Simplify a ratio to its lowest terms, or solve a proportion with one missing number.
How to simplify a ratio
- Find the HCF (highest common factor) of both numbers.
- Divide both numbers by it.
Example: 24 : 36 → HCF is 12 → 2 : 3. For decimals, first multiply both sides by 10, 100… to make them whole: 1.5 : 2.5 → 15 : 25 → 3 : 5.
Solving proportions
A : B = C : D ⟹ A × D = B × CExample: 3 : 4 = 12 : ? → ? = 4 × 12 ÷ 3 = 16. This "cross-multiplication" solves recipe scaling, map scales, mixing ratios and exam word problems.
Everyday ratios
- Cement mortar 1:4 — 1 part cement to 4 parts sand.
- Screen 16:9 — use the aspect ratio calculator to resize.
- Profit sharing 2:3 — ₹50,000 split as ₹20,000 and ₹30,000 (A gets 2/5, B gets 3/5).
Step-by-step: dividing ₹12,000 in the ratio 2 : 3 : 5
- Add the parts: 2 + 3 + 5 = 10.
- Value of one part: 12,000 ÷ 10 = ₹1,200.
- Shares: 2 × 1,200 = ₹2,400; 3 × 1,200 = ₹3,600; 5 × 1,200 = ₹6,000.
- Check: 2,400 + 3,600 + 6,000 = 12,000 ✓
Scaling a recipe 2 : 3
A recipe for 2 people needs 150 g rice; for 3 people: 150 × 3 ÷ 2 = 225 g. Every ingredient is multiplied by the same 1.5.
Worked examples
| Situation | Working | Answer |
|---|
| Map scale 1 : 50,000 — 3 cm on the map | 3 × 50,000 cm | 1.5 km on the ground |
| Concrete mix 1 : 2 : 4 (M15) for 7 bags of cement | cement : sand : aggregate | 14 bags of sand, 28 of aggregate |
| 16 : 9 screen that is 1366 px wide | 1366 × 9 ÷ 16 | 768 px tall |
| Partners invest ₹3 lakh and ₹5 lakh; profit ₹1.2 lakh | 3 : 5 → 8 parts of ₹15,000 | ₹45,000 and ₹75,000 |
| Milk : water 5 : 1 in 18 litres — how much water to add for 3 : 1? | 15 l milk needs 5 l water | add 2 litres |
Tips and common mistakes
- A ratio has no units — 500 g : 2 kg must become 500 : 2000 = 1 : 4 before simplifying (the LCM & HCF Calculator finds the HCF).
- Ratio to percentage: 3 : 5 means 3 ÷ 8 = 37.5% and 62.5%.
- Combining ratios a : b = 2 : 3 and b : c = 4 : 5 → make b equal (12) → a : b : c = 8 : 12 : 15.
- Compare ratios by converting to decimals: 7 : 9 (0.778) is bigger than 5 : 7 (0.714).
Frequently asked questions
How do I simplify the ratio 15:25?
Divide both by their HCF, 5, to get 3:5.
How do I divide an amount in a ratio?
Add the ratio parts, divide the amount by that total, then multiply by each part. ₹1,000 in 2:3 → 1,000 ÷ 5 = 200 → ₹400 and ₹600.
How do I solve 2:5 = x:20?
Cross-multiply: 5x = 2 × 20 = 40, so x = 8.