Free Ratio and Proportion Worksheets With Answers
These free ratio and proportion worksheets cover simplifying ratios, sharing in a given ratio, unit rates, and solving proportions, with the working shown under every answer. Ratio reasoning underpins percentages, similarity, and slope, so time spent here pays off across several later units. The same skills can be generated as a printable ratio and proportion test with an answer key.
Grades 6–7 · 9 free questions with worked answers · No sign-up to practise
Skills covered in these ratio and proportion worksheets
- Writing and simplifying ratios
- Equivalent ratios and ratio tables
- Sharing a quantity in a given ratio
- Unit rates and best-buy comparisons
- Solving proportions by cross-multiplication
- Scale drawings and maps
Free ratio and proportion practice questions with answers
Every question below includes the final answer and the steps behind it, so the sheet doubles as its own answer key. Filter by grade or difficulty to build the set you need.
- Question 1easyGrade 6
Simplify the ratio 12 : 18.
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Answer: 2 : 3
The greatest common factor of 12 and 18 is 6. Dividing both parts by 6 gives 2 : 3.
- Question 2easyGrade 6
A recipe uses flour and sugar in the ratio 4 : 1. How much sugar goes with 12 cups of flour?
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Answer: 3 cups
Flour has been multiplied by 3 to go from 4 to 12, so multiply the sugar by 3 as well: 1 × 3 = 3.
- Question 3easyGrade 6
In a class the ratio of boys to girls is 3 : 2. What fraction of the class are boys?
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Answer: 3/5
Add the parts: 3 + 2 = 5 total parts. Boys are 3 of those 5 parts, so 3/5 of the class.
- Question 4mediumGrade 6
Share $60 in the ratio 2 : 3.
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Answer: $24 and $36
Total parts = 2 + 3 = 5, so one part is 60 ÷ 5 = 12. Then 2 × 12 = 24 and 3 × 12 = 36.
- Question 5mediumGrade 7
A car travels 240 km in 3 hours. What is the unit rate?
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Answer: 80 km per hour
Divide to reduce to one hour: 240 ÷ 3 = 80 km per hour.
- Question 6mediumGrade 7
Which is better value: 500 g for $3.20 or 750 g for $4.50?
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Answer: The 750 g pack
Price per gram: 3.20 ÷ 500 = $0.0064 and 4.50 ÷ 750 = $0.006. The 750 g pack is cheaper per gram.
- Question 7hardGrade 7
Solve 4/6 = x/15.
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Answer: x = 10
Cross-multiply: 4 × 15 = 6x, so 60 = 6x and x = 10.
- Question 8hardGrade 7
A map has a scale of 1 : 50,000. Two towns are 6 cm apart on the map. How far apart are they in reality?
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Answer: 3 km
6 × 50,000 = 300,000 cm. Converting gives 3,000 m, which is 3 km.
- Question 9hardGrade 7
Two numbers are in the ratio 5 : 7 and differ by 18. What are they?
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Answer: 45 and 63
The difference is 7 − 5 = 2 parts, so one part is 18 ÷ 2 = 9. Then 5 × 9 = 45 and 7 × 9 = 63.
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Ratios compare parts; fractions compare part to whole
If a class has boys and girls in the ratio 3 : 2, then three fifths of the class are boys — not three halves. Converting a ratio into a fraction requires adding the parts to find the whole first, and skipping that step is the most frequent error in the topic. Once students total the parts before doing anything else, sharing problems become mechanical.
Unit rates make comparison possible
A 500 g pack for $3.20 and a 750 g pack for $4.50 cannot be compared directly, but their prices per gram can. Reducing every quantity to a rate per one unit turns a judgement call into arithmetic, and it is the same move that later becomes slope in algebra and density in science. The medium questions below all use this reduction.
Common mistakes to watch for
- Treating the ratio 3 : 2 as the fraction 3/2 instead of adding the parts to get 3/5 of the whole.
- Sharing a total by dividing by the largest part rather than by the total number of parts.
- Cross-multiplying in the wrong direction when solving a proportion.
- Comparing prices without first reducing both to the same unit.