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Ratio

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# Using ratios

Ratios are used in everyday life and can help you work out problems including scale drawings and reading maps.

## Scale drawing

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

### Example

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

Question

a) If the 1:20 model boat is 15cm wide, how wide is the actual boat?
b) If the boat has a mast of height 4m, how high is the mast on the model?

The scale is 1:20. This means that every cm on the model is equivalent to 20cm on the boat.

a) 1cm on the model = 20cm on the boat, so:
15cm × 20 = 300cm.
15cm on the model = 300cm (3m) on the boat

b) 20cm on the boat = 1cm on the model
so mast height on real boat ÷ 20 = mast height on model
400cm (4m) on the boat = 400cm ÷ 20 = 20cm on the model

## Map scales

Maps scales can be written in ratios and tell you how many units of land, sea etc are equal to one unit on the map.

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

### Example

The scale of a map is 1:50 000. A distance is measured as 3cm on the map.
How many cm, m and km is this equivalent to in real life?

1 cm on the map represents 50 000cm. Therefore, 3cm on the map represents 150 000cm.
To convert from cm to m, divide by 100.
150 000cm ÷ 100 = 1500m
To convert from m to km divide by 1000.
1500m ÷ 1000 = 1.5km

Question

The scale of a map is 1:50 000. What distance on the map will represent 5km?