Percentage multipliers

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

Place value Arithmetic Percentages to decimal

This topic is relevant for:

GCSE Maths Number Percentages

Percentage Multipliers

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.

What is a percentage multiplier?

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% of a number we can multiply the number by a multiplier:

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

So 0.12 is the multiplier.

What is a percentage multiplier?

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.

How to find a decimal multiplier from a percentage

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

Explain how to write a decimal multiplier from a percentage in 3 steps

Percentage multipliers worksheet

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

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Percentage multipliers worksheet

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

DOWNLOAD FREE

Percentage multiplier examples

Example 1: finding the decimal multiplier

What is the decimal multiplier for $58 \%$ ?

Write down the percentage required

\[58 \%\]

2Convert the percentage to a decimal by dividing by 100

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

The decimal multiplier is 0.58.

Example 2: finding the decimal multiplier

What is the decimal multiplier for 26%?

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.

Example 3: finding the decimal multiplier

What is the decimal multiplier for 4.5%?

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.

How to use a percentage multiplier to calculate the percentage of an amount

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

Example 4: finding the percentage of an amount

Work out 34% of £700

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? 700

What is the decimal multiplier? 0.34

\[700\times0.34=238\]

The answer is £238.

Example 5: finding the percentage of an amount

Work out 8% of £650

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? 650

What is the decimal multiplier? 0.08

\[650\times0.08=52\]

The answer is £52.

Example 6: finding the percentage of an amount

Work out 15.6% of 200 kg

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? 200

What is the decimal multiplier? 0.156

\[200\times0.156=31.2\]

The answer is 31.2 kg.

Example 7: calculating a percentage increase

Increase £320 by 25%

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? 320

What is the decimal multiplier? 1.25

\[320\times1.25=400\]

The answer is £400.

Example 8: calculating a percentage decrease

Decrease £600 by 7%

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? 600

What is the decimal multiplier? 0.93

\[600\times0.93=558\]

The answer is £558.

Common misconceptions

Decimal multipliers greater than 1

If you need the decimal multiplier of 135% it would be 1.35, so multipliers can in fact be greater than 1.

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

Take care to remember pence when you are working with money

An answer of £43.7 should be written as £43.70. You need two decimal places for the pence part of the answer.

Percentage multipliers 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:

Practice percentage multiplier questions

$0.61$

$6.10$

$610$

$0.061$

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

So $0.61$ is the multiplier.

$0.5$

$5.00$

$500$

$0.05$

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

So $0.05$ is the multiplier.

$0.183$

$1.83$

$18.3$

$0.0183$

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

So $0.183$ is the multiplier.

$\pounds 371$

$\pounds 116$

$\pounds 29$

$\pounds 429$

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

So $0.29$ is the multiplier.

0.29 \times 400 = 116

$45.0$ 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

$8.288$ 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

Percentage multiplier GCSE questions

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

$0.38 \times 600$

(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

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

$0.85 \times 700$

(1)

$\pounds 595$

(1)

Learning checklist

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

Next lessons

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