Ratio 2 (AQA GCSE Maths): Revision Notes
Ratio 2
Introduction to ratio problem-solving
Ratio is an essential concept that appears frequently in problem-solving questions. You'll need to master ratio techniques to answer questions effectively, particularly since calculators aren't permitted in some exam sections.
The key to success with ratio problems is understanding what different parts of the ratio actually represent in real-world contexts.
Ratio problems appear throughout mathematics exams and require a systematic approach to solve efficiently. The techniques you'll learn here will help you tackle these problems with confidence.
Golden rule for ratio problems
The Golden Rule for Ratio Problems
You can solve many ratio problems by determining what one part of the ratio represents.
This approach allows you to break down complex problems into manageable steps and find the value of individual components before calculating final answers.
Method for dividing quantities in given ratios
When you need to split a quantity according to a specific ratio, follow this three-step process:
- Calculate the total number of parts in the ratio by adding all the numbers together
- Divide the total quantity by this sum to find the value of one part
- Multiply the value of one part by each number in the ratio to find individual amounts
Important about Order
The order in which people or items are listed corresponds directly to the order of numbers in the ratio. This means the first person receives the amount represented by the first number, the second person gets the amount from the second number, and so on.
Worked example: sharing costs
Worked Example: Sharing a Phone Bill
Alexis, Nisha and Paul share a phone bill totalling £120. They decide to split the cost in the ratio 3:5:2.
Step 1: Find total parts parts
Step 2: Find value of one part
per part
Step 3: Calculate individual amounts
- Alexis:
- Nisha:
- Paul:
Check: ✓
Working with ratio differences
Sometimes problems give you the difference between parts rather than the total amount. Here's how to handle these situations:
Worked Example: Fundraising Swim
In a fundraising swim, Jamie and Chaaya raised money in the ratio 5:7. Chaaya raised £12 more than Jamie.
Step 1: Find the difference in parts parts represent the £12 difference
Step 2: Calculate one part value 2 parts = £12, so 1 part =
Step 3: Find individual amounts
- Jamie:
- Chaaya:
Check: ✓
Practice problems
Try these problems to test your understanding:
Problem 1: Ruth, Sue and Tess share £400 between them. Ruth receives £80 more than Sue. The ratio of Ruth's share to Sue's share is 9:5. Work out how much Tess receives.
Problem 2: Terri mixed 300g of rice with 240g of fish, then added some onion. The ratio of fish weight to onion weight was 3:2. Work out the ratio of rice weight to onion weight.
Practice Tip
Work through these problems step by step using the golden rule. Remember to identify what one part of the ratio represents first, then build up to find all the required values.
Exam tips
Essential Exam Preparation
You'll encounter ratio problem-solving throughout your exam, so thorough preparation is essential. Practice identifying what one part represents, as this skill applies to numerous question types.
Always check your final answer by verifying that all parts add up to the original total or that differences match the given information.
Remember!
Key Points to Remember:
- Golden rule: Find what one part of the ratio represents first
- Three-step method: Total parts → Divide quantity → Multiply by each part
- Order matters: The sequence of people/items matches the sequence of ratio numbers
- Always check: Your final amounts should add up to the original total
- Handle differences: When given differences between parts, work out how many parts that difference represents