How this calculator works
First clear all denominators with one common multiple. Divide the resulting whole numbers by their greatest common divisor. To normalise a selected term, divide every term by it instead. Zero terms are allowed, but an all-zero ratio has no scale and a zero term cannot become one.
Formula
For terms nᵢ/dᵢ, let D=lcm(dᵢ), zᵢ=nᵢD/dᵢ and g=gcd(zᵢ). Reduced ratio = z₁/g : z₂/g : z₃/g. Normalisation to term j divides all zᵢ by zⱼ.
Worked example
1.5 : 2.25 : 3 becomes 6 : 9 : 12 after multiplying by four, then 2 : 3 : 4 after dividing by three. Normalising 2 : 4 : 6 to its middle term gives 1/2 : 1 : 3/2.
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Frequently asked questions
Can three terms be simplified together?
Yes. One common divisor must divide all three whole-number terms; reducing pairs separately can change the ratio.
Can a ratio include fractions?
Yes. Their denominators are cleared exactly before simplification.
Must the units match?
Use matching units when comparing the same kind of quantity. A ratio between unlike quantities describes a rate and keeps its units separately.