Ratio and proportion, Year 7: proportion tables and scale drawings

£1.50

HintFind the cost of one pen first.

The whyOne pen costs 90 ÷ 3 = 30p, so five cost 5 × 30 = 150p.

2.5

HintDivide an output by the input that made it.

The why10 ÷ 4 = 2.5 and 15 ÷ 6 = 2.5. In a proportion table every pair is linked by the same multiplier.

500 g

HintWork out the flour for one biscuit.

The why200 ÷ 8 = 25 g for each biscuit, and 20 × 25 = 500 g. Or notice that 20 is 2.5 times 8.

6 kg for £10

HintCheck the price of 1 kg in each column.

The why2 kg for £3 and 4 kg for £6 are both £1.50 per kilogram. At that rate 6 kg should cost £9.

8

HintFind the price of a single ticket.

The whyOne ticket costs 40 ÷ 5 = £8, and 64 ÷ 8 = 8 tickets.

8 m

HintEach centimetre on paper stands for the same real length.

The why4 cm on the plan is 4 lots of 2 m, which is 8 m.

3.5 cm

HintThe number stays; only the unit changes.

The whyEach metre becomes one centimetre, so 3.5 m is drawn as 3.5 cm, which is 35 mm on the ruler.

1 : 100

HintPut both lengths into centimetres.

The why1 m is 100 cm, so 1 cm on the paper stands for 100 cm in real life. A ratio scale has no units because both sides use the same one.

6 cm

HintThis time you are going from real life down to paper, so divide.

The why30 ÷ 5 = 6, so the garden is drawn 6 cm long.

1 m

HintMultiply, then change the unit.

The why2 × 50 = 100 cm, and 100 cm is 1 m.