Using ratios

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

Scale drawings

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. 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.

Question

a) If the 1:20 model boat is {15}~{cm} wide, how wide is the actual boat?

b) If the boat has a mast of height {4}~{m}, how high is the mast on the model?

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

The mathematical symbol for equivalent is: ≡

a) {1}~{cm} on the model ≡ {20}~{cm} on the boat

So, because: {15}\times{20}={300}

{15}~{cm} on the model ≡ {300}~{cm} (or {3}~{m}) on the boat

b) {20}~{cm} on the boat ≡ {1}~{cm} on the model

So, because: {4}~{m}={400}~{cm},

and {400}\div{20}={20}

{4}~{m} (or {400}~{cm}) on the boat ≡ {20}~{cm} on the model