How to use
- Choose what you want to do: simplify a ratio, solve a proportion, or split a total.
- Enter A and B, the two terms of the ratio. Decimals are fine.
- For a proportion, add C; to split an amount, add the total.
- Read the answer, plus the 1 : n form, the decimal and the percentage split.
How it works
- Simplify: divide both terms by their greatest common divisor (GCD). If a term has decimals, first multiply both by 10, 100 and so on until they are whole numbers.
- Solve A : B = C : ? Cross-multiply, so ? = B × C ÷ A.
- Split a total: add the parts to get the number of shares. Each share is total ÷ (A + B).
- Percentages: each part ÷ (A + B) × 100.
Examples
- 12 : 18: the GCD is 6, so it simplifies to 2 : 3.
- 1.5 : 2.5: multiply by 10 to get 15 : 25, then divide by 5: 3 : 5.
- 3 : 4 = 9 : ? ? = 4 × 9 ÷ 3 = 12.
- Split 100 in 2 : 3: 5 shares of 20, so 40 and 60.
- Split 240 in 7 : 5: 12 shares of 20, so 140 and 100.
Common ratios as percentages
| Ratio | First part | Second part |
|---|---|---|
| 1 : 1 | 50% | 50% |
| 1 : 2 | 33.33% | 66.67% |
| 1 : 3 | 25% | 75% |
| 2 : 3 | 40% | 60% |
| 3 : 4 | 42.86% | 57.14% |
| 3 : 7 | 30% | 70% |
| 16 : 9 | 64% | 36% |
Ratios versus fractions
A ratio compares parts with each other; a fraction compares a part with the whole. In 2 : 3 the first part is 2/5 of the total, not 2/3.
Ratios with one term of 0, such as 0 : 5, simplify to 0 : 1. A ratio of 0 : 0 is undefined.
Working with parts of a whole instead? The fraction calculator simplifies with the GCD too, and the percentage calculator handles percentage change.