You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
Proportion questions ask you to determine how one quantity changes when another changes. The key skill is recognising whether the relationship is direct (both increase together) or inverse (one increases as the other decreases). This lesson covers both types with the methods for solving them.
Two quantities are in direct proportion if they increase (or decrease) at the same rate. When one doubles, the other doubles.
Ask: "If I increase X, does Y increase too?"
| Scenario | Directly Proportional? |
|---|---|
| More hours worked → more pay | Yes |
| More litres of paint → more area covered | Yes |
| More items bought → higher total cost | Yes |
| More people → less time to complete a job | No (inverse) |
The most reliable method for direct proportion:
Example: 8 pens cost £6.40. How much do 13 pens cost?
Set up equivalent ratios:
Example: 5 kg of apples cost £12.50. How much do 8 kg cost?
Find the multiplier between the known and target quantities:
Example: 12 metres of fabric costs £54. How much does 20 metres cost?
Two quantities are in inverse proportion if one increases as the other decreases, and their product is constant.
Ask: "If I increase X, does Y decrease?"
| Scenario | Inversely Proportional? |
|---|---|
| More workers → less time | Yes |
| Faster speed → less time for journey | Yes |
| Larger packs → fewer packs needed | Yes |
| More items → higher cost | No (direct) |
For inverse proportion, the product of the two quantities is constant.
Formula: X₁ × Y₁ = X₂ × Y₂
Example: 6 workers can paint a building in 10 days. How long would 15 workers take?
Example: A journey takes 3 hours at 60 km/h. How long at 90 km/h?
Alternatively:
In QR, you must quickly identify whether a problem involves direct or inverse proportion. Use this test:
"If the first quantity doubles, does the second quantity double (direct) or halve (inverse)?"
| Problem | Type | Reasoning |
|---|---|---|
| "15 textbooks cost £180. What do 25 cost?" | Direct | More books → more cost |
| "4 taps fill a pool in 6 hours. How long for 12 taps?" | Inverse | More taps → less time |
| "A car uses 8 litres per 100 km. How much for 350 km?" | Direct | More distance → more fuel |
| "A supply lasts 12 days for 5 people. How long for 8 people?" | Inverse | More people → fewer days |
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.