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

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