Ratio & Proportion
Simplifying ratios, dividing amounts in a given ratio, scaling recipes and solving proportion problems.
What is Ratio & Proportion?
A ratio compares two or more quantities. For example, if a recipe uses 2 cups of flour and 3 cups of sugar, the ratio of flour to sugar is 2:3.
Proportion means that two ratios are equal. In the 11+ exam, you may need to simplify ratios, divide an amount in a given ratio, scale recipes up or down, or solve proportion problems using the unitary method.
Step-by-Step Method
Simplify ratios like fractions
Divide both parts by their highest common factor. For example, 12:8 simplifies to 3:2 (divide both by 4).
To divide an amount in a ratio, find the total parts
Add the ratio numbers together. For example, dividing in ratio 2:3 means 5 parts total.
Find the value of one part
Divide the total amount by the total number of parts.
Multiply to find each share
Multiply the value of one part by each ratio number.
For proportion, use the unitary method
Find the value of one item first, then multiply by the number you need.
Worked Examples
Simplify 15:25.
Working
- Find the HCF of 15 and 25 = 5.
- Divide both by 5: 15/5 = 3, 25/5 = 5.
Divide 45 in the ratio 2:3.
Working
- Total parts = 2 + 3 = 5.
- Value of one part = 45 / 5 = 9.
- First share = 2 x 9 = 18.
- Second share = 3 x 9 = 27.
A recipe for 4 people uses 300g of flour. How much flour for 10 people?
Working
- Find flour per person: 300 / 4 = 75g.
- Multiply by 10: 75 x 10 = 750g.
Common Mistakes
Dividing by the ratio numbers instead of the total parts (e.g. dividing 45 by 2 and by 3).
Add the ratio numbers first to get total parts (2+3=5), then divide the amount by 5.
Not simplifying the ratio fully.
Keep dividing by common factors until no more are possible. 8:12 = 4:6 = 2:3.
Mixing up which share goes with which part of the ratio.
Write clearly which quantity corresponds to which ratio number.
Top Tips
- Always check your ratio shares add up to the total amount.
- The unitary method (find the value of one, then multiply) works for almost every proportion question.
- Remember: ratios can be written as fractions. A ratio of 2:3 means the first part is 2/5 of the total.
- If a question says “for every 3 red balls there are 5 blue balls”, the ratio is 3:5.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions