Every card in Ratio and proportion, Year 8: more practice
The whole deck, in order — so you can read it through before your child ever sees it.
- Red and white paint are mixed in the ratio 3 : 2. How many litres of red paint are needed to make 20 litres of the mixture? (number only)
12
HintFind the total number of parts, then the size of one part.
Why3 + 2 = 5 parts, so one part is 20 ÷ 5 = 4 litres, and red is 3 × 4 = 12 litres.
- On a map, 1 cm represents 2 km. Write the scale as a ratio 1 : n.
1 : 200 000
HintChange the kilometres into centimetres first.
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 A has 6 pens for £2.40. Pack B has 10 pens for £3.50. Which pack is the better buy?
Pack B
HintWork out the price of a single pen in each set.
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.
- A 250 g jar of jam costs £1.80. How many pence does 100 g cost? (number only)
72
HintFind the price of 1 g, or of 50 g, and then scale up.
Why£1.80 is 180p. 180 ÷ 250 = 0.72p per gram, so 100 g costs 72p.
- A cyclist rides 45 km at a steady 15 km/h. How many hours does the ride take? (number only)
3
HintRearrange speed = distance ÷ time to find time.
Whytime = distance ÷ speed = 45 ÷ 15 = 3 hours.
- A stone has a mass of 270 g and a density of 2.7 g/cm³. What is its volume?
100 cm³
HintDensity is mass ÷ volume, so volume is mass ÷ density.
Why270 ÷ 2.7 = 100, so the stone's volume is 100 cm³.
- The price of a coat falls from £80 to £68. What is the percentage decrease?
15%
HintCompare the change with the original price, not the new one.
WhyThe fall is £80 − £68 = £12, and 12/80 × 100 = 15%.
- Two people share money in the ratio 4 : 7, and the larger share is £21 more than the smaller. How much is the larger share?
£49
HintThe difference between the shares covers a known number of parts.
WhyThe difference is 7 − 4 = 3 parts, which is £21, so one part is £7. The larger share is 7 × £7 = £49.
- A toy costs $26. The exchange rate is £1 = $1.30. What does the toy cost in pounds?
£20
HintDollars to pounds means going from the bigger number to the smaller one.
Why26 ÷ 1.30 = 20, so the toy costs £20. Each £1 buys $1.30, so you divide the dollars by 1.30.
- The cost of apples is directly proportional to their mass, and 5 kg cost £8. What is the gradient of the straight-line graph of cost against mass?
£1.60 per kg
HintThe gradient of such a graph is the cost of one unit of mass.
WhyThe line passes through the origin, so gradient = 8 ÷ 5 = 1.6, which is £1.60 for each kilogram.
1★ KS3-MATH-RAT-0082
2★ KS3-MATH-RAT-0083
3★ KS3-MATH-RAT-0084
4★ KS3-MATH-RAT-0085
5★ KS3-MATH-RAT-0086
6★ KS3-MATH-RAT-0087
7★ KS3-MATH-RAT-0088
8★ KS3-MATH-RAT-0089
9★ KS3-MATH-RAT-0090
10★ KS3-MATH-RAT-0091
Keep what you learn
Here, nothing is saved. In your child’s own sky every card is scheduled — it comes back just before they’d forget it — and the professor who wrote it is one tap away.