Free Grade 3 Working with Pi as an Irrational Quizzes
Free Grade 3 quizzes for Working with Pi as an Irrational: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with pi as an irrational
Identify working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with pi as an irrational
Explain working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with pi as an irrational
Calculate working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with pi as an irrational
Compare working with pi as an irrational 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 Working with Pi as an Irrational 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 32:32.[1]
- 2.Simplify the ratio 12:4.[1]
- 3.Simplify the ratio 50:10.[1]
- 4.Simplify the ratio 10:50.[1]
- 5.Share 72 in the ratio 3:3.[2]
- 6.Share 54 in the ratio 3:3.[2]
- 7.Share 77 in the ratio 3:4.[2]
- 8.Share 42 in the ratio 5:1.[2]
- 9.Share 72 in the ratio 4:5.[3]
- 10.Share 56 in the ratio 3:5.[3]
- 11.Share 8 in the ratio 2:2.[3]
- 12.Share 60 in the ratio 4:1.[3]
Show answers and working
1. 1:1
HCF of 32 and 32 is 32. Divide both parts by it: 1:1.
2. 3:1
HCF of 12 and 4 is 4. Divide both parts by it: 3:1.
3. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
4. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
5. 36 and 36
Total parts: 3 + 3 = 6. One part: 72 ÷ 6 = 12. 3 × 12 = 36, 3 × 12 = 36.
6. 27 and 27
Total parts: 3 + 3 = 6. One part: 54 ÷ 6 = 9. 3 × 9 = 27, 3 × 9 = 27.
7. 33 and 44
Total parts: 3 + 4 = 7. One part: 77 ÷ 7 = 11. 3 × 11 = 33, 4 × 11 = 44.
8. 35 and 7
Total parts: 5 + 1 = 6. One part: 42 ÷ 6 = 7. 5 × 7 = 35, 1 × 7 = 7.
9. 32 and 40
Total parts: 4 + 5 = 9. One part: 72 ÷ 9 = 8. 4 × 8 = 32, 5 × 8 = 40.
10. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
11. 4 and 4
Total parts: 2 + 2 = 4. One part: 8 ÷ 4 = 2. 2 × 2 = 4, 2 × 2 = 4.
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 12:16.
- HCF of 12 and 16 is 4.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 28 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 28 ÷ 4 = 7.
- 3 × 7 = 21, 1 × 7 = 7.
- Answer: 21 and 7
Share 30 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 30 ÷ 6 = 5.
- 1 × 5 = 5, 5 × 5 = 25.
- Answer: 5 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
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Pi as an Irrational 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 Introducing Pi as an Irrational, Simplifying Surds. 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 Working with Pi as an Irrational?
- Move on to Pi as an Irrational in Context, Surds, Simplifying Surds, which build directly on this idea.
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