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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

Keep the ratios equal

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

The variable is the numerator of a fraction equal to twelve twenty-firsts.

02

Set the cross products equal

\[21x~=~7(12)~=~84\]

Equal ratios have equal diagonal products.

03

Isolate x

\[x~=~84/21~=~4\]

Dividing both sides by 21 leaves the unknown alone.

04

Check and answer

\[4\]

Substitution gives 4/7 = 12/21 after reducing 12/21 by 3.

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Another way

  1. Reduce 12/21 to 4/7; matching denominators then gives x = 4.

!

Common mistake

Do not stop at the cross product 84. That value equals 21x, so one final division by 21 is required.

Solution walkthrough video