What is the rule of three
The rule of three is used to solve proportionality problems between two or more quantities: given that A is to B as C is to an unknown value X, the rule of three finds X.
Direct proportion
When the quantities are directly proportional (as one increases, the other increases in the same ratio): X = (B × C) / A. Example: if 3 items cost $30, how much do 7 items cost? X = (30 × 7) / 3 = $70.
Inverse proportion
When the quantities are inversely proportional (as one increases, the other decreases in the same ratio): X = (A × B) / C. Example: if 4 workers finish a job in 12 days, how many days would 6 workers take? X = (4 × 12) / 6 = 8 days.
How to tell direct from inverse
Ask yourself: as one quantity increases, does the other also increase (direct) or decrease (inverse)? Price and quantity is usually direct; number of workers and time to finish a job is usually inverse.
Frequently asked questions
How do I know whether to use direct or inverse proportion?
Think about whether, as one quantity increases, the other also increases (direct) or decreases (inverse). Total price and quantity is a direct example; speed and travel time is an inverse example.
Does this calculator solve a compound rule of three (three or more quantities)?
No — this calculator only solves the simple rule of three, with two quantities involved.