Ratio Simplifier
Simplify and compare ratios
About This Calculator
A ratio expresses the relationship between two quantities and can be simplified by dividing both values by their Greatest Common Divisor. Ratios appear in recipes, maps, scale models, finance, and statistics. This calculator simplifies any ratio to its lowest terms and can scale it to equivalent forms.
Formula
Simplify a:b → divide both by GCD(a, b)
Equivalent ratios: a:b = (a×k):(b×k) for any k
Example Calculation
Simplify the ratio 24:36.
- Find GCD(24, 36): factors of 24 = 1,2,3,4,6,8,12,24; factors of 36 = 1,2,3,4,6,9,12,18,36
- GCD = 12
- 24 ÷ 12 = 2; 36 ÷ 12 = 3
24:36 simplifies to 2:3
Common Ratios and Simplified Forms
| Original Ratio | Simplified | Original Ratio | Simplified |
|---|---|---|---|
| 6:9 | 2:3 | 15:25 | 3:5 |
| 12:16 | 3:4 | 18:24 | 3:4 |
| 10:15 | 2:3 | 100:250 | 2:5 |
Frequently Asked Questions
What is the difference between a ratio and a fraction?
A fraction represents a part of a whole (a/b), while a ratio compares two separate quantities (a:b). They are mathematically equivalent but used in different contexts.
How do I compare two ratios?
Convert both to the same denominator or to decimal form. For example, 3:4 = 0.75 and 5:7 = 0.714, so 3:4 is the larger ratio.
What does it mean when a ratio is in simplest form?
A ratio a:b is in simplest form when GCD(a, b) = 1 — the only common factor is 1, and neither number can be reduced further.