Proportional equations · grades 6–7

Solving Proportions Worksheet Generator

Create proportions such as 3 : 5 = 12 : ____, with the missing value appearing in any of the four positions. Every equation is generated from one reduced ratio and one whole-number scale factor.

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Solving Proportions Practice

Solve proportions · Medium whole numbers · Seed 261401

5 : 11 = ____ : 99

5 : 11 = ____ : 110

7 : 10 = 49 : ____

9 : ____ = 36 : 40

____ : 13 = 6 : 26

10 : ____ = 60 : 66

4 : ____ = 12 : 21

10 : 11 = 50 : ____

____ : 12 = 39 : 36

10.

13 : ____ = 78 : 48

11.

13 : 14 = 65 : ____

12.

2 : 5 = ____ : 50

13.

2 : ____ = 20 : 90

14.

5 : 14 = ____ : 126

15.

4 : 13 = ____ : 65

16.

10 : ____ = 60 : 54

17.

11 : ____ = 77 : 91

18.

____ : 11 = 56 : 88

Exact-construction rule: simplified ratios begin from coprime terms, ratio tables and proportions use whole-number scale factors, unit prices use integer cents, and percent proportions are built from exact part-whole relationships.

Solving a proportion with a missing value

A proportion states that two ratios are equal. To find the missing number, look for the factor that scales one ratio into the other, or cross-multiply and divide. Both methods give the same answer, and a quick check is that the two fractions simplify to the same value. Keep the same quantity in the same position in both ratios, such as dollars on top and items on the bottom.

Worked examples

3/4 = x/20. The denominator goes from 4 to 20, a factor of 5, so x = 3 × 5 = 15.
6/9 = 10/y. Cross-multiplying gives 6y = 9 × 10 = 90, so y = 90 ÷ 6 = 15.
5 pencils cost $2. How much do 20 pencils cost? 20 is 4 times 5, so the cost is 2 × 4 = $8.
Check 3/4 = 15/20: both fractions equal 0.75, so the proportion is true.

Common slips

Adding instead of multiplying. In 3/4 = x/20, going from 4 to 20 adds 16, but the numerator is multiplied by 5, not increased by 16.
Putting the quantities in different positions. If dollars are on top in one ratio, they must be on top in the other.
Cross-multiplying and then forgetting to divide. In 6/9 = 10/y, the product 90 is not the answer; divide by 6.
Mixing units, such as comparing minutes to hours without converting.

How to use this worksheet

Have students show either the scale factor or the cross-multiplication, then check by simplifying both fractions. The answer key gives the missing value, which makes the check quick.

Common Core connection

6.RP.A.3 · Use ratio and rate reasoning, including equivalent ratios, to find a missing value in a real-world problem.

A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.

Classroom note 1

Encourage scale-factor reasoning before cross multiplication when one ratio is an obvious whole-number multiple of the other.

Classroom note 2

Move the blank among all four positions so students learn the relationship rather than one memorized layout.

Classroom note 3

A final cross-product check is useful: the two diagonal products should match for every valid proportion.

Classroom note 4

Model both routes for 3 : 5 = 12 : blank. Scale factor: the left term was multiplied by 4, so the blank is 5 times 4, which is 20. Cross-products: 3 times the blank equals 5 times 12, so the blank is 60 divided by 3, which is 20.

Classroom note 5

Watch for students who multiply terms that sit side by side. The products always come from the two diagonals, a times d and b times c.

All ratio & proportion skills →

Mix simplifying, tables, unit rates, proportions, and percent proportions in one generator.

Connect ratios to percents →

Practice part / whole = percent / 100 after equivalent ratios are secure.

More skills in this set

Questions people ask

Can the missing value appear anywhere?

Yes. The blank can replace any of the four terms in the proportion.

Which standard does this practice?

CCSS 6.RP.A.3 uses equivalent ratios to solve for a missing value; 7.RP.A.2c formalizes it as a proportional equation.

Should students use scale factor or cross multiplication?

Scale-factor reasoning is faster when one ratio is a clear whole-number multiple of the other. Cross products always work and make a reliable final check.

Are the answers whole numbers?

Yes. Each proportion is constructed from a reduced ratio and a whole-number multiplier.

Are all proportions exact?

Yes. The two ratios are mathematically equivalent by construction.

Can I control difficulty?

Yes. The number-size setting changes the base terms and scale-factor range.