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

Dividing by a whole number

Place value

Simplifying fractions

This topic is relevant for:

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.

A **percentage of an amount** can be calculated by writing the percentage as a decimal or a fraction and then multiplying it by the amount. There are different methods you can use to calculate a** percentage of a quantity**.

For example, what is 35% of 60?

**Method 1: **The one percent method

Find 1% first by dividing the amount by 100 and then multiply this by the amount.

\frac{60}{100} \times 35 = 21**Method 2:** The decimal multiplier method

Write the percentage as a decimal and then multiply the amount by this decimal.

35\%=0.35 60 \times 0.35=21**Method 3:** Using equivalent fractions

Write the percentage as a fraction in its simplest form and then multiply the amount by this fraction.

35\% = \frac{35}{100} =\frac{7}{20} 60 \times \frac{7}{20} = \frac{60\times 7}{20} = \frac{420}{20} =\frac{42}{2}= 21Alternatively you can calculate the fraction of the quantity like this,

35\% of 60 = \frac{7}{20} of 60

\frac{1}{20} of 60 = 60 \div 20 = 3

\frac{7}{20} of 60 = 60 \div 20 \times 7 = 21

**Method 4: **Building up an answer from simple percentages

Using simple percentages, you can build up to the answer to the question.

This question could be broken down into the following steps.

10\% of 60 = 6 (To find 10% we divide by 10)

5\% of 60 = 3 (5% is half of 10%)

30\% of 60 = 18 (30% is three lots of 10%)

35\% of 60 = 18+3=21 (30% plus 5%)

Methods 1 and 2 lend themselves to questions where a calculator is allowed. Methods 3 and 4 lend themselves to questions where calculators are not permitted.

You may be asked to express an amount as a percentage of another.

For example, express 40 as a percentage of 50.

This would mean writing the numbers as a fraction, and multiplying by 100. The first amount is the numerator and the second amount is the denominator.

\frac{40}{50}\times 100=80%A different question could ask you to write 50 as a percentage of 20. Here it is very important to make sure that the first amount is the numerator and the second amount is the denominator.

\frac{50}{20}\times 100=250%In order to find the percentage of an amount without a calculator:

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

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

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

DOWNLOAD FREEFind

**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

3 **Work out the answer.**

\[120\div 4 = 30\]

The answer is

Find

**Identify the percentage.**

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

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

Since

**Work out the answer.**

\[450\div 10 = 45\]

The answer is

Find

**Identify the percentage.**

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

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

Since

\[300\div 10 = 30\]

Then we divide by

\[30\div 10 = 3\]

**Work out the answer.**

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

Therefore,

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

The answer is

Find

**Identify the percentage.**

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

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

Since

\[700\div 10 = 70\]

Then we divide by

\[70\div 10 = 7\]

**Work out the answer.**

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

Therefore,

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

The answer is

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

**Identify the percentage.****Find the decimal multiplier.****Work out the answer by multiplying the original amount by the decimal multiplier.**

Step by step guide**:** Percentage Multipliers

Work out

**Identify the percentage.**

\[78\%\]

**Find the decimal multiplier.**

Let’s find the decimal equivalent of

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

We can calculate this by dividing the numerator of

Writing

**Work out the answer by multiplying the original amount by the decimal multiplier.**

\[411 \times 0.78=320.58\]

The answer is

Work out

**Identify the percentage.**

\[61\%\]

**Find the decimal multiplier.**

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

We can calculate this by dividing the numerator of

**Work out the answer by multiplying the original amount by the decimal multiplier.**

\[728 \times 0.61=444.08\]

The answer is

**Money and two decimal places**

E.g.

An answer of

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

If you are asked to find

E.g.

Calculate

\[391 \times 0.29=£ 113.39\]

**Dividing by 10 – taking care with the decimal points**

E.g.

Find

10%

\[53\div 10 = 5.3\]

\[5.3\div 10 = 0.53\]

\[(4 × 5.3) + 0.53 = 21.73\]

The answer is

Percentage of an amount is part of our series of lessons to support revision on percentages. You may find it helpful to start with the main 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. 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

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)**

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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