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Percentage of an Amount

Percentage of an Amount

Here we will learn how to find percentage of an amount with and without using a calculator.

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

What is a percentage of an amount?

A percentage of an amount allows us to calculate a percentage of a given number.
To calculate the percentage of an amount we can either find simple percentages such as 10% and 1% and build it up or use a percentage multiplier.


Let’s look at an example using two different methods:

E.g.
21% of £500

Using simple percentages

100% is the original amount.

What is 10%? £50

What is 1%? £5

\begin{aligned} 21 \% \text { of } £ 500 &=2 \times £ 50+£ 5 \\\\ &=£ 105 \end{aligned}

Using percentages multipliers

\begin{aligned} 21 \%=\frac{21}{100}&=0.21 \\\\ 21 \% \text { of } £ 500&=0.21 \times 500 \\\\ &=£ 105 \end{aligned}

What is a percentage of an amount?

What is a percentage of an amount?

How to find the percentage of an amount (non-calculator)

In order to find the percentage of an amount without a calculator:

  1. Identify the percentage and consider if there is a simple equivalent fraction.
  2. Decide which method to use.  Either a division or finding simple percentages and building it up.
  3. Work out the answer.

Explain how to calculate a percentage of an amount without a calculator in 3 steps

Explain how to calculate a percentage of an amount without a calculator in 3 steps

Percentage of an amount worksheet

Get your free percentage of an amount worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Percentage of an amount worksheet

Get your free percentage of an amount worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Percentage of an amount examples

Example 1: percentage has a simple equivalent fraction

Find 25% of 120 km.

  1. Identify the percentage.

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

2 Decide which method to use.  Either a division or finding 10%, 1% and building it up.

Since 25% = ¼, to find 25% we can divide by 4.

3 Work out the answer.

\[120\div 4 = 30\]

The answer is 30 km.

Example 2: percentage has a simple equivalent fraction

Find 10% of 450 kg.

\[10\%=\frac{10}{100}=\frac{1}{10}\]

Since 10% = ⅟₁₀, to find 10% we can divide by 10.

\[450\div 10 = 45\]


The answer is 45 kg.

Example 3: percentage can be made up from 10% and 1%

Find 16% of £300.

\[16\%= 10\% + 6\times 1\% \]

Since 10% = ⅟₁₀, to find 10% we can divide by 10.


\[300\div 10 = 30\]


Then we divide by 10 again to find 1%.


\[30\div 10 = 3\]

\[16\%= 10\% + 6\times 1\%\]


Therefore,


16% of 300 is


\[30 + (6\times 3) = 30 + 18 = 48\]


The answer is £48.

Example 4: percentage can be made up from 10% and 1%

Find 23% of £700.

\[23\%= 2\times 10\% + 3\times 1\%\]

Since 10% = ⅟₁₀, to find 10% we can divide by the denominator 10.


\[700\div 10 = 70\]


Then we divide by 10 again to find 1%.


\[70\div 10 = 7\]

\[23\%= 2\times 10\% + 3\times 1\%\]


Therefore,


23% of 700 is


\[(2 × 70) + 3\times 7 = 140 + 21 = 161\]


The answer is £161.

How to find the percentage of an amount (with calculator)

In order to the percentage of an amount with a calculator:

  1. Identify the percentage.
  2. Find the decimal multiplier.
  3. Work out the answer by multiplying the original amount by the decimal multiplier.

Explain how to calculate the percentage of an amount with a calculator in 3 steps

Explain how to calculate the percentage of an amount with a calculator in 3 steps

Step by step guide: Percentage Multipliers

Example 5: when you have a calculator

Work out 78% of £411.

\[78\%\]

Let’s find the decimal equivalent of 78%:


\[78\%=\frac{78}{100}=0.78\]


We can calculate this by dividing the numerator of 78 by the denominator of 100.


Writing 78% in its decimal form is 0.78.

\[411 \times 0.78=320.58\]


The answer is £320.58.

Example 6: when you have a calculator

Work out 61% of £728.

\[61\%\]

\[61\%=\frac{61}{100}=0.61\]


We can calculate this by dividing the numerator of 61 by a hundred.

\[728 \times 0.61=444.08\]


The answer is £444.08.

Common misconceptions

  • Money and two decimal places

E.g.
An answer of £16.5 should be written as £16.50.  There are two digits needed for the pence.

  • Using a non-calculator method when you have a calculator

If you are asked to find 29% of £391 you can do it by finding 10% and 1% and building it up to find 20% and 9% and adding them together. However it is much more simpler here to use a multiplier.

E.g.
Calculate 29% of £391

\[391 \times 0.29=£ 113.39\]

  • Dividing by 10 – taking care with the decimal points

E.g.
Find 41% of 53 kg:

10%
is:

\[53\div 10 = 5.3\]

1% is:

\[5.3\div 10 = 0.53\]

41% of £53 is:

\[(4 × 5.3) + 0.53 = 21.73\]


The answer is 21.73 kg.

Practice percentage of an amount questions

1. Find 25\% of \pounds 280 without a calculator

\pounds 140
GCSE Quiz False

\pounds 28
GCSE Quiz False

\pounds 240
GCSE Quiz False

\pounds 70
GCSE Quiz True

25\% is the same as \frac{1}{4},

 

so we can calculate

 

\pounds 280 \div 4 = \pounds 70

2. Find 50\% of 70 kg without a calculator

35kg
GCSE Quiz True

7kg
GCSE Quiz False

17.5kg
GCSE Quiz False

50kg
GCSE Quiz False

50\% is the same as \frac{1}{2},

 

so we can calculate

 

70 \div 2 = 35

3. Find 12\% of 200g without a calculator

40g
GCSE Quiz False

24g
GCSE Quiz True

16.67g
GCSE Quiz False

25g
GCSE Quiz False

10\% of  200:

 

200 \div 10 = 20

 

1\% of  200:

 

200 \div 100 = 2

 

\begin{aligned} 12\%&=10\%+(2 \times 1\%)\\\\ &=20+(2 \times 2)\\\\ &=24 \end{aligned}

4. Find 27\% of 300 km without a calculator

75km
GCSE Quiz False

81km
GCSE Quiz True

67km
GCSE Quiz False

27km
GCSE Quiz False

10\% of  300km:

 

300 \div 10 = 30

 

1\% of  300km:

 

300 \div 100 = 3

 

\begin{aligned} 27\%&=(2 \times 10\%) + (7 \times 1\%)\\\\ &=(2 \times 30) + (7 \times 3)\\\\ &=60+21\\\\ &=81km \end{aligned}

5. Find 57\% of \pounds 710 with a calculator

\pounds 404.70
GCSE Quiz True

\pounds 404.07
GCSE Quiz False

\pounds 12.46
GCSE Quiz False

\pounds 570
GCSE Quiz False
57\%=\frac{57}{100} = 0.57

 

£710 \times 0.57 = \pounds 404.70

6. Find 83\% of \pounds 179 with a calculator

\pounds 30.43
GCSE Quiz False

\pounds 83.79
GCSE Quiz False

\pounds 148.57
GCSE Quiz True

\pounds 143.20
GCSE Quiz False
83\%=\frac{83}{100}=0.83

 

£179 \times 0.83 = \pounds 148.57

Percentage of an amount GCSE questions

1. Without a calculator,


work out 20\% of 600 g.

 

(2 marks)

Show answer

for finding 10\%,

600 ÷ 10 = 60

(1)

 

for the correct answer

120 g

(1)

2. Andy is paid £1400 per month. He gets a 2 % increase in his monthly earnings. How much money will Andy earn per month after the increase?
 

(2 marks)

Show answer

2\% = £28,

1400 + 28

(1)

 

for the correct answer

£1428

(1)

3. At a shop T-shirts cost £4.60 each. If you buy 20 or more T-shirts, you can get 10\% off the total cost of all of the T-Shirts you have bought.

Work out the total cost of buying 26 T-shirts.

(3 Marks)

Show answer

26 × £4.60 = £119.60 

(1)

10\% of £119.60=£11.96 ,

(1)

£119.60 – £11.96 = 107.64  

(1)

Learning checklist

You have now learned how to:

  • Interpret percentages as a fraction.
  • Interpret percentages as a decimal.
  • Interpret percentage multiplicatively.
  • Use a calculator to calculate results accurately.

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