How to use the rule of three calculator
- Choose the type: direct if more of one thing means more of the other (more apples cost more), inverse if more of one means less of the other (more workers need fewer days).
- Enter the known pair in the first row, for example 3 kg → $7.50.
- Enter the new value in the second row, for example 5 kg. The answer x appears instantly, together with the three steps of the working.
Direct and inverse proportion
The rule of three works by going through one unit. In a direct proportion you divide both sides by the first value, then multiply both by the new one: 3 kg cost $7.50, so 1 kg costs $2.50 and 5 kg cost $12.50.
In an inverse proportion one side is divided while the other is multiplied: 4 workers need 6 days, so 1 worker needs 24 days and 3 workers need 8 days.
| Type | Formula | Example |
|---|---|---|
| Direct | x = B ÷ A × C | 7.50 ÷ 3 × 5 = 12.50 |
| Inverse | x = B × A ÷ C | 6 × 4 ÷ 3 = 8 |
Everyday examples
- Recipes: a recipe for 4 people needs 300 g of flour; for 6 people you need 450 g (direct).
- Fuel: 40 litres take you 600 km; 25 litres take you 375 km (direct).
- Speed and time: at 60 km/h a trip takes 2 hours; at 80 km/h it takes 1.5 hours (inverse).
- Supplies: food for 10 hikers lasts 6 days; for 12 hikers it lasts 5 days (inverse).
Frequently asked questions
How do I know whether a problem is direct or inverse?
Ask what happens when the first quantity doubles. If the second one doubles too, it is direct. If it halves, it is inverse.
What if neither type fits?
Some relationships are not proportional at all, for example a taxi fare with a fixed base charge. The rule of three then gives a wrong answer.
Can I use decimals?
Yes, with a decimal point. Thousands separators such as 1,250 are understood as well.