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a : b = c : x

Ratio and proportion calculator

Two jobs on one page: reduce a ratio to its simplest form, and solve a missing term in a proportion.

Short answer: 12 : 18 simplifies to 2 : 3, and if 2 : 4 = 6 : x then x = 12, because 2 × 12 = 4 × 6.

Simplifying and solving are different jobs

Simplifying divides both parts by a common factor and keeps the relationship; solving finds a missing part from three known ones by cross-multiplication. Recipes, maps and concrete mixes use the first; "if this many covers that much, how many for the rest?" uses the second.

Worked example

A concrete mix of 1 : 2 : 3 by volume is not offered here, but its two-part cousin is: 1 : 5 cement to sand, needing 40 kg of sand means x = 5 × 8 ÷ 1 = 40 when 8 kg of cement is used — the same cross-multiplication the page performs.

Ratio questions

How do I simplify a ratio?

Divide both parts by their greatest common divisor: 12 : 18 becomes 2 : 3. Decimals are converted to whole numbers first, so 1.5 : 0.5 simplifies to 3 : 1 rather than staying fractional.

How is a proportion solved?

a : b = c : x means a × x = b × c, so x = b × c ÷ a. If 2 : 4 equals 6 : x, then x = 4 × 6 ÷ 2 = 12. The page prints that check so the answer can be verified by hand.

Where are ratios used in practice?

Scale drawings and maps, recipe scaling, mixing concrete and paint, gear ratios and financial ratios like debt to equity. All of them are the same operation on two or three numbers.

Why must both parts be above zero?

A ratio of zero to something is degenerate, and a zero first term in a proportion divides by zero when solved. The page refuses both rather than returning infinity or an arbitrary value.

Related tools

Fraction calculatorExact fraction arithmetic.Percentage calculatorThe same comparison as a percentage.GCD and LCM calculatorThe divisor behind the simplification.