Rule of three (proportions)
Enter three values and find the fourth: A is to B as C is to X. Choose between direct and inverse proportion, with the calculation explained step by step.
Example: a recipe for 6 people (A) needs 4 eggs (B); for 9 people (C), how many eggs (X)? Answer: 6.
Direct or inverse rule of three: what's the difference?
The direct rule of three applies when the two quantities grow together: more guests at dinner, more pasta to cook; more pounds of fruit, more dollars to pay. The formula is X = B × C ÷ A. The inverse rule applies when one quantity grows while the other shrinks: more workers on the job, fewer days to finish; more speed, less travel time. In that case X = A × B ÷ C. Picking the wrong type is the most common mistake — always ask yourself: "if A doubles, does X double or get cut in half?"
Real-world examples: recipes and prices
A recipe for 4 people calls for 2 cups of rice, but you're cooking for 6? Direct: 2 × 6 ÷ 4 = 3 cups. Coffee costs $12 per pound and you want 2.5 lb? Direct: 12 × 2.5 ÷ 1 = $30. Three painters finish a room in 8 hours — how long would two take? Inverse: 3 × 8 ÷ 2 = 12 hours. Once you get the pattern down, the rule of three instantly solves everyday servings, discounts, fuel use, and unit conversions.