Free Grade 3 Irrational Numbers Quizzes
Free Grade 3 quizzes for Irrational Numbers: 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 irrational numbers
Explain irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate irrational numbers
Calculate irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare irrational numbers
Compare irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify irrational numbers
Justify irrational numbers 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 Irrational Numbers 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 8:16.[1]
- 3.Simplify the ratio 32:32.[1]
- 4.Simplify the ratio 30:18.[1]
- 5.Share 20 in the ratio 2:3.[2]
- 6.Share 66 in the ratio 5:1.[2]
- 7.Share 96 in the ratio 2:6.[2]
- 8.Share 49 in the ratio 5:2.[2]
- 9.Share 27 in the ratio 5:4.[3]
- 10.Share 55 in the ratio 4:1.[3]
- 11.Share 56 in the ratio 4:3.[3]
- 12.Share 63 in the ratio 3:4.[3]
Show answers and working
1. 2:1
HCF of 32 and 16 is 16. Divide both parts by it: 2:1.
2. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
3. 1:1
HCF of 32 and 32 is 32. Divide both parts by it: 1:1.
4. 5:3
HCF of 30 and 18 is 6. Divide both parts by it: 5:3.
5. 8 and 12
Total parts: 2 + 3 = 5. One part: 20 ÷ 5 = 4. 2 × 4 = 8, 3 × 4 = 12.
6. 55 and 11
Total parts: 5 + 1 = 6. One part: 66 ÷ 6 = 11. 5 × 11 = 55, 1 × 11 = 11.
7. 24 and 72
Total parts: 2 + 6 = 8. One part: 96 ÷ 8 = 12. 2 × 12 = 24, 6 × 12 = 72.
8. 35 and 14
Total parts: 5 + 2 = 7. One part: 49 ÷ 7 = 7. 5 × 7 = 35, 2 × 7 = 14.
9. 15 and 12
Total parts: 5 + 4 = 9. One part: 27 ÷ 9 = 3. 5 × 3 = 15, 4 × 3 = 12.
10. 44 and 11
Total parts: 4 + 1 = 5. One part: 55 ÷ 5 = 11. 4 × 11 = 44, 1 × 11 = 11.
11. 32 and 24
Total parts: 4 + 3 = 7. One part: 56 ÷ 7 = 8. 4 × 8 = 32, 3 × 8 = 24.
12. 27 and 36
Total parts: 3 + 4 = 7. One part: 63 ÷ 7 = 9. 3 × 9 = 27, 4 × 9 = 36.
Worked examples
Simplify the ratio 12:12.
- HCF of 12 and 12 is 12.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 90 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 90 ÷ 9 = 10.
- 5 × 10 = 50, 4 × 10 = 40.
- Answer: 50 and 40
Share 70 in the ratio 4:6.
- Total parts: 4 + 6 = 10.
- One part: 70 ÷ 10 = 7.
- 4 × 7 = 28, 6 × 7 = 42.
- Answer: 28 and 42
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.
Every free resource for Irrational Numbers
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Frequently asked
- Is this Grade 3 Irrational Numbers 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 Numbers, Percentages. 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 Irrational Numbers?
- Move on to Real Numbers, Complex Numbers, Ratio, Proportion, which build directly on this idea.
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