When do you use the inverse rule of three?

When increasing one quantity decreases the other proportionally, such as speed and travel time, or number of workers and days of work.

What is the formula for the direct rule of three?

If A is to B as C is to X, then X = B × C ÷ A. For example: if 3 cost 12, then 5 cost 12 × 5 ÷ 3 = 20.

Calculators

Rule of three calculator

Solve proportions in a second: if A corresponds to B, what corresponds to C? Available in direct form (more, more) and inverse form (more, less).

is to B

as C

is to X

Direct: more A, more B (price per unit, recipe ingredients…).

X =—

X = B × C ÷ A

Direct and inverse rule of three

The direct rule of three is used when the quantities are proportional: if 3 kilos cost €12, then 5 kilos will cost X = 12 × 5 ÷ 3 = €20. More quantity, more cost.

The inverse form applies when one quantity grows as the other shrinks: if 4 workers take 6 days, then 8 workers will take X = 4 × 6 ÷ 8 = 3 days. More workers, fewer days. Correctly identifying the type of proportion is the key to getting it right.

Rule of three calculator

Direct and inverse rule of three

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