Missing Value in a Proportion

What a proportion means

A proportion is an equation saying two ratios are equal. If one value is missing, you can find it by keeping the same multiplicative relationship on both sides.

Method

1. Write the proportion clearly. Identify the two ratios that are equal.
2. Find the missing term. Decide whether the unknown is a numerator or a denominator.
3. Use cross-multiplication. Multiply the numerator of one ratio by the denominator of the other ratio, then set the products equal.
4. Solve for the unknown. Divide both sides by the coefficient of the missing value.
5. Simplify the result. Give the exact answer in lowest terms.

Example pattern

If (\frac{a}{b} = \frac{c}{x}), then cross-multiply to get (ax = bc), and solve by dividing by (a): (x = \frac{bc}{a}).

Check your answer

Substitute your value back into the original proportion. The two ratios should be equal after simplification. If they are not, recheck the multiplication and division steps.