Dreisatz-Rechner

Was ist der rule of three?

The rule of three is the most widely used method of proportional calculation in applied math. It lets you find an unknown value when you know three related values through a direct proportion (more of one, more of the other) or inverse proportion (more of one, less of the other). It's essential in cooking, commerce, engineering, and everyday life.

Rule of three formulas

Direct rule of three: If A→B, what corresponds to C?
x = (B × C) / A

Inverse rule of three: If A→B with an inverse relationship, what corresponds to C?
x = (A × B) / C

The key distinction: in direct proportionality, both quantities increase together. In inverse proportionality, when one increases the other decreases.

Step-by-step examples

Direct: If 3 kg of apples cost $7.50, how much do 5 kg cost?

1. 3 kg → $7.50
2. 5 kg → x = (7.50 × 5) / 3 = $12.50

Inverse: 4 workers take 6 days to finish a job. How long do 8 workers take?

1. 4 workers → 6 days
2. 8 workers → x = (4 × 6) / 8 = 3 days

Practical applications

• Recipes: Scale ingredients for 4 people when a recipe serves 6.
• Shopping: Compare unit prices between different package sizes.
• Maps and blueprints: If 1 cm on the map equals 50 km, what real distance does 3.5 cm represent?
• Speed and time: If a vehicle covers 120 km in 1.5 h, how long to cover 450 km?
• Finance: Calculate commissions, interest, or proportional distributions.

Häufige Fehler vermeiden

• Always identify the two quantities: In "more km, more time" the two quantities are distance and time — a direct relationship.
• Verify proportionality: Not all value pairs are proportional. A taxi fare with a fixed charge plus variable rate can't be solved with simple rule of three alone.
• Check units: If one quantity is in kg and another in grams, convert before applying the formula.