Complete guide: Rule of Three
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The rule of three solves proportions: if 2 kg of apples cost 10, how much do 5 kg cost? The answer is 25, because X = B × C ÷ A. It is one of the most useful math tools in daily life: recipes, prices, distances, doses and times.
The inverse rule of three applies when the quantities move in opposite directions: if 2 workers take 10 hours, 5 workers take less, not more. There X = A × B ÷ C. Choosing correctly between direct and inverse is the key: ask yourself whether increasing one quantity increases the other (direct) or decreases it (inverse).
Everyday examples: a car that travels 300 km on 20 liters, how many liters does it need for 450 km? Direct: 20 × 450 ÷ 300 = 30 liters. A job that 4 people finish in 12 days, how long do 6 take? Inverse: 4 × 12 ÷ 6 = 8 days.
How it works
- 1Direct: X = B × C ÷ A (both quantities grow together).
- 2Inverse: X = A × B ÷ C (one grows while the other falls).
- 3Enter A, B and C and get X instantly.
Frequently asked questions
When do I use the inverse rule of three?
When increasing one quantity decreases the other: more workers, less time; more speed, fewer travel hours.
How do I know if it is direct or inverse?
Ask yourself: if A doubles, does the result double (direct) or halve (inverse)?