4⁄7 = n⁄21
Show answer
n = 12
Free printable worksheet
Proportions Worksheet
Twenty proportions solved with equivalent ratios and cross products.
Middle School MathGrades 6-83 pagesAnswer key included
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What this worksheet includes
- Twenty proportions solved with equivalent ratios and cross products.
- 3-page printable PDF with a complete answer key
- Designed for Grades 6-8 middle school math practice
- Available as an immediate free download with no email required
How to use it
Use this proportions worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 6-8 students working on middle school math. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Middle School Math worksheets.
Topic guide
How to approach proportions
A proportion states that two ratios are equal. Equivalent ratios share a scale factor, and cross products provide an efficient equation for finding a missing value.
Keep corresponding quantities in matching numerator and denominator positions. After solving, substitute the value and check that both ratios represent the same comparison.
Learning objectives
- Recognize proportional relationships
- Solve proportions
- Check solutions with equivalent ratios
Skills to review first
- Ratios
- Fraction multiplication
- One-step equations
Worked example
Follow the reasoning step by step
Solve 3⁄5 = x⁄20.
- Notice that 5 × 4 = 20.
- Multiply the numerator by the same scale factor.
- Compute x = 3 × 4.
- Check 12⁄20 simplifies to 3⁄5.
Solution: x = 12.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
5⁄x = 15⁄24
Show answer
x = 8
6 tickets cost $18; 10 tickets cost c.
Show answer
c = $30
Error check
Common mistakes to watch for
- Mismatching corresponding quantities
- Cross multiplying and then adding
- Failing to divide after finding a product