Ratio 2 (Edexcel GCSE Maths): Revision Notes
Ratio 2
Understanding ratios in problem-solving
Ratios are frequently used in mathematical problem-solving questions. You need to be confident answering ratio questions without using a calculator, as you won't have access to one in certain exam papers.
The key to success with ratio problems is understanding what each part of the ratio represents and working systematically through the steps.
In many exams, calculators are not permitted for ratio questions, so developing strong mental arithmetic skills and systematic approaches is essential for success.
The golden rule
Understanding the fundamental principle behind ratio problem-solving is crucial for tackling any ratio question effectively.
Golden rule: You can answer lots of ratio questions by working out what one part of the ratio represents.
This fundamental principle will help you tackle most ratio problems effectively. By finding the value of one part, you can then calculate the values of all other parts.
Method for dividing quantities in given ratios
When you need to divide a quantity according to a given ratio, follow these three systematic steps:
- Work out the total number of parts in the ratio
- Divide the quantity by this total
- Multiply your answer by each part of the ratio
The order in which people are mentioned in the problem matches the order of the numbers in the ratio. This means the first person mentioned corresponds to the first number in the ratio.
Worked example 1: Sharing a phone bill
Worked Example: Sharing a Phone Bill
Problem: Alexis, Nisha and Paul share a flat. Their monthly phone bill is £120. They decide to split the bill in the ratio 3:5:2. How much does each person pay?
Solution:
- The ratio is 3:5:2
- Total parts: 3 + 5 + 2 = 10
- Value of each part: £120 ÷ 10 = £12
Calculate each person's payment:
- Alexis pays: 3 × £12 = £36
- Nisha pays: 5 × £12 = £60
- Paul pays: 2 × £12 = £24
Check: £36 + £60 + £24 = £120 ✓
Worked example 2: Fundraising problem
Worked Example: Fundraising Problem
Problem: Jamie and Chaaya took part in a sponsored swim to raise money for charity. The ratio of Jamie's total to Chaaya's total is 5:7. Chaaya raised £12 more than Jamie. How much money did they raise in total?
Solution:
- The ratio is 5:7, so the difference between parts is 7 - 5 = 2
- Since Chaaya raised £12 more than Jamie, two parts of the ratio represent £12
- Therefore, one part of the ratio represents £6
Calculate each person's total:
- Jamie raised: 5 × £6 = £30
- Chaaya raised: 7 × £6 = £42
- Total raised: £30 + £42 = £72
Check: £42 - £30 = £12 ✓
Key problem-solving strategies
Developing a systematic approach to ratio problems will improve both your accuracy and confidence. These strategies work consistently across different types of ratio questions.
Essential Problem-Solving Strategies:
When solving ratio problems:
- Start by identifying what one part of the ratio represents
- Use the given information to find the value of one part
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- Work systematically through the three-step method
- Always check your answer by ensuring all parts add up to the original total
- Pay attention to the order - the first person mentioned corresponds to the first number in the ratio
Remember!
Key Points to Remember:
- The golden rule: find what one part of the ratio represents first
- Follow the three-step method: find total parts, divide quantity, multiply by each part
- The order of names matches the order of ratio numbers
- Always check your final answer adds up to the original total
- Practice solving problems without a calculator to build confidence