator in the percentage increase formula**

Using the new value instead of the original value for the denominator when calculating percentage change.

1. Increase £520 by 20\% .

£540

£104

£624

£640

20\% of 520 is 104 . This can be added to the original amount to find the quantity after the increase.

2. Increase 3420m by 43\% .

3463m

4890.6m

1470.6m

3563m

43\% of 3420 is 1470.6 . This can be added to the original amount to find the quantity after the increase.

3. Use a multiplier to increase 38 by 14\% .

5.32

43.32

42

33.3

The multiplier we need to use is 1.14 , so the calculation is 1.14\times38 .

4. Use a multiplier to increase 650kg by 26.5\% .

172.25kg

822.25kg

513.83kg

676.5kg

The multiplier we need to use is 1.265 , so the calculation is 1.265\times650 .

5. Find the percentage increase when 400ml is increased to 620ml .

55\%

155\%

220\%

110\%

The amount has increased by 220ml . As a percentage of the original amount, this is \frac{220}{400}\times100 .

6. Find the percentage profit when Karam buys a house for £124000 and sells the house for £137640 .

111\%

89\%

11\%

136.4\%

The percentage profit is calculated as \frac{137640-124000}{124000}\times100 .

1. (a) Catrin’s salary is £18000 . She receives a 3.5\% pay rise.

Work out Catrin’s new salary.

(b) How much extra money will Catrin earn each week?

**(3 marks)**

Show answer

(a)

3.5\% of \pounds 18000 = \pounds 630

**(1)**

\pounds 18000 + \pounds 630 = \pounds 18630

**(1)**

(b)

\pounds 630 \div 52 = \pounds 12.12**(1)**

2. In 2010 the population of the UK was approximately 62220000 .

By 2020 it had increased to 66520000 .

Find the percentage increase in population over these 10 years.

Give your answer to 2dp .

**(2 marks)**

Show answer

66520000 - 62220000 = 4300000

**(1)**

\frac{4300000}{62220000} \times 100=6.91\%

**(1)**

3. Thomas bought a box containing 100 packets of crisps for £30 .

He sold 96 packets of crisps for 50p each.

Calculate Thomas’s percentage profit.

**(3 marks)**

Show answer

96 \times 50 p = \pounds 48

**(1)**

\pounds 48-\pounds 30=\pounds 18

**(1)**

\frac{18}{30} \times 100=60 \%

**(1)**

You have now learned how to:

- Increase a value by a given percentage
- Use a percentage multiplier to increase a value by a percentage
- Calculate percent increase between two values

- Percentage decrease
- Compound interest
- Reverse percentages

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