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Rule of three
If A is to B, then C is to D:
Practical examples
| Situation | Math | Result |
|---|---|---|
| 3 lb cost $12; how much do 5 lb cost? | 12 × 5 ÷ 3 | $20 |
| Recipe for 4 people uses 300 g; for 7? | 300 × 7 ÷ 4 | 525 g |
| Car covers 380 mi on 30 gal; fuel for 950 mi? | 30 × 950 ÷ 380 | 75 gal |
Direct or inverse?
Direct: D = B × C ÷ A · Inverse: D = A × B ÷ C
The direct rule applies when quantities grow together (more pounds → more dollars). The inverse rule applies when one grows and the other shrinks: if 4 workers take 12 days, 8 workers take 4 × 12 ÷ 8 = 6 days. Doubling the crew halves the time. The classic mistake is applying the direct rule to an inverse problem; always ask: "if A doubles, does D double or halve?"
Last updated: · Methodology and sources