Proportion (Cross Multiply)
Two equal ratios; solve using cross multiplication.
Formula
Variables
Example
If 2/3 = x/9 then x = 6
How it works
A proportion says that two fractions or ratios are equal. Cross multiplication works because if two ratios are equal, multiplying both sides by the denominators removes the fractions and leaves an equivalent statement: the product of the outer terms matches the product of the inner terms. This lets you find an unknown term by turning a fraction equation into a simple multiplication equation.
When to use it
Use this when you have two equal ratios and one missing value, such as in scaling recipes, map distances, unit conversions, or similar triangles. It is especially helpful when one of the four terms is unknown and the other three are known.
Worked example, step by step
Suppose 5/8 = x/24 Cross multiply: 5 × 24 = 8 × x 120 = 8x Divide both sides by 8: x = 15
Common mistakes to avoid
- Multiplying the two numerators and the two denominators instead of cross multiplying
- Putting the unknown in the wrong place and setting up the proportion incorrectly
- Forgetting to divide at the end after cross multiplying
Did You Know?
Cross-multiplication lets you solve for an unknown in a proportion — the basis of scaling recipes, maps, and models.
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