The rule of three is one of the most practical calculation methods in everyday life: if 3 parcels cost €7.50, what do 11 parcels cost? If 6 helpers complete a task in 4 hours, how long do 9 helpers need? These two questions describe direct proportion and inverse proportion – both can be solved instantly with our rule of three calculator.
Step by Step: How to Use the Rule of Three Calculator
- Choose the type: Decide whether the quantities are directly proportional (both increase or decrease together) or inversely proportional (one increases as the other decreases).
- Enter the known pair: Enter the starting pair, e.g. "5 kg of apples cost €8.50".
- Enter the value you're looking for: Enter the value for which you want the result, e.g. "3.5 kg".
- Read the result: The calculator shows the answer and the working steps – ideal for following along and for school assignments.
- Check your answer: For direct proportion, both ratios must be equal (a₁/b₁ = a₂/b₂).
Practical Examples
Example 1 – Scaling a recipe (direct proportion): A cake recipe for 4 people needs 320 g of flour. For 7 people: 320 / 4 × 7 = 560 g of flour. Multiply all other ingredients by the same factor of 1.75.
Example 2 – Building site (inverse proportion): 8 bricklayers lay a foundation in 6 days. Due to a deadline, 12 bricklayers are deployed. New duration: (8 × 6) / 12 = 4 days. More workers, less time – classic inverse proportion.
Example 3 – Fuel consumption (direct proportion): Your car uses exactly 17.5 litres over 250 km. How much for 780 km? 17.5 / 250 × 780 = 54.6 litres. At €1.72 per litre: €93.91 in fuel costs.
Rule of Three: Direct and Inverse Proportion
Direct proportion: 3 apples cost €1.50 → 5 apples = €2.50. Inverse proportion: 4 workers need 6 days → 3 workers need 8 days. Formula: x = (a × c) / b.
Frequently Asked Questions (FAQ)
- How do I tell whether a problem is direct or inverse proportion?
- Ask yourself: if one quantity increases, does the other also increase (direct) or decrease (inverse)? More km → more fuel = direct. More pumps → shorter fill time = inverse. Check: does the product a × b stay constant (inverse proportion) or does the ratio a/b stay constant (direct proportion)?
- What is the difference between simple and compound proportion?
- Simple proportion deals with two quantities. Compound proportion (also called "chain rule") links three or more quantities. For more complex problems, a ratio table is recommended.
- Can I use the rule of three for map scale calculations?
- Yes – map scale is a classic direct proportion problem. On a 1:50,000 map, 1 cm on the map equals 500 m in reality. If you measure 7.3 cm on the map: 7.3 × 500 m = 3,650 m = 3.65 km real distance.
