How do you solve a proportion?

Use a scale factor when the numbers are friendly. Otherwise cross-multiply and divide: in 6/8 = x/12, 8x = 72, so x = 9.

What grade is this solving proportions worksheet for?

It is written for grade 7 and matches Common Core standard 7.RP.A.2c.

Can I get a different version of this solving proportions worksheet?

Yes. Use the free Mathify Kids test maker to make a new solving proportions worksheet with different numbers every time, with its own answer key.

Solving proportions worksheets

Solving proportions for a missing number, checking proportions and setting them up from word problems.

The stories use prices, recipes, maps and shadows.

Download the free solving proportions worksheet (PDF)

Solving proportions worksheet

PDF · US Letter · Grade 7 · 30 questions · answer key included

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What’s on the worksheet

30 questions on solving proportions, sized for US Letter paper
2 pages of questions plus an answer key on the last page
Written for grade 7, matching Common Core 7.RP.A.2c
Name and date lines at the top, and room to show the work

Sample questions from this worksheet

x/12 = 27/36
35/x = 21/24
12/15 = x/25
Is 25/30 = 20/24 a proportion?
5 pencils cost $2. How much do 12 pencils cost?
A 6 ft person casts a 4 ft shadow. A tree casts a 12 ft shadow. How tall is the tree?

Quick reference: solving proportions

A proportion says two ratios are equal, like 3/4 = 15/20. To find a missing number, use one of three methods.

Scale factor: 4 × 5 = 20, so 3 × 5 = 15.
Unit rate: go through 1 when the scale factor is awkward.
Cross-multiply: in 6/8 = x/12, 8x = 6 × 12 = 72, so x = 9.

When you set up a proportion from a story, keep the same kind of amount in the same place on both sides. The solving proportions lesson shows all three methods, and the ratio calculator checks answers.

Preview the worksheet and answer key

Solving proportions worksheet answer key

Make a new solving proportions worksheet

Need another page for extra practice, a retake or a second group in class? The free Mathify Kids test maker builds a fresh solving proportions worksheet with different numbers every time. Choose how many questions, print it with its own answer key, or let your child take it on screen and see the score straight away.

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Solving proportions: a worked example (6/8 = x/12)

There is no whole-number scale factor from 8 to 12, so cross-multiply.
8 × x = 6 × 12 = 72.
Divide both sides by 8: x = 9.
Check: 6/8 = 0.75 and 9/12 = 0.75.

How to use it at home and in class

At home

Practice with recipes and shadows. Measure your shadow and a lamppost’s shadow, then set up a proportion to find the lamppost’s height. Ten problems a day works better than a whole sheet at once. Mark them together with the answer key, then ask your child to explain one they got wrong: finding the mistake themselves is where the learning happens.

In class

Use the first row as a warm-up, a full page for independent practice, or five questions as an exit ticket. For a retake or a second group, make a new version with the test maker so every child gets different numbers.

Mistakes to watch for

Putting the amounts in a different order on each side.
Adding instead of multiplying to scale.
Cross-multiplying top with top.

What to practice before and after solving proportions

Before: proportional relationships. If this sheet is a struggle, go back a step.
After: scale drawings, once this one is mostly right.
Learn it first: the solving proportions lesson.