Free Grade 3 Irrational Numbers Worksheets
Free Grade 3 worksheets 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
Stretch
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 6:30.[1]
- 2.Simplify the ratio 30:12.[1]
- 3.Simplify the ratio 32:16.[1]
- 4.Simplify the ratio 50:30.[1]
- 5.Share 32 in the ratio 3:5.[2]
- 6.Share 10 in the ratio 3:2.[2]
- 7.Share 15 in the ratio 4:1.[2]
- 8.Share 12 in the ratio 3:1.[2]
- 9.Share 16 in the ratio 3:1.[3]
- 10.Share 108 in the ratio 4:5.[3]
- 11.Share 36 in the ratio 3:3.[3]
- 12.Share 10 in the ratio 4:1.[3]
Show answers and working
1. 1:5
HCF of 6 and 30 is 6. Divide both parts by it: 1:5.
2. 5:2
HCF of 30 and 12 is 6. Divide both parts by it: 5:2.
3. 2:1
HCF of 32 and 16 is 16. Divide both parts by it: 2:1.
4. 5:3
HCF of 50 and 30 is 10. Divide both parts by it: 5:3.
5. 12 and 20
Total parts: 3 + 5 = 8. One part: 32 ÷ 8 = 4. 3 × 4 = 12, 5 × 4 = 20.
6. 6 and 4
Total parts: 3 + 2 = 5. One part: 10 ÷ 5 = 2. 3 × 2 = 6, 2 × 2 = 4.
7. 12 and 3
Total parts: 4 + 1 = 5. One part: 15 ÷ 5 = 3. 4 × 3 = 12, 1 × 3 = 3.
8. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
9. 12 and 4
Total parts: 3 + 1 = 4. One part: 16 ÷ 4 = 4. 3 × 4 = 12, 1 × 4 = 4.
10. 48 and 60
Total parts: 4 + 5 = 9. One part: 108 ÷ 9 = 12. 4 × 12 = 48, 5 × 12 = 60.
11. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
12. 8 and 2
Total parts: 4 + 1 = 5. One part: 10 ÷ 5 = 2. 4 × 2 = 8, 1 × 2 = 2.
Worked examples
Simplify the ratio 4:12.
- HCF of 4 and 12 is 4.
- Divide both parts by it: 1:3.
- Answer: 1:3
Share 32 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 32 ÷ 8 = 4.
- 4 × 4 = 16, 4 × 4 = 16.
- Answer: 16 and 16
Share 70 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 70 ÷ 7 = 10.
- 3 × 10 = 30, 4 × 10 = 40.
- Answer: 30 and 40
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 worksheet really free?
- Yes. Every worksheets 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 worksheet 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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