# Finding a percentage of an amount using a multiplier

## Home learning focus

In this lesson, you will learn how to find percentages of amounts using decimal multipliers. You will need a calculator.

This lesson includes:

- a learning summary
two activities

*Created in partnership with Numerise.*

# Learn

### Recap: Finding percentages of amounts by hand

You should have already learnt how to find percentages of amounts by hand (without a calculator), but here is a quick recap.

If you needed to find 15% of 400 by hand, then there are a couple of different methods you could use:

**Method 1: Find 1% of 400 and then multiply by 15**

To find **1%** of a number, you divide by **100**, so:

1% of 400

400 ÷ 100 = 4

1% of 400 = 4

**15%** is **15 lots of 1%**, so:

15% of 400

15 × 4 = 60

15% of 400 = *60*

**Method 2: Add together 10% and 5% of 400**

You can break 15% into smaller percentages, for example:

15% = 10% + 5%

To find 10% of a number, divide by 10, so:

10% of 400

400 ÷ 10 = 40

5% is half of 10%, so 5% of 400 is half of 40, which is 20

15% of 400 = 10% of 400 + 5% of 400

15% of 400 = 40 + 20

15% of 400 = *60*

## Finding percentages of amounts using a decimal multiplier

Sometimes **Method 1** and **Method 2** can be slow, or the percentage may be hard to break down into smaller chunks. In these cases, you can use **decimals**.

Remember, percentages can be written as decimals. Look at the diagram below.

For our 15% of 400 example above, 15% written as a decimal is 0.15

You can use the decimal equivalent of a percentage to help us find percentages of amounts - you just need to multiply the amount by the decimal.

So to find 15% of 400, you would multiply **0.15** by **400**. You can use a calculator.

0.15 × 400 = **60**

## Example: Find 27% of 300

First, rewrite 27% as a decimal.

27 ÷ 100 = 0.27

27% = 0.27

Then, use a calculator to multiply the original amount by the decimal multiplier.

0.27 × 300 = 81

So, 27% of 300 is **81**.

## Example: Find 36.2% of 640

First, rewrite 36.2% as a decimal.

36.2 ÷ 100 = 0.362

36.2% = 0.362

Then, use a calculator to multiply the original amount by the decimal multiplier.

0.362 × 640 = 231.68

So, 36.2% of 640 is **231.68**.

## Example: Find 112% of 86

Here the percentage is greater than 100%, but you can still use the same method.

First, rewrite 112% as a decimal.

112 ÷ 100 = 1.12

112% = 1.12

Then, use a calculator to multiply the original amount by the decimal multiplier.

1.12 × 86 = 96.32

So, 112% of 86 is **96.32**.

# Practise

## Activity 1

**Worksheet: Decimal multipliers**

Practise finding percentages of amounts using this worksheet from Numerise.

You can print it out or write your answers on a piece of paper.

You will need to use a calculator, but don’t forget to write down your workings!

## Activity 2

**Worksheet: Finding the percentage of an amount using a multiplier**

Have a go at this worksheet from Beyond where you have to find the percentage of amounts using a multiplier. You can print it out or write your answers on a piece of paper.

Finished? Click here for the answer sheet.