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Direct proportion, best buys and scales
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When two quantities are in direct proportion, doubling one doubles the other. Recipes, prices, maps and exchange rates all work this way.
The unitary method
Find the value of one, then multiply.
5 pens cost £3.50. One pen costs 3.50 ÷ 5 = £0.70. Eight pens cost 8 × 0.70 = £5.60.
A recipe for 4 people uses 300 g of flour. For 6 people: 300 ÷ 4 × 6 = 450 g.
5 pens cost £3.50. One pen costs 3.50 ÷ 5 = £0.70. Eight pens cost 8 × 0.70 = £5.60.
A recipe for 4 people uses 300 g of flour. For 6 people: 300 ÷ 4 × 6 = 450 g.
Best buys
Compare the cost of the same amount (or the amount per £1).
500 g for £2.40: 48p per 100 g.
750 g for £3.30: 44p per 100 g. The 750 g pack is better value.
500 g for £2.40: 48p per 100 g.
750 g for £3.30: 44p per 100 g. The 750 g pack is better value.
Scales and maps
A map scale of 1 : 50 000 means 1 cm on the map is 50 000 cm in real life.
6 cm on the map = 300 000 cm = 3 000 m = 3 km.
A scale drawing of 1 cm to 2 m: a 7 m wall is drawn 3.5 cm long.
6 cm on the map = 300 000 cm = 3 000 m = 3 km.
A scale drawing of 1 cm to 2 m: a 7 m wall is drawn 3.5 cm long.
£1 = €1.15. Change £40 into euros.
- Each pound is worth €1.15
- 40 × 1.15
Answer: €46
Find the value of one, then scale up. For best buys, compare the same quantity. Map scales multiply map lengths to get real lengths.
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