Proportion
Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations
What a learner can do afterwards
- Identify whether a real-world relationship is direct or inverse proportion and justify the choice
- Set up and solve a direct-proportion equation (e.g. if 4 pens cost £6, find the cost of 10)
- Sketch graphs showing direct proportion (straight line through origin) and inverse proportion (curve)
The lesson
You already know that direct proportion makes a straight line through the origin. Two quantities are in direct proportion when their ratio always stays the same, so one quantity is always a fixed multiple of the other.
4 pens cost £6. Find the cost of 10 pens. First find the cost of one pen: £6 ÷ 4 = £1.50. Then multiply by 10: £1.50 × 10 = £15.
Inverse proportion works the opposite way. As one quantity goes up, the other goes down, and their product always stays the same fixed number.
To tell the two apart, check what stays fixed. If dividing one quantity by the other gives the same number every time, it's direct proportion. If multiplying them together gives the same number every time, it's inverse proportion.
In direct proportion one quantity is a constant multiple of the other, but in inverse proportion one goes up as the other goes down and their product stays fixed.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.