Simplify a ratio, or solve a:b = c:x for the missing value.
Simplified ratio
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How this works
Simplify: A : B → (A ÷ gcd) : (B ÷ gcd)
Proportion: A : B = C : x → x = (B × C) ÷ A
A ratio is fully simplified when the two numbers share no common factor greater than 1 — divide both by their greatest common factor.
Equivalent ratios describe the same relationship at different scales: 2:3, 4:6 and 10:15 are all the same ratio.
A proportion is two ratios set equal — cross-multiplying (A × x = B × C) is what solving for the missing value comes from.
How do I simplify a ratio?
Find the greatest common factor (GCF) of both numbers and divide each by it. 12:18 has a GCF of 6, so it simplifies to 2:3.
How do I solve a:b = c:x?
Cross-multiply: x = (b × c) ÷ a. For 2:5 = 9:x, that is x = (5 × 9) ÷ 2 = 22.5.
Can a ratio include decimals?
Yes — this calculator accepts decimal inputs for both simplifying and solving, though "simplified" ratios of decimal numbers are shown as a reduced decimal ratio rather than whole numbers.