What is the rule of three?
The rule of three is a mathematical method used to find an unknown value by using a proportional relationship between two known quantities. You input three values (A, B, and C), and the calculator determines the fourth (X) while preserving the proportion between A and B.
Direct rule of three
Used when two quantities are directly proportional: as one increases, the other increases at the same rate. The formula is:
X = (B × C) ÷ A
Example: If 5 kg of a product cost $20, how much do 8 kg cost? A = 5, B = 20, C = 8, so X = (20 × 8) ÷ 5 = $32.
Inverse rule of three
Used when quantities are inversely proportional: as one increases, the other decreases. The formula is:
X = (A × B) ÷ C
Example: If 3 workers build a wall in 12 hours, how many hours will 6 workers take? A = 3, B = 12, C = 6, so X = (3 × 12) ÷ 6 = 6 hours. This makes sense: with twice as many workers, the job takes half the time.
How to know which one to use
Ask yourself: when one quantity increases, does the other increase too? Use direct. When one increases, does the other decrease? Use inverse. Speed and travel time, for example, are inversely proportional: the faster you go, the less time it takes.