Free Grade 3 Surds Worksheets
Free Grade 3 worksheets for Surds: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain surds
Explain surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate surds
Calculate surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare surds
Compare surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify surds
Justify surds 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 Surds 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 6:18.[1]
- 2.Simplify the ratio 10:20.[1]
- 3.Simplify the ratio 36:60.[1]
- 4.Simplify the ratio 18:24.[1]
- 5.Share 45 in the ratio 4:1.[2]
- 6.Share 54 in the ratio 3:6.[2]
- 7.Share 54 in the ratio 2:4.[2]
- 8.Share 63 in the ratio 3:4.[2]
- 9.Share 77 in the ratio 1:6.[3]
- 10.Share 55 in the ratio 5:6.[3]
- 11.Share 45 in the ratio 1:4.[3]
- 12.Share 33 in the ratio 4:7.[3]
Show answers and working
1. 1:3
HCF of 6 and 18 is 6. Divide both parts by it: 1:3.
2. 1:2
HCF of 10 and 20 is 10. Divide both parts by it: 1:2.
3. 3:5
HCF of 36 and 60 is 12. Divide both parts by it: 3:5.
4. 3:4
HCF of 18 and 24 is 6. Divide both parts by it: 3:4.
5. 36 and 9
Total parts: 4 + 1 = 5. One part: 45 ÷ 5 = 9. 4 × 9 = 36, 1 × 9 = 9.
6. 18 and 36
Total parts: 3 + 6 = 9. One part: 54 ÷ 9 = 6. 3 × 6 = 18, 6 × 6 = 36.
7. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
8. 27 and 36
Total parts: 3 + 4 = 7. One part: 63 ÷ 7 = 9. 3 × 9 = 27, 4 × 9 = 36.
9. 11 and 66
Total parts: 1 + 6 = 7. One part: 77 ÷ 7 = 11. 1 × 11 = 11, 6 × 11 = 66.
10. 25 and 30
Total parts: 5 + 6 = 11. One part: 55 ÷ 11 = 5. 5 × 5 = 25, 6 × 5 = 30.
11. 9 and 36
Total parts: 1 + 4 = 5. One part: 45 ÷ 5 = 9. 1 × 9 = 9, 4 × 9 = 36.
12. 12 and 21
Total parts: 4 + 7 = 11. One part: 33 ÷ 11 = 3. 4 × 3 = 12, 7 × 3 = 21.
Worked examples
Simplify the ratio 32:32.
- HCF of 32 and 32 is 32.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 64 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 64 ÷ 8 = 8.
- 2 × 8 = 16, 6 × 8 = 48.
- Answer: 16 and 48
Share 121 in the ratio 4:7.
- Total parts: 4 + 7 = 11.
- One part: 121 ÷ 11 = 11.
- 4 × 11 = 44, 7 × 11 = 77.
- Answer: 44 and 77
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 Surds
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Surds 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. 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 Surds?
- Move on to Simplifying Surds, Pi as an Irrational, Whole Numbers, Counting, which build directly on this idea.
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