Proportion (Edexcel GCSE Maths): Revision Notes
Proportion
What is proportion?
Proportion describes the relationship between two quantities and how they change relative to each other. Understanding how quantities relate to each other is essential for solving many real-world problems. There are two main types of proportion you need to understand for your GCSE exam.
Direct proportion
Direct proportion occurs when two quantities increase or decrease at the same rate. As one quantity gets bigger, the other gets bigger in the same proportion. As one gets smaller, the other gets smaller in the same proportion.
For example, if you buy more cinema tickets, the total cost increases. If you buy 3 tickets for £135, then buying 9 tickets (3 times as many) will cost £405 (3 times as much).
The key feature is that both quantities change in the same direction - if one doubles, the other doubles too.
Inverse proportion
Inverse proportion occurs when one quantity increases at the same rate as another quantity decreases. As one gets bigger, the other gets smaller in a predictable way.
For example, if you travel faster, your journey time decreases. At 40 km/h, a journey takes 2 hours. At 80 km/h (twice as fast), the same journey takes 1 hour (half the time).
The key feature is that the quantities change in opposite directions - if one doubles, the other halves.
Working with direct proportion
When solving direct proportion problems, you need to find the rate or cost per unit first, then scale up or down accordingly.
Worked Example: Picture Frame Cost
Suresh buys 4 picture frames for £11.40. Calculate the cost of 7 frames.
Step 1: Find the cost of 1 frame Cost of 1 frame = £11.40 ÷ 4 = £2.85
Step 2: Calculate the cost of 7 frames
Cost of 7 frames = £2.85 × 7 = £19.95
Exam Tip: When working with money, always write your answer in pounds to 2 decimal places, and choose either £ or p symbols throughout your calculation (not both).
Working with inverse proportion
Inverse proportion problems often involve time, people, and work. The more people working on a task, the less time it takes to complete.
Deciding whether to multiply or divide
This is where many students get confused. Use this systematic approach to avoid common mistakes:
Method for Inverse Proportion:
- Step 1: Work out what 1 unit would do
- Step 2: Use common sense to decide if you need more or less
Worked Example: Wall Building
6 people can build a wall in 4 days. How long would 8 people take?
Step 1: Find how long 1 person would take 6 × 4 = 24, so 1 person would take 24 days (You multiply because 1 person would take longer)
Step 2: Find how long 8 people would take
24 ÷ 8 = 3, so 8 people would take 3 days
(You divide because more people means less time)
Practice approach
When you encounter proportion problems, follow this systematic approach to ensure accuracy and avoid common pitfalls:
Key Steps for Proportion Problems:
- Identify the type: Are both quantities changing in the same direction (direct) or opposite directions (inverse)?
- For direct proportion: Find the rate per unit, then multiply
- For inverse proportion: Find what 1 unit would do, then adjust using common sense
- Check your answer: Does it make logical sense?
Key Points to Remember:
- Direct proportion means both quantities change in the same direction at the same rate
- Inverse proportion means quantities change in opposite directions
- Always find the rate for 1 unit first, then scale appropriately
- Use common sense to check if your answer is reasonable
- In money problems, keep your units consistent and write answers to 2 decimal places