Free Grade 3 Operations with Rationals in Context Techniques Lessons
Free Grade 3 lessons 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 30:10.[1]
- 2.Simplify the ratio 40:50.[1]
- 3.Simplify the ratio 60:24.[1]
- 4.Simplify the ratio 6:18.[1]
- 5.Share 14 in the ratio 1:6.[2]
- 6.Share 30 in the ratio 3:2.[2]
- 7.Share 40 in the ratio 4:1.[2]
- 8.Share 60 in the ratio 4:2.[2]
- 9.Share 18 in the ratio 3:3.[3]
- 10.Share 48 in the ratio 3:5.[3]
- 11.Share 10 in the ratio 4:1.[3]
- 12.Share 40 in the ratio 1:4.[3]
Show answers and working
1. 3:1
HCF of 30 and 10 is 10. Divide both parts by it: 3:1.
2. 4:5
HCF of 40 and 50 is 10. Divide both parts by it: 4:5.
3. 5:2
HCF of 60 and 24 is 12. Divide both parts by it: 5:2.
4. 1:3
HCF of 6 and 18 is 6. Divide both parts by it: 1:3.
5. 2 and 12
Total parts: 1 + 6 = 7. One part: 14 ÷ 7 = 2. 1 × 2 = 2, 6 × 2 = 12.
6. 18 and 12
Total parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. 3 × 6 = 18, 2 × 6 = 12.
7. 32 and 8
Total parts: 4 + 1 = 5. One part: 40 ÷ 5 = 8. 4 × 8 = 32, 1 × 8 = 8.
8. 40 and 20
Total parts: 4 + 2 = 6. One part: 60 ÷ 6 = 10. 4 × 10 = 40, 2 × 10 = 20.
9. 9 and 9
Total parts: 3 + 3 = 6. One part: 18 ÷ 6 = 3. 3 × 3 = 9, 3 × 3 = 9.
10. 18 and 30
Total parts: 3 + 5 = 8. One part: 48 ÷ 8 = 6. 3 × 6 = 18, 5 × 6 = 30.
11. 8 and 2
Total parts: 4 + 1 = 5. One part: 10 ÷ 5 = 2. 4 × 2 = 8, 1 × 2 = 2.
12. 8 and 32
Total parts: 1 + 4 = 5. One part: 40 ÷ 5 = 8. 1 × 8 = 8, 4 × 8 = 32.
Worked examples
Simplify the ratio 48:60.
- HCF of 48 and 60 is 12.
- Divide both parts by it: 4:5.
- Answer: 4:5
Share 42 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 42 ÷ 6 = 7.
- 5 × 7 = 35, 1 × 7 = 7.
- Answer: 35 and 7
Share 70 in the ratio 1:6.
- Total parts: 1 + 6 = 7.
- One part: 70 ÷ 7 = 10.
- 1 × 10 = 10, 6 × 10 = 60.
- Answer: 10 and 60
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
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- 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 lesson 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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