- Define and explain Direct Proportion in your own words
- Use key terms such as Ratio accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
This lesson focuses on Direct Proportion: solve problems where two quantities grow together.
Solve problems where two quantities grow together.
Key ideas
Direct proportion
When one quantity doubles, the other doubles too — the ratio between them never changes. Recipes, currency and map scales all work this way.
Simplifying ratios
Divide every part by the same number, just like cancelling fractions: 10:15 simplifies to 2:3. A ratio in simplest form is easiest to read.
Key term — Ratio: A comparison of two or more quantities, written with a colon, such as 3:2.
A recipe for 4 pancakes uses 200 g flour and 300 ml milk. How much flour and milk are needed for 10 pancakes?
Find the scale factor: 10 ÷ 4 = 2.5. Scale the flour: 200 × 2.5 = 500 g. Scale the milk: 300 × 2.5 = 750 ml.
Answer: 500 g flour and 750 ml milk.
- Adding instead of multiplying when scaling Doubling a recipe means multiply by 2, not add 2 — scaling is always multiplication.
- Simplifying only one part of a ratio Every part must be divided by the same number, or the comparison changes.
Practice
2:3 — both divide by 6.
£24 and £16 — 5 shares of £8 each.
£12 — one notebook costs £1.50, and 8 × £1.50 = £12.
3 km — 6 × 50,000 = 300,000 cm = 3 km.
Quick check
Which of these best defines "Ratio"?
A drink mixes juice and water in the ratio 1:4. How much juice is in 500 ml of drink?
Are the ratios 4:6 and 10:15 equivalent?
- Direct Proportion: solve problems where two quantities grow together.
- Direct proportion: When one quantity doubles, the other doubles too — the ratio between them never changes.
- Proportion: A statement that two ratios are equal, such as 1:2 = 2:4.
- Watch out for: adding instead of multiplying when scaling