Curriculum fit: GCSE Maths Ratio, proportion and rates of change (Foundation and Higher). US: Grade 6-7 ratios and proportional relationships.
On this page
What Is It?
A ratio compares quantities. If a recipe uses 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is 2 : 1. Ratios can be simplified by dividing both parts by a common factor.
Proportion means two quantities change at the same rate. If 3 books cost £12, then 6 books cost £24 because the cost per book stays the same.
Key Formulas and Ideas
- To share an amount in the ratio a : b, divide by (a + b) to find one part, then multiply.
- Unit method: find the value of one unit, then scale up or down.
- Ratio a : b can be written as the fraction a/(a + b) for the first part.
Worked Examples
Simplify a Ratio
Simplify 36 : 24.
- The HCF of 36 and 24 is 12.
- Divide both by 12: 3 : 2.
✓ Answer 3 : 2
Sharing in a Ratio
Share £150 between Ana and Ben in the ratio 2 : 3.
- Total parts: 2 + 3 = 5.
- One part: 150 ÷ 5 = 30.
- Ana: 2 × 30 = 60. Ben: 3 × 30 = 90.
✓ Answer Ana £60, Ben £90
Unit Method
5 notebooks cost £8.50. How much do 8 notebooks cost?
- Cost of one notebook: 8.50 ÷ 5 = 1.70.
- Cost of 8: 8 × 1.70 = 13.60.
✓ Answer £13.60
Common Mistakes to Avoid
- Dividing by only one of the parts instead of the total number of parts when sharing.
- Forgetting to keep the units the same before simplifying.
- Writing a ratio in the wrong order.
- Adding the same amount to both sides of a ratio instead of multiplying.
Practice Questions
Frequently Asked Questions
Is a ratio the same as a fraction?
No. In the ratio 2 : 3 the total is 5 parts, so the first part is 2/5 of the whole, not 2/3.
How do I solve 'ratio of boys to girls is 3 : 4 and there are 12 boys'?
3 parts = 12 boys, so one part is 4, and 4 parts is 16 girls.
Keep Going With These Guides
Direct and Inverse Proportion: Find k and Solve Problems
Use y = kx and y = k/x to solve direct and inverse proportion problems, including y proportional to x squared, with worked examples.
GCSEHigh SchoolPercentages: How to Find, Increase and Decrease Them
Work out a percentage of an amount, increase or decrease by a percentage and calculate percentage change, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolSimilar Shapes: Scale Factors, Area and Volume
Use scale factors to find missing lengths, and learn how area and volume scale with k squared and k cubed, with worked examples.
GCSEHigh SchoolSources and Review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.