Ratio Basics
A ratio compares two or more quantities. 3:4 means "3 of the first for every 4 of the second." Ratios can be written as 3:4, 3/4, or "3 to 4" — all equivalent.
Common Ratio Applications
| Context | Ratio Meaning | Example |
|---|---|---|
| Recipe scaling | Ingredient proportions | Flour:Water = 3:1; double → 6:2 |
| Map reading | Map : Real distance | 1:50,000 → 3 cm on map = 1,500 m |
| Finance (P/E) | Price to earnings | P/E of 20 = $20 per $1 of earnings |
| Aspect ratio | Width : Height | 16:9 widescreen, 4:3 classic TV |
| Mixing (paint, fuel) | Component A : Component B | 2-stroke fuel 50:1 (gas:oil) |
Solving for a Missing Value
Cross-multiply: if A:B = C:D, then A × D = B × C. Isolate the unknown.
- Find D: D = (B × C) ÷ A
- Recipe example: 3:4 = 9:D → D = (4 × 9) ÷ 3 = 12
- Map example: 1:50,000 = 5:D → D = 50,000 × 5 = 250,000 cm = 2.5 km
Simplifying Ratios
Divide both parts by their GCD. 24:36 → GCD = 12 → 2:3. Always simplify before comparing ratios to see if they are equivalent.