Free Grade 3 Introducing Operations with Rationals Quizzes
Free Grade 3 quizzes for Introducing 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing operations with rationals
Explain introducing operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing operations with rationals
Calculate introducing operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing operations with rationals
Compare introducing operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing operations with rationals
Justify introducing 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 Introducing 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 32:16.[1]
- 2.Simplify the ratio 48:24.[1]
- 3.Simplify the ratio 40:40.[1]
- 4.Simplify the ratio 6:30.[1]
- 5.Share 45 in the ratio 4:1.[2]
- 6.Share 96 in the ratio 4:4.[2]
- 7.Share 24 in the ratio 5:3.[2]
- 8.Share 50 in the ratio 2:3.[2]
- 9.Share 21 in the ratio 2:1.[3]
- 10.Share 55 in the ratio 4:7.[3]
- 11.Share 54 in the ratio 5:1.[3]
- 12.Share 40 in the ratio 3:5.[3]
Show answers and working
1. 2:1
HCF of 32 and 16 is 16. Divide both parts by it: 2:1.
2. 2:1
HCF of 48 and 24 is 24. Divide both parts by it: 2:1.
3. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
4. 1:5
HCF of 6 and 30 is 6. Divide both parts by it: 1:5.
5. 36 and 9
Total parts: 4 + 1 = 5. One part: 45 ÷ 5 = 9. 4 × 9 = 36, 1 × 9 = 9.
6. 48 and 48
Total parts: 4 + 4 = 8. One part: 96 ÷ 8 = 12. 4 × 12 = 48, 4 × 12 = 48.
7. 15 and 9
Total parts: 5 + 3 = 8. One part: 24 ÷ 8 = 3. 5 × 3 = 15, 3 × 3 = 9.
8. 20 and 30
Total parts: 2 + 3 = 5. One part: 50 ÷ 5 = 10. 2 × 10 = 20, 3 × 10 = 30.
9. 14 and 7
Total parts: 2 + 1 = 3. One part: 21 ÷ 3 = 7. 2 × 7 = 14, 1 × 7 = 7.
10. 20 and 35
Total parts: 4 + 7 = 11. One part: 55 ÷ 11 = 5. 4 × 5 = 20, 7 × 5 = 35.
11. 45 and 9
Total parts: 5 + 1 = 6. One part: 54 ÷ 6 = 9. 5 × 9 = 45, 1 × 9 = 9.
12. 15 and 25
Total parts: 3 + 5 = 8. One part: 40 ÷ 8 = 5. 3 × 5 = 15, 5 × 5 = 25.
Worked examples
Simplify the ratio 8:32.
- HCF of 8 and 32 is 8.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 70 in the ratio 2:5.
- Total parts: 2 + 5 = 7.
- One part: 70 ÷ 7 = 10.
- 2 × 10 = 20, 5 × 10 = 50.
- Answer: 20 and 50
Share 60 in the ratio 1:4.
- Total parts: 1 + 4 = 5.
- One part: 60 ÷ 5 = 12.
- 1 × 12 = 12, 4 × 12 = 48.
- Answer: 12 and 48
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 Introducing Operations with Rationals 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 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 Introducing Operations with Rationals?
- Move on to Working with Operations with Rationals, Operations with Rationals in Context, Defining Rational Numbers, Rational Number Line, which build directly on this idea.
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