Free Grade 3 Operations with Rationals in Context Quizzes
Free Grade 3 quizzes 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
Core
15 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 24:8.[1]
- 2.Simplify the ratio 40:50.[1]
- 3.Simplify the ratio 24:6.[1]
- 4.Simplify the ratio 12:6.[1]
- 5.Share 63 in the ratio 5:4.[2]
- 6.Share 21 in the ratio 1:6.[2]
- 7.Share 36 in the ratio 3:3.[2]
- 8.Share 36 in the ratio 5:4.[2]
- 9.Share 12 in the ratio 1:5.[3]
- 10.Share 48 in the ratio 4:2.[3]
- 11.Share 54 in the ratio 3:6.[3]
- 12.Share 80 in the ratio 5:5.[3]
Show answers and working
1. 3:1
HCF of 24 and 8 is 8. 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. 4:1
HCF of 24 and 6 is 6. Divide both parts by it: 4:1.
4. 2:1
HCF of 12 and 6 is 6. Divide both parts by it: 2:1.
5. 35 and 28
Total parts: 5 + 4 = 9. One part: 63 ÷ 9 = 7. 5 × 7 = 35, 4 × 7 = 28.
6. 3 and 18
Total parts: 1 + 6 = 7. One part: 21 ÷ 7 = 3. 1 × 3 = 3, 6 × 3 = 18.
7. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
8. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
9. 2 and 10
Total parts: 1 + 5 = 6. One part: 12 ÷ 6 = 2. 1 × 2 = 2, 5 × 2 = 10.
10. 32 and 16
Total parts: 4 + 2 = 6. One part: 48 ÷ 6 = 8. 4 × 8 = 32, 2 × 8 = 16.
11. 18 and 36
Total parts: 3 + 6 = 9. One part: 54 ÷ 9 = 6. 3 × 6 = 18, 6 × 6 = 36.
12. 40 and 40
Total parts: 5 + 5 = 10. One part: 80 ÷ 10 = 8. 5 × 8 = 40, 5 × 8 = 40.
Worked examples
Simplify the ratio 12:8.
- HCF of 12 and 8 is 4.
- Divide both parts by it: 3:2.
- Answer: 3:2
Share 84 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 84 ÷ 7 = 12.
- 4 × 12 = 48, 3 × 12 = 36.
- Answer: 48 and 36
Share 12 in the ratio 3:3.
- Total parts: 3 + 3 = 6.
- One part: 12 ÷ 6 = 2.
- 3 × 2 = 6, 3 × 2 = 6.
- Answer: 6 and 6
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 quiz really free?
- Yes. Every quizzes 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 quiz 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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