Practical uses of ratios

Home learning focus

Today we’re looking at the ways ratios can be used in everyday life. Including sharing money, using maps and scale drawings.

This lesson includes:

  • two videos
  • two interactive activities

Learn

Sharing money

Dave and Lisa win £500 between them. They agree to divide the money in the ratio 2:3.

How much does each person receive?

Answer

The ratio 2:3 tells us that for every £2 that Dave receives, Lisa will receive £3.

In other words, the total amount, Dave will receive 2 parts and Lisa will receive 3 parts. This means that there are 5 parts in total.

£500 represents 5 parts. Therefore, £100 represents 1 part.

Dave receives 2 parts: 2 x £100 = £200

Lisa receives 3 parts: 3 x £100 = £300

Map scales

Map scales can be written in ratios and tell us how many units of length on land, or sea, are equal to one unit of length on a map.

For example, if you are travelling from Manchester to Newcastle and need to know how far it is, it would be very difficult to work this out from a map if the map does not have a scale.

Example

The scale of a map is 1:50,000. 1 cm on the map represents 50,000 cm.

To convert from cm to m, divide by 100.

50,000 cm ÷ 100 = 500 m

Each cm on the map is 500 m or 0.5 km.

Watch the video below and find out what happens if a map scale isn’t used properly.

Scale drawings and models

In a scale drawing or model, all dimensions have been reduced by the same proportion.

Example

A model boat is made to a scale of 1:20. This scale can be applied to any units, so 1 mm measured on the model is 20 mm on the actual boat. 1 cm measured on the model is 20 cm on the actual boat.

Practise

Activity 1

Scale drawing video

Watch this video about making a scale drawing of a football pitch then have a go at making a scale drawing yourself!

A short video showing how to make a scale drawing of a football pitch, based on the FIFA standard pitch size for World Cup and UEFA Champions League matches.

Scale drawing activity

Using a tape measure, calculator, paper and pencil; make a scale drawing of a room in your house.

Add the table, chair, bed, even you and your pets - make sure to use the same scale for everything.

Activity 2

Sharing an amount worksheet

Have a go at this worksheet from Twinkl below on sharing an amount into a given ratio.

Sharing an amount into a given ratio

Finished? Check your answers here.

There's more to learn

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

KS3 Maths
BBC Bitesize Daily
How to write a song
11-14 Maths
See an exhibit from home
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