About the ratio calculation
A ratio compares two quantities without stating either one. 10:15 and 2:3 describe exactly the same relationship, which is why simplifying to lowest terms makes ratios comparable. The key distinction from a fraction is what the second number means: in 2:3 the whole is five parts, not three.
Formula
Divide both terms by their greatest common divisor.
As a fraction of the whole: a ÷ (a + b)
Proportion: a : b = c : d means a × d = b × cWorked example
10 : 15 — the greatest common divisor is 5, so it simplifies to 2 : 3. As shares of the whole that is 40% and 60%, because the total is five parts.
Frequently asked questions
Is a ratio of 2:3 the same as the fraction 2/3?
Not quite. The ratio 2:3 describes a whole of five parts, where the first is 2/5 of the total. The fraction 2/3 means two parts out of three. Reading a ratio as a fraction is the most common error with them.
How do I scale a recipe with a ratio?
Multiply both terms by the same factor. A 2:3 ratio scaled by four becomes 8:12. The relationship is preserved as long as both sides change by the same multiple.
Can a ratio have decimals?
Yes, but it is conventionally converted to whole numbers by multiplying both sides. A ratio of 1.5:2 becomes 3:4 when both sides are doubled, which is easier to read and to work with.
Sources
- Standard ratio and proportion arithmetic