Direct and Inverse Rule of Three: When to Use Each with Examples
thecalculator.tech
20 June 2026 · 4 min read
The difference between direct and inverse proportion, how to identify which applies to each problem, and solved exercises on price, speed, mixtures and more.
Direct proportion: more of one, more of the other
Two quantities are directly proportional when multiplying one by a factor k also multiplies the other by k. Examples: price and quantity (if you buy twice as much, you pay twice as much); time and distance at constant speed. Formula: if A/B = C/X, then X = B × C / A.
Inverse proportion: more of one, less of the other
Two quantities are inversely proportional when multiplying one by k divides the other by k. Examples: number of workers and time to complete a task (more workers → less time); speed and time to cover a fixed distance. Formula: A × B = C × X, so X = A × B / C.
How to identify the type
Ask yourself: if I increase the first quantity, does the second increase (direct) or decrease (inverse)? If 3 workers take 10 days, do 6 workers take more or less? → Less. It's inverse. If 3 kg cost €9, do 6 kg cost more or less? → More. It's direct.
Solved example: mixtures
A recipe for 4 people needs 300 g of flour. How much for 7 people? Direct: 4 people → 300 g; 7 people → X. X = 7 × 300 / 4 = 525 g. Another example: if one tap fills a tank in 6 hours, how long do 4 taps take? Inverse: 1 × 6 = 4 × X; X = 6/4 = 1.5 hours.
Results are exact for perfect proportionality relationships. Real-world problems may have factors that alter proportionality.
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