Ratio and proportion, Year 8: more practice

12

HintFind the total number of parts, then the size of one part.

The why3 + 2 = 5 parts, so one part is 20 ÷ 5 = 4 litres, and red is 3 × 4 = 12 litres.

1 : 200 000

HintChange the kilometres into centimetres first.

The why2 km = 2000 m = 200 000 cm, so 1 cm on the map stands for 200 000 cm, giving 1 : 200 000. A ratio scale needs both sides in the same unit.

Pack B

HintWork out the price of a single pen in each set.

The whyPack A is £2.40 ÷ 6 = 40p a pen. Pack B is £3.50 ÷ 10 = 35p a pen. Pack B is cheaper per pen, so it is better value.

72

HintFind the price of 1 g, or of 50 g, and then scale up.

The why£1.80 is 180p. 180 ÷ 250 = 0.72p per gram, so 100 g costs 72p.

3

HintRearrange speed = distance ÷ time to find time.

The whytime = distance ÷ speed = 45 ÷ 15 = 3 hours.

100 cm³

HintDensity is mass ÷ volume, so volume is mass ÷ density.

The why270 ÷ 2.7 = 100, so the stone's volume is 100 cm³.

15%

HintCompare the change with the original price, not the new one.

The whyThe fall is £80 − £68 = £12, and 12/80 × 100 = 15%.

£49

HintThe difference between the shares covers a known number of parts.

The whyThe difference is 7 − 4 = 3 parts, which is £21, so one part is £7. The larger share is 7 × £7 = £49.

£20

HintDollars to pounds means going from the bigger number to the smaller one.

The why26 ÷ 1.30 = 20, so the toy costs £20. Each £1 buys $1.30, so you divide the dollars by 1.30.

£1.60 per kg

HintThe gradient of such a graph is the cost of one unit of mass.

The whyThe line passes through the origin, so gradient = 8 ÷ 5 = 1.6, which is £1.60 for each kilogram.