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All courses Math Foundations · MF.PR.7 21 of 60
Solve proportion equations and explain why the setup matches the context.

Solve a basic proportion

Problem
Solve the proportion x/7 = 12/21. What is x?
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Hint

Set the diagonal cross-products equal: multiply x by 21 and 7 by 12.

In a proportion like x/7 = 12/21, the cross-products are equal: numerator × opposite denominator = denominator × opposite numerator.

Solution walkthrough

01

Recognize the two equal ratios

\[x/7~=~12/21\]

This is a proportion, so the ratio on the left must equal the ratio on the right. To solve for x, use the diagonal cross-products.

02

Set the cross-products equal

\[21x~=~7~·~12\]

In a proportion a/b = c/d, the cross-products match: a·d = b·c. Here, x·21 and 7·12 must be equal.

03

Solve the equation

\[21x~=~84,~\text{so}~x~=~84/21~=~4\]

First multiply 7 · 12 to get 84. Then divide both sides by 21 to isolate x.

04

Check and state the answer

\[4/7~=~12/21\]

Since 12/21 simplifies to 4/7, x = 4 makes both ratios equal. So x = 4.

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Another way

  1. Simplify 12/21 first: 12/21 = 4/7. Then x/7 = 4/7, so x = 4.

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Common mistake

A common mistake is multiplying straight across the numerators or denominators instead of using diagonals. For x/7 = 12/21, the correct setup is 21x = 7·12, not 7x = 12·21.