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

Place value

Multiplying

Converting percentages to decimals

This topic is relevant for:

Here we will learn about about using a **percentage multiplier** including how to find the single multiplier from a percentage and use the single multiplier to answer percentage questions.

There are also percentage multiplier 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 multiplier** is a number which is used to calculate a percentage of an amount or used to increase or decrease an amount by a percentage.

E.g.

In order to find

\[12\% = \frac{12}{100} = 0.12\]

So

These questions will often involve interest rates in financial situations such as simple interest or compound interest. It is sometimes referred to as the multiplier method.

In order to write a decimal multiplier from a percentage:

- Write down the percentage
- Convert this percentage to a decimal by dividing by
100 – this is the multiplier - Multiply the original amount by the multiplier

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

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

DOWNLOAD FREEWhat is the decimal multiplier for 58 \%?

- Write down the percentage required

\[58 \%\]

2Convert the percentage to a decimal by dividing by

\[58\% = \frac{58}{100} = 0.58\]

**The decimal multiplier is 0.58**.

What is the decimal multiplier for

Write down the percentage

\[26 \%\]

Convert the percentage to a decimal by dividing by 100

\[26\% = \frac{26}{100} = 0.26\]

**The decimal multiplier is 0.26**.

What is the decimal multiplier for

Write down the percentage.

\[4.5 \%\]

Convert the percentage to a decimal by dividing by 100

\[4.5\% = \frac{4.5}{100} = 0.045\]

**The decimal multiplier is 0.045**.

In order to use a percentage multiplier to calculate the percentage of an amount:

- Write down what percentage you need
- Convert this percentage to a decimal by dividing by
100 ; this is the decimal multiplier - Multiply the original amount in the question by the decimal multiplier

Work out

Write down the percentage

\[34 \%\]

Convert the percentage to a decimal by dividing by 100

\[34\% = \frac{34}{100} = 0.34\]

Multiply the original amount in the question by the decimal multiplier

What is the original amount?

What is the decimal multiplier?

\[700\times0.34=238\]

**The answer is £238**.

Work out

Write down the percentage

\[8 \%\]

Convert the percentage to a decimal by dividing by 100

\[8\% = \frac{8}{100} = 0.08\]

Multiply the original amount in the question by the decimal multiplier

What is the original amount?

What is the decimal multiplier?

\[650\times0.08=52\]

**The answer is £52**.

Work out

Write down the percentage

\[15.6 \%\]

Convert the percentage to a decimal by dividing by 100

\[15.6\% = \frac{15.6}{100} = 0.156\]

Multiply the original amount in the question by the decimal multiplier

What is the original amount?

What is the decimal multiplier?

\[200\times0.156=31.2\]

**The answer is 31.2 kg.**

Increase

Write down the percentage. It is an increase so we need to add it to 100 \%

\[100\%+25\%=125\%\]

Convert the percentage to a decimal by dividing by 100

\[125\% = \frac{125}{100} = 1.25\]

Multiply the original amount in the question by the decimal multiplier

What is the original amount?

What is the decimal multiplier?

\[320\times1.25=400\]

**The answer is £400**.

Decrease

Write down the percentage. It is a decrease so we need to subtract it from 100 \%

\[100\%-7\%=93\%\]

Convert the percentage to a decimal by dividing by 100

\[93\% = \frac{93}{100} = 0.93\]

Multiply the original amount in the question by the decimal multiplier

What is the original amount?

What is the decimal multiplier?

\[600\times0.93=558\]

**The answer is £558**.

**Decimal multipliers greater than**1

If you need the decimal multiplier of

\[135\% = \frac{135}{100} = 1.35\]

**Take care to remember pence when you are working with money**

An answer of

1. What is the decimal multiplier of 61\% ?

0.61

6.10

610

0.061

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

So 0.61 is the multiplier.

2. What is the decimal multiplier of 5\% ?

0.5

5.00

500

0.05

5\% = \frac{5}{100} = 0.05

So 0.05 is the multiplier.

3. What is the decimal multiplier of 18.3\% ?

0.183

1.83

18.3

0.0183

18.3\% = \frac{18.3}{100} = 0.183

So 0.183 is the multiplier.

4. Work out 29\% of £400

\pounds 371

\pounds 116

\pounds 29

\pounds 429

29\% = \frac{29}{100} = 0.29

So 0.29 is the multiplier.

0.29 \times 400 = 116

5. Work out 9\% of 450 km?

45.0 km

40.5 km

441 km

50.0 km

9\% = \frac{9}{100} = 0.09

So 0.09 is the multiplier.

0.09 \times 450 = 40.5

6. Work out 14.8\% of 560 kg?

8.288 kg

412 kg

148 kg

82.88 kg

14.8\% = \frac{14.8}{100} = 0.148

So 0.148 is the multiplier.

0.148 \times 560 = 82.88

1. Write 61\% as a decimal

**(1 mark)**

Show answer

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

0.61

** (1)**

2. Work out 38\% of 600 kg

**(2 marks)**

Show answer

0.38 × 600

**(1)**

= 228 kg

**(1)**

3. Fiona is booking a holiday.

The holiday costs £700 .

She pays a 15\% deposit.

Work out how much she has left to pay.

**(2 marks)**

Show answer

100\% \hspace{1mm}- 15\% = 85\%=0.85

0.85 × 700

**(1)**

\pounds 595

**(1)**

You have now learned how to:

- Find the decimal multiplier of a percentage
- Interpret percentages and percentage changes as a decimal
- Use the decimal multiplier to work out the percentage of an amount
- Interpret percentages multiplicatively

- Reverse percentages
- Percentage increase
- Percentage decrease
- Percentage change
- Simple & compound interest
- Standard form
- Straight line graphs
- Surface area

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