Ratio Basics
A ratio compares two quantities by division. 3:2 means "for every 3 of one thing, there are 2 of another." Ratios can be written three ways: 3:2, 3/2, or "3 to 2." All mean the same thing.
A proportion states that two ratios are equal: A/B = C/D. To solve for an unknown, cross-multiply: A × D = B × C.
Equivalent Ratios
| Original Ratio | ×2 | ×3 | ×5 | ×10 |
|---|---|---|---|---|
| 1:2 | 2:4 | 3:6 | 5:10 | 10:20 |
| 2:3 | 4:6 | 6:9 | 10:15 | 20:30 |
| 3:4 | 6:8 | 9:12 | 15:20 | 30:40 |
| 4:5 | 8:10 | 12:15 | 20:25 | 40:50 |
Common Uses
Recipes: Scale ingredients up or down. A recipe for 4 uses 2 cups flour; for 6 people, use 2 × (6/4) = 3 cups.
Maps: A 1:50,000 scale map means 1 cm on the map = 50,000 cm (500 m) in reality.
Finance: Debt-to-income ratio, price-to-earnings (P/E) ratio, and current ratio are all comparisons of two financial values.
Mixing: Concrete mix ratios (1:2:3 for cement:sand:gravel), paint dilution ratios, chemical solutions.