What is a ratio?
A ratio compares quantities in terms of “parts”.
A ratio tells you how much of one quantity there is compared to another, using the idea of parts. For example, 2:3 means that for every 2 parts of the first quantity, there are 3 parts of the second.
Ratios can be written as a:b, a/b, or a,b. All of these forms communicate the same proportional relationship.
- Paint mix 2:3 means 2 parts base + 3 parts tint (total 5 parts).
Try it: Simplify a ratio
A ratio is about proportion, not absolute size.
How to simplify a ratio
Simplify by dividing all parts by their greatest common divisor (GCD).
To simplify a ratio, reduce it to the smallest whole-number parts that keep the same proportion.
A practical method is to compute the GCD of the parts and divide each part by that GCD.
- 10:15 → divide both by 5 → 2:3
Try it: Simplify a ratio
Simplified ratios are equivalent ratios in lowest terms.
How to scale a ratio
Scaling multiplies every part by the same factor.
Scaling keeps the same proportion, but changes the absolute values. This is useful when you want a ratio to sum to a specific total, or you want one part to hit a target value.
Example: if you want 2:3 to total 100, the factor is 100 ÷ (2+3) = 20, so the scaled ratio is 40:60.
- 2:3 scaled to total 100 → 40:60
Try it: Scale to a target total
Scaling changes size but preserves the proportion.
How to compare two ratios
Two ratios are equivalent if their simplified forms match.
If two ratios simplify to the same result, they are equivalent (for example: 1:2 and 2:4).
If they are not equivalent, you can compare a/b to decide which ratio is larger. A safe way is cross-multiplication: compare a₁×b₂ vs a₂×b₁.
- Compare 2:3 vs 3:4 → 2×4 = 8, 3×3 = 9 → 3:4 is larger (as a fraction).
Try it: Compare two ratios
Simplify first; if needed, compare via cross-multiplication.
FAQs
Can a ratio include decimals?▼
Yes. A decimal ratio like 1.5:2.5 is valid; you can convert it to whole-number parts by multiplying to clear decimals (1.5:2.5 → 15:25 → 3:5).
Is 0 allowed in a ratio?▼
Yes, if it’s meaningful (0:5 means only the second part). But 0:0 is undefined because there’s no proportion to compare.
Are 2:3 and 4:6 the same ratio?▼
Yes. Both simplify to 2:3, so they represent the same proportion.
How do I scale a ratio to a total?▼
Compute factor = targetTotal ÷ (sum of parts), then multiply each part by the factor. If the result isn’t a whole number, you’ll get decimals.