GCSE Maths Number FDP Percentages

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? ## 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.

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

$120\div 4 = 30$

### 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.

$450\div 10 = 45$

### 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

$30 + (6\times 3) = 30 + 18 = 48$

### 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

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

## 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 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.

$411 \times 0.78=320.58$

### 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.

$728 \times 0.61=444.08$

### 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:

$(4 × 5.3) + 0.53 = 21.73$

### Practice percentage of an amount questions

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

\pounds 140 \pounds 28 \pounds 240 \pounds 70 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 7kg 17.5kg 50kg 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 24g 16.67g 25g 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 81km 67km 27km 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 \pounds 404.07 \pounds 12.46 \pounds 570 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 \pounds 83.79 \pounds 148.57 \pounds 143.20 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)

for finding 10\%,

600 ÷ 10 = 60

(1)

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)

2\% = £28,

1400 + 28

(1)

£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)

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.

## Still stuck?

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