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§ Ratios & Proportions·Grades 6–7

Ratios & Proportions Worksheets

Free PDF · Problems + answer key · Instant download

Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable ratios & proportions worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from simplify and find equivalent ratios at the easy level through to workers, mixtures, similar triangles at the advanced level.

CCSS.6.RPCCSS.7.RP

What is ratios & proportions?

A ratio expresses the relationship between two quantities by showing how many times one contains the other, written as a:b or a/b. Proportions occur when two ratios are equal, such as 3:4 = 6:8, forming the foundation for solving problems involving scaling, rates, and comparisons. The cross-multiplication method (if a/b = c/d, then a×d = b×c) provides a systematic way to find unknown values in proportional relationships.

Why it matters

Ratios and proportions appear throughout daily life and advanced mathematics. Architects use proportions when scaling blueprints where 1 inch represents 10 feet of actual building dimensions. Pharmacists calculate medication dosages using ratios — if 5 mg works for a 100-pound patient, a 150-pound patient needs 7.5 mg. Recipe scaling relies on proportional reasoning: doubling a recipe that serves 4 people to serve 8 requires maintaining the same ingredient ratios. In finance, gear ratios in cars typically range from 3:1 to 5:1, affecting fuel efficiency and performance. These concepts extend into similar triangles in geometry, probability calculations, and unit conversions in physics and chemistry, making ratio reasoning essential for STEM fields.

Common mistakes to watch for

  • ✗Setting up proportions backwards, such as writing 3 apples/2 dollars = x apples/8 dollars as 3/2 = 8/x instead of 3/2 = x/8, leading to x = 12 apples instead of the correct 12 apples
  • ✗Adding instead of multiplying when cross-multiplying, solving 4/5 = x/10 as 4 + 10 = 5 + x, giving x = 9 instead of the correct x = 8
  • ✗Forgetting to simplify ratios by dividing by the greatest common factor, leaving 12:18 as the final answer instead of reducing it to 2:3

Questions teachers ask

What is the difference between a ratio and a proportion?+
A ratio compares two quantities (like 3:4), while a proportion states that two ratios are equal (like 3:4 = 6:8). Think of a ratio as a single comparison and a proportion as an equation showing two ratios have the same relationship.
How do you check if your proportion answer is correct?+
Substitute your answer back into the original proportion and cross-multiply. For example, if solving 2/3 = x/12 gives x = 8, check by verifying 2 × 12 = 3 × 8, which equals 24 = 24, confirming the answer is correct.
When should you use unit rates versus proportions?+
Use unit rates when finding cost per item or speed per hour (like $3.50 per pound). Use proportions when you know corresponding values and need to find a missing quantity (like if 3 pounds costs $10.50, what does 5 pounds cost).
What does it mean to simplify a ratio?+
Simplifying a ratio means dividing both numbers by their greatest common factor to get the smallest possible whole numbers. For example, 8:12 simplifies to 2:3 by dividing both sides by 4, making the ratio easier to understand and work with.
How do you solve word problems involving ratios?+
Identify what quantities are being compared, write the ratio using the same units, set up a proportion if needed, and cross-multiply to solve. Always label your units and check that your answer makes sense in the context of the problem.
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Pick a difficulty

Click any level to open the generator with that difficulty pre-selected.

Beginner

Generate →
Concepts
Simplify and find equivalent ratios
Range
values 2–12
Steps
1–2 steps
Example
Simplify 6:9

Easy

Generate →
Concepts
Cross-multiplication, map scales, recipes
Range
varied
Steps
2 steps
Example
1:50000 scale, 5 cm = ? km

Medium

Generate →
Concepts
Unit rates, better-deal comparison
Range
varied
Steps
2 steps
Example
4 items cost 12, 7 items = ?

Hard

Generate →
Concepts
Workers, mixtures, similar triangles
Range
varied
Steps
2–3 steps
Example
3 workers paint 5 walls, 12 workers = ?

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