# Use multipliers to calculate percentage increase and decrease

## Home learning focus

Learn how to calculate percentage increase and decrease using multipliers.

This lesson includes:

- two videos
- a learning summary
- four activities

*Created in partnership with NCETM*

# Learn

## Percentage increase

By understanding how any two numbers can be connected by a single multiplier you can calculate percentage increase and decrease quickly and efficiently.

Imagine if you had to increase a sum of money by 50%. In this situation most people would probably just work out what half of the amount was (ie 50%) and then add it on to the original amount. For example, £1.24 increased by 50% would result in the calculation £1.24 + £0.62 (so half of £1.24) which gives £1.86. Easy!

But, reaching this answer has required **two** steps:

**1.** £1.24 × 0.5 (to find 50% of £1.24) = £0.62

**2.** £0.62 + £1.24 = £1.86

It's better to be able to find the answer in **one** go, making your percentage increases (*or* decreases) quicker and more accurate.

Another way to think about it is to imagine that your resulting amount is 1.5 times as big as your starting amount, so instead, you can write the calculation as '× 1.5':

£1.24 **→** × 1.5 **→** £1.86

This calculation describes **two** operations (finding 50% of the original amount and then adding it on) all in **one** operation.

To check, use a calculator to make sure that 1.24 × 1.5 gives the same answer as finding 50% (or half) of the starting amount first, and then adding it on.

Watch this short video from BBC Bitesize to look at calculating percentage increases in more depth, using **decimal methods** (as in the last example).

Work through the step-by-step slideshow next to check your understanding.

Increasing something by 25% means needing to work out 25% (× 0.25) and adding it on to the original quantity. In other words: 1.25 of the original value or × 1.25.

To check, you can try the original two-step method at the start of this guide. Find 25% of £1.24 by dividing 1.24 by 4 (or multiplying it by 0.25) and then adding that amount on. This is the same as multiplying by 1.25.

## Percentage decrease

In a similar way to increasing by a percentage, *decreasing* by a percentage means finding a percentage and then **subtracting**.

For example, to decrease £6.00 by 20%, you need to find 20% of £6.00 first, and then subtract that amount from the original total.

Using the two-step method:

**1.** £6.00 × 0.2 (20% as a decimal) = £1.20

**2.** £6.00 - £1.20 = £4.80

This is the same as multiplying £6.00 by 0.8 (1.0 - 0.2)

£6.00 × 0.8 = £4.80

Again, to check, use a calculator to make sure that £6.00 × 0.8 gives the same answer as finding 20% of the starting amount first (by multiplying it by 0.2), and then subtracting it from £6.00.

Now watch this short video from BBC Bitesize to look further at calculating percentage decrease, again using the decimal method.

Work through the accompanying step-by-step slideshow too, to check your understanding.

# Practise

## Activity 1

**Percentage increase skills**

To get you testing your knowledge, first have a go at these two percentage increase activities from BBC Bitesize.

## Activity 2

**Percentage decrease skills**

Now try this activity that deals with percentage decrease, again from BBC Bitesize.

## Activity 3

**Interactive activity - real-life situations**

Check out this interactive activity from MyMaths (Oxford University Press) to test your knowledge of percentage increase and decrease. Click on the 'Practice' tab to enter the activity.

## Activity 4

**Extension - test**

Finally, have a go at this test on percentage increase and decrease from BBC Bitesize.

# There's more to learn

Have a look at these other resources around the BBC and the web.