Free Grade 3 Operations with Rationals Worksheets
Free Grade 3 worksheets for Operations with Rationals: 12 real questions with a full answer key and worked solutions. A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
Free
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify operations with rationals
Identify operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain operations with rationals
Explain operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate operations with rationals
Calculate operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare operations with rationals
Compare operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Operations with Rationals works
A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Simplify the ratio 4:4.[1]
- 2.Simplify the ratio 36:36.[1]
- 3.Simplify the ratio 4:8.[1]
- 4.Simplify the ratio 40:16.[1]
- 5.Share 72 in the ratio 3:3.[2]
- 6.Share 110 in the ratio 5:6.[2]
- 7.Share 90 in the ratio 4:5.[2]
- 8.Share 54 in the ratio 3:6.[2]
- 9.Share 48 in the ratio 4:2.[3]
- 10.Share 21 in the ratio 1:2.[3]
- 11.Share 36 in the ratio 1:2.[3]
- 12.Share 25 in the ratio 2:3.[3]
Show answers and working
1. 1:1
HCF of 4 and 4 is 4. Divide both parts by it: 1:1.
2. 1:1
HCF of 36 and 36 is 36. Divide both parts by it: 1:1.
3. 1:2
HCF of 4 and 8 is 4. Divide both parts by it: 1:2.
4. 5:2
HCF of 40 and 16 is 8. Divide both parts by it: 5:2.
5. 36 and 36
Total parts: 3 + 3 = 6. One part: 72 ÷ 6 = 12. 3 × 12 = 36, 3 × 12 = 36.
6. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
7. 40 and 50
Total parts: 4 + 5 = 9. One part: 90 ÷ 9 = 10. 4 × 10 = 40, 5 × 10 = 50.
8. 18 and 36
Total parts: 3 + 6 = 9. One part: 54 ÷ 9 = 6. 3 × 6 = 18, 6 × 6 = 36.
9. 32 and 16
Total parts: 4 + 2 = 6. One part: 48 ÷ 6 = 8. 4 × 8 = 32, 2 × 8 = 16.
10. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
11. 12 and 24
Total parts: 1 + 2 = 3. One part: 36 ÷ 3 = 12. 1 × 12 = 12, 2 × 12 = 24.
12. 10 and 15
Total parts: 2 + 3 = 5. One part: 25 ÷ 5 = 5. 2 × 5 = 10, 3 × 5 = 15.
Worked examples
Simplify the ratio 40:24.
- HCF of 40 and 24 is 8.
- Divide both parts by it: 5:3.
- Answer: 5:3
Share 54 in the ratio 4:5.
- Total parts: 4 + 5 = 9.
- One part: 54 ÷ 9 = 6.
- 4 × 6 = 24, 5 × 6 = 30.
- Answer: 24 and 30
Share 80 in the ratio 3:5.
- Total parts: 3 + 5 = 8.
- One part: 80 ÷ 8 = 10.
- 3 × 10 = 30, 5 × 10 = 50.
- Answer: 30 and 50
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Divides the total by the ratio numbers directly.
Correction: Add the parts first to find what one part is worth.
Writes the ratio in the wrong order.
Correction: Keep the order the question uses.
Teacher tips
- · Use bar models with equal-sized boxes for each part.
Parent tips
- · Make squash in a 1:4 ratio.
Real-life applications
- · Mixing paint or squash, scaling recipes.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Operations with Rationals
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Frequently asked
- Is this Grade 3 Operations with Rationals worksheet really free?
- Yes. Every worksheets on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Rational Number Line, Defining Rational Numbers, Percentages. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Operations with Rationals?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
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