Free Grade 3 Pi as an Irrational Quizzes
Free Grade 3 quizzes for 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify pi as an irrational
Identify pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain pi as an irrational
Explain pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate pi as an irrational
Calculate pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare pi as an irrational
Compare 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 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 30:50.[1]
- 2.Simplify the ratio 30:20.[1]
- 3.Simplify the ratio 24:32.[1]
- 4.Simplify the ratio 48:60.[1]
- 5.Share 10 in the ratio 1:1.[2]
- 6.Share 30 in the ratio 5:1.[2]
- 7.Share 50 in the ratio 4:6.[2]
- 8.Share 88 in the ratio 2:6.[2]
- 9.Share 42 in the ratio 3:4.[3]
- 10.Share 45 in the ratio 4:5.[3]
- 11.Share 81 in the ratio 4:5.[3]
- 12.Share 90 in the ratio 2:7.[3]
Show answers and working
1. 3:5
HCF of 30 and 50 is 10. Divide both parts by it: 3:5.
2. 3:2
HCF of 30 and 20 is 10. Divide both parts by it: 3:2.
3. 3:4
HCF of 24 and 32 is 8. Divide both parts by it: 3:4.
4. 4:5
HCF of 48 and 60 is 12. Divide both parts by it: 4:5.
5. 5 and 5
Total parts: 1 + 1 = 2. One part: 10 ÷ 2 = 5. 1 × 5 = 5, 1 × 5 = 5.
6. 25 and 5
Total parts: 5 + 1 = 6. One part: 30 ÷ 6 = 5. 5 × 5 = 25, 1 × 5 = 5.
7. 20 and 30
Total parts: 4 + 6 = 10. One part: 50 ÷ 10 = 5. 4 × 5 = 20, 6 × 5 = 30.
8. 22 and 66
Total parts: 2 + 6 = 8. One part: 88 ÷ 8 = 11. 2 × 11 = 22, 6 × 11 = 66.
9. 18 and 24
Total parts: 3 + 4 = 7. One part: 42 ÷ 7 = 6. 3 × 6 = 18, 4 × 6 = 24.
10. 20 and 25
Total parts: 4 + 5 = 9. One part: 45 ÷ 9 = 5. 4 × 5 = 20, 5 × 5 = 25.
11. 36 and 45
Total parts: 4 + 5 = 9. One part: 81 ÷ 9 = 9. 4 × 9 = 36, 5 × 9 = 45.
12. 20 and 70
Total parts: 2 + 7 = 9. One part: 90 ÷ 9 = 10. 2 × 10 = 20, 7 × 10 = 70.
Worked examples
Simplify the ratio 24:12.
- HCF of 24 and 12 is 12.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 22 in the ratio 1:1.
- Total parts: 1 + 1 = 2.
- One part: 22 ÷ 2 = 11.
- 1 × 11 = 11, 1 × 11 = 11.
- Answer: 11 and 11
Share 56 in the ratio 3:5.
- Total parts: 3 + 5 = 8.
- One part: 56 ÷ 8 = 7.
- 3 × 7 = 21, 5 × 7 = 35.
- Answer: 21 and 35
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 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 Simplifying Surds, Surds, Rational Numbers. 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 Pi as an Irrational?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
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