GCSE Mathematics

Ratio & Proportion

Aims

• To simplify ratios• To write ratios in unitary form• To compare ratios and fractions

What is a Ratio

• What is a ratio?

Notation

This is read as 2 to 3.It means that for every 2 units of the first quantity there are 3 units of the second.

2 : 3

Maps

• For example scales on a map 1:2000

Scale Models

Scale models 1:25

Recipes

If you had a recipe that used 100g of margarine to 250g of flour, the ratio of margarine to flour is 100 : 250.

Ratios

There are a few ways of expressing ratios.

Simplest Form

Unitary Form

Equivalent Form

Simplest Form

• If a ratio is in its simplest form the numbers do not share a common factor.

• The numbers are whole numbers. • Simplifying ratios is similar to

simplifying fractions.

Question

• Write down the ratio 100 : 250 in its simplest form.

:2 5

:100 250÷ 50 ÷ 50

Question

• Write down a ratio that is equivalent to

2 : 5

Question

• Write down the ratio 2 : ½ in its simplest form.

:2x 2 2 x ½

:2 ½ x2 x2

:4 1

Question

• Write down the ratio 1.1 : 0.2 in its simplest form.

:1.1 x 10 0.2 x 10

:1.1 0.2x10 x10

:11 2

Unitary Form

Ratios expressed in unitary form are either of the form

1 : nOr

n : 1In these cases n may be a fraction or a decimal

Unitary Form

Write the ratio 6 : 10 in the form 1 : n

:6 ÷ 6 10 ÷ 6

:6 10÷ 6 ÷ 6

:1

This side needs to be 1

61 .

Unitary Form

Write the ratio 6 : 10 in the form n : 1

:6 ÷ 10 10 ÷ 10

:6 10÷ 10 ÷ 10

:0.6 1

This side needs to be 1

Question

• Write the ratio 40 : 10 1. In its simplest form

2. In the form 1 : n

Solutions

Write the ratio 40 : 10 In its simplest form

4 : 1

In the form 1 : n 1 : 0.25

Divide both sides by 10

Divide both sides by 40