Proportion · Year 11
In Year 11 you learn: proportion equations.
Two quantities are in direct proportion when they grow together at the same rate: twice as many tickets cost twice as much. In inverse proportion one goes up as the other goes down: twice as many workers take half the time. The unitary method — find the value of one — solves almost every proportion problem.
Key facts
- Direct proportion: both quantities are multiplied by the same number.
- Inverse proportion: when one is multiplied by k, the other is divided by k. Their product stays the same.
- Exchange rates: multiply to change into the new currency; divide to change back.
Worked examples
Example 1
6 builders take 10 days to build a wall. How long would 4 builders take, working at the same rate?
Answer: 15 days