Free Grade 3 Operations with Rationals in Context Worksheets
Free Grade 3 worksheets for Operations with Rationals in Context: 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
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify operations with rationals in context
Identify operations with rationals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain operations with rationals in context
Explain operations with rationals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate operations with rationals in context
Calculate operations with rationals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare operations with rationals in context
Compare operations with rationals in context 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 in Context 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 40:40.[1]
- 2.Simplify the ratio 48:36.[1]
- 3.Simplify the ratio 24:12.[1]
- 4.Simplify the ratio 24:18.[1]
- 5.Share 36 in the ratio 3:6.[2]
- 6.Share 60 in the ratio 4:2.[2]
- 7.Share 8 in the ratio 1:3.[2]
- 8.Share 9 in the ratio 2:1.[2]
- 9.Share 40 in the ratio 3:7.[3]
- 10.Share 120 in the ratio 5:5.[3]
- 11.Share 30 in the ratio 3:2.[3]
- 12.Share 60 in the ratio 4:1.[3]
Show answers and working
1. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
2. 4:3
HCF of 48 and 36 is 12. Divide both parts by it: 4:3.
3. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
4. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
5. 12 and 24
Total parts: 3 + 6 = 9. One part: 36 ÷ 9 = 4. 3 × 4 = 12, 6 × 4 = 24.
6. 40 and 20
Total parts: 4 + 2 = 6. One part: 60 ÷ 6 = 10. 4 × 10 = 40, 2 × 10 = 20.
7. 2 and 6
Total parts: 1 + 3 = 4. One part: 8 ÷ 4 = 2. 1 × 2 = 2, 3 × 2 = 6.
8. 6 and 3
Total parts: 2 + 1 = 3. One part: 9 ÷ 3 = 3. 2 × 3 = 6, 1 × 3 = 3.
9. 12 and 28
Total parts: 3 + 7 = 10. One part: 40 ÷ 10 = 4. 3 × 4 = 12, 7 × 4 = 28.
10. 60 and 60
Total parts: 5 + 5 = 10. One part: 120 ÷ 10 = 12. 5 × 12 = 60, 5 × 12 = 60.
11. 18 and 12
Total parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. 3 × 6 = 18, 2 × 6 = 12.
12. 48 and 12
Total parts: 4 + 1 = 5. One part: 60 ÷ 5 = 12. 4 × 12 = 48, 1 × 12 = 12.
Worked examples
Simplify the ratio 30:40.
- HCF of 30 and 40 is 10.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 88 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 88 ÷ 8 = 11.
- 2 × 11 = 22, 6 × 11 = 66.
- Answer: 22 and 66
Share 40 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 40 ÷ 8 = 5.
- 4 × 5 = 20, 4 × 5 = 20.
- Answer: 20 and 20
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.
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Frequently asked
- Is this Grade 3 Operations with Rationals in Context 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 Working with Operations with Rationals, Introducing Operations with Rationals, Rational Number Line. 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 in Context?
- Move on to Defining Rational Numbers, Rational Number Line, which build directly on this idea.
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