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- Direct and inverse proportion
Direct and inverse proportion
When two quantities are in proportion, knowing one tells you the other. Find the value of one first.
Direct proportion
As one doubles, the other doubles.
5 pens cost £3.50, so 1 pen costs £0.70, and 8 pens cost £5.60.
This is the unitary method.
5 pens cost £3.50, so 1 pen costs £0.70, and 8 pens cost £5.60.
This is the unitary method.
Best buys
Compare the cost of one unit (per gram, per item) to find better value.
500 g for £2.40 is 0.48p per gram. 750 g for £3.45 is 0.46p per gram, which is better value.
500 g for £2.40 is 0.48p per gram. 750 g for £3.45 is 0.46p per gram, which is better value.
Inverse proportion
As one doubles, the other halves.
4 workers take 6 days. 1 worker takes 24 days. 3 workers take 8 days.
The total amount of work (workers × days) stays the same.
4 workers take 6 days. 1 worker takes 24 days. 3 workers take 8 days.
The total amount of work (workers × days) stays the same.
6 builders take 10 days to build a wall. How long would 4 builders take?
- Total work = 6 × 10 = 60 builder-days
- 60 ÷ 4 = 15
Answer: 15 days
Direct proportion: find the value of one, then multiply. Inverse proportion: the product stays constant, so more of one means less of the other.
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