What is a Ratio?
A ratio compares two quantities of the same kind. It answers 'how many times is one quantity compared to another.' Ratios can be written as A:B, A/B, or 'A to B'. They are used in recipes, map scales, financial analysis, mixing chemicals, photography, and countless other applications.
Ratio Simplification — GCD MethodA : B → (A ÷ GCD) : (B ÷ GCD)
Example: 12 : 8 → GCD(12,8) = 4 → 3 : 2
Example: 12 : 8 → GCD(12,8) = 4 → 3 : 2
Proportions — Finding Missing Values
A proportion states that two ratios are equal: A:B = C:D. If three values are known, the fourth can always be found by cross-multiplication:
Cross-MultiplicationA/B = C/D → D = (B × C) ÷ A
Example: 3:4 = 6:D → D = (4 × 6) ÷ 3 = 8
Example: 3:4 = 6:D → D = (4 × 6) ÷ 3 = 8
Real-World Ratio Examples
| Scenario | Ratio | Use |
|---|---|---|
| Recipe (flour:water) | 2:1 | Scaled cooking |
| Map scale | 1:50,000 | 1 cm = 500 m |
| Cement:sand:aggregate | 1:2:4 | Construction mixing |
| Aspect ratio HD | 16:9 | Screen dimensions |
| Golden ratio | 1:1.618 | Design & aesthetics |
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