What is the rule of three?
The rule of three is a method for calculating a fourth, unknown value from three known values. It is based on the principle of proportionality: when one quantity changes, another quantity changes in the same (proportional) or inverse (inversely proportional) ratio.
Proportional rule of three (direct ratio)
In the proportional rule of three, more of one quantity means more of the other. Example: 5 rolls cost €4.50. How much do 8 rolls cost?
| Step | The invoice | Result |
|---|---|---|
| 1. Initial value | 5 rolls | €4.50 |
| 2. Value for 1 unit | €4.50 ÷ 5 | €0.90 |
| 3. Value for 8 units | €0.90 × 8 | €7.20 |
Inverse proportion (inverse ratio)
In the inverse proportion rule, a larger quantity of one quantity means a smaller quantity of the other. Example: 4 workers need 6 hours to complete a task. How long will it take 3 workers?
| Step | The invoice | Result |
|---|---|---|
| 1. Initial value | 4 workers | 6 hours |
| 2. Total working time | 4 x 6 hours | 24 person-hours |
| 3. Time for 3 workers | 24 ÷ 3 | 8 hours |
Key characteristic: Ask yourself: “If the first quantity increases, will the second quantity also increase or decrease?” If it also increases → proportionally. If it decreases → inversely proportionally.
Rule of three in percentage calculations
Percentage calculations are always a proportional rule of three, where the base value corresponds to 100%:
| Step | percent | Value |
|---|---|---|
| 1 | 100% | Base value (e.g. 200) |
| 2 | 1% | 200 ÷ 100 = 2 |
| 3 | 15% | 2 × 15 = 30 |
Common areas of application
- Mathematics lessons, grades 7 and 8 (proportional/inversely proportional relationships)
- Value added tax and discount calculations in retail
- Converting recipe quantities (e.g. for more or fewer people)
- Currency conversions and scale calculations
- Working time and personnel planning in the workplace