Free Grade 3 Operations with Rationals in Context Techniques Worksheets
Free Grade 3 worksheets for Operations with Rationals in Context Techniques: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify operations with rationals in context techniques
Identify operations with rationals in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain operations with rationals in context techniques
Explain operations with rationals in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate operations with rationals in context techniques
Calculate operations with rationals in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare operations with rationals in context techniques
Compare operations with rationals in context techniques 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 Techniques 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 30:24.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 8:8.[1]
- 4.Simplify the ratio 50:10.[1]
- 5.Share 28 in the ratio 5:2.[2]
- 6.Share 64 in the ratio 3:5.[2]
- 7.Share 90 in the ratio 4:6.[2]
- 8.Share 120 in the ratio 4:6.[2]
- 9.Share 36 in the ratio 1:5.[3]
- 10.Share 55 in the ratio 3:2.[3]
- 11.Share 28 in the ratio 4:3.[3]
- 12.Share 42 in the ratio 3:4.[3]
Show answers and working
1. 5:4
HCF of 30 and 24 is 6. Divide both parts by it: 5:4.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 1:1
HCF of 8 and 8 is 8. Divide both parts by it: 1:1.
4. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
5. 20 and 8
Total parts: 5 + 2 = 7. One part: 28 ÷ 7 = 4. 5 × 4 = 20, 2 × 4 = 8.
6. 24 and 40
Total parts: 3 + 5 = 8. One part: 64 ÷ 8 = 8. 3 × 8 = 24, 5 × 8 = 40.
7. 36 and 54
Total parts: 4 + 6 = 10. One part: 90 ÷ 10 = 9. 4 × 9 = 36, 6 × 9 = 54.
8. 48 and 72
Total parts: 4 + 6 = 10. One part: 120 ÷ 10 = 12. 4 × 12 = 48, 6 × 12 = 72.
9. 6 and 30
Total parts: 1 + 5 = 6. One part: 36 ÷ 6 = 6. 1 × 6 = 6, 5 × 6 = 30.
10. 33 and 22
Total parts: 3 + 2 = 5. One part: 55 ÷ 5 = 11. 3 × 11 = 33, 2 × 11 = 22.
11. 16 and 12
Total parts: 4 + 3 = 7. One part: 28 ÷ 7 = 4. 4 × 4 = 16, 3 × 4 = 12.
12. 18 and 24
Total parts: 3 + 4 = 7. One part: 42 ÷ 7 = 6. 3 × 6 = 18, 4 × 6 = 24.
Worked examples
Simplify the ratio 12:6.
- HCF of 12 and 6 is 6.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 8 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 8 ÷ 4 = 2.
- 3 × 2 = 6, 1 × 2 = 2.
- Answer: 6 and 2
Share 45 in the ratio 4:5.
- Total parts: 4 + 5 = 9.
- One part: 45 ÷ 9 = 5.
- 4 × 5 = 20, 5 × 5 = 25.
- Answer: 20 and 25
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
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Frequently asked
- Is this Grade 3 Operations with Rationals in Context Techniques 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 Operations with Rationals in Context Essentials, Working with Operations with Rationals. 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 Techniques?
- Move on to Operations with Rationals in Context Word Problems, Operations with Rationals in Context Common Errors, Introducing Operations with Rationals, Working with Operations with Rationals, which build directly on this idea.
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