Maths⏱ 5 min read
How to Calculate and Simplify Ratios
Ratios describe proportional relationships — in recipes, finance, construction, and chemistry. Here's how to write, simplify, divide, and apply ratios with worked examples.
Ratios express the relationship between two or more quantities. They come up everywhere from concrete mixing to share portfolio allocation, and the maths is simpler than it looks.
Writing and Reading Ratios
A ratio of 3:2 means "3 parts to 2 parts"
Total parts = 3 + 2 = 5 parts
3:2 is the same as 6:4, 9:6, 1.5:1, 3/5 : 2/5
Ratios can also be written as fractions:
3:2 = 3/2 (meaning for every 2 of B, there are 3 of A)
Simplifying Ratios
Divide both sides by their Greatest Common Factor (GCF):
Simplify 24:36
GCF(24,36) = 12
24 ÷ 12 = 2, 36 ÷ 12 = 3
Simplified: 2:3
Simplify 45:30:15
GCF = 15
= 3:2:1
Dividing a Quantity in a Given Ratio
Method: Total parts → value per part → multiply
Example: Divide £840 in ratio 3:4:5
Total parts = 3 + 4 + 5 = 12
Value per part = £840 ÷ 12 = £70
Share A: 3 × £70 = £210
Share B: 4 × £70 = £280
Share C: 5 × £70 = £350
Check: £210 + £280 + £350 = £840 ✓
Scaling Recipes (Ratio Application)
Original recipe serves 4: flour 300g, butter 150g, sugar 100g
Ratio: 3:1.5:1 (or simplified 6:3:2)
Scale to serve 10 (multiply by 10/4 = 2.5):
Flour: 300g × 2.5 = 750g
Butter: 150g × 2.5 = 375g
Sugar: 100g × 2.5 = 250g
Ratios in Finance: Gearing and Leverage
Debt-to-equity ratio = Total Debt : Total Equity
A business with £200k debt and £300k equity:
= 200:300 = 2:3
Gearing ratio (%) = Debt ÷ (Debt + Equity) × 100
= 200 ÷ 500 × 100 = 40%
Unit Ratios (1:n or n:1)
Unit ratios make comparison easier. Divide so one side equals 1.
Map scale 1:50,000 means 1cm on map = 50,000cm real
= 1cm : 500m
Exchange rate 1:1.27 means £1 = $1.27
Gear ratio 3:1 means input shaft spins 3× for each output revolution
Ratio vs Proportion vs Fraction
Ratio: 3:5 (relationship between parts)
Proportion: 3/8 (one part as fraction of total)
Percentage: 37.5% (proportion as per hundred)
3:5 ratio → 3/(3+5) = 3/8 = 37.5% for the first part
5/(3+5) = 5/8 = 62.5% for the second part
Concrete and Mortar Mix Ratios
Mix TypeCement:Sand:AggregateUse
General purpose concrete1:2:4Paths, bases
Structural concrete1:1.5:3Foundations, driveways
Bricklaying mortar1:4–6 (cement:sand)Standard brickwork
Plastering1:3 (cement:sand)Undercoat render