Two quantities are in direct proportion if the graph of one quantity against the other quantity is a straight line through the origin.

So if one quantity doubles then the other quantity doubles.

Number of apples sold

Cos

t of

app

les

($)

1 The cost of five apples is $3.25. What is the cost of eight apples?

5 apples cost $3.25

1 apple cost $3.25 ÷ 5 =

8 apples cost $0.65 × 8 =

$0.65

$5.20

2 The recipe is for making cakes. The mixture will make two cakes. Helen wants to make seven cakes. Calculate the amount of each ingredient needed.

RECIPE:

200 g butter

160 g sugar4 eggs

150 g self-raising

flour1 tsp vanilla

essence

RECIPE:

200 g butter

160 g sugar4 eggs

150 g self-raising

flour1 tsp vanilla

essence

BUTTER: (200 ÷ 2) × 7 = 700 g

SUGAR: (160 ÷ 2) × 7 = 560g

EGGS: (4 ÷ 2) × 7 = 14 eggs

SELF-RAISING FLOUR: (150 ÷ 2) × 7 = 525 g

VANILLA ESSENCE: (1 ÷ 2) × 7 = 3.5 tsp

Two quantities are in inverse proportion if one quantity increases at the same rate as the other quantity decreases.So if one quantity doubles the other quantity halves.

1 It takes two men six hours to paint a fence. How long would it take three men to paint the

same fence?

2 men take 6 hours

1 man will take 2 × 6 hours =

3 men will take 12 ÷ 3 hours =

12 hours

4 hours

CHIRP

BIRD SEED

CHIRP

BIRD SEED

2 A box of bird seed lasts 5 birds 15 days. How long would the same packet of bird seed

last 30 birds?

5 birds for 15 days

1 bird for 15 × 5 days =

30 birds for 75 ÷ 30 days =

75 days

2.5 days

The graph can be used to convert between UK pounds (£) and US dollars ($).

0 20 40 60 80 1000

80

120

160

200

40

UK pounds (£)

US

dol

lars

($)

a Use the graph to convert £70 to US dollars. £70 ≈ $116

b Use the graph to convert $60 to UK pounds. $60 ≈ £36