Free Grade 3 Working with Surds Worksheets
Free Grade 3 worksheets for Working with 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with surds
Identify working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with surds
Explain working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with surds
Calculate working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with surds
Compare working with 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 Working with 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 20:12.[1]
- 2.Simplify the ratio 24:12.[1]
- 3.Simplify the ratio 20:16.[1]
- 4.Simplify the ratio 12:36.[1]
- 5.Share 55 in the ratio 5:6.[2]
- 6.Share 54 in the ratio 2:4.[2]
- 7.Share 90 in the ratio 5:4.[2]
- 8.Share 84 in the ratio 5:2.[2]
- 9.Share 90 in the ratio 3:7.[3]
- 10.Share 30 in the ratio 3:7.[3]
- 11.Share 42 in the ratio 1:5.[3]
- 12.Share 15 in the ratio 1:4.[3]
Show answers and working
1. 5:3
HCF of 20 and 12 is 4. Divide both parts by it: 5:3.
2. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
3. 5:4
HCF of 20 and 16 is 4. Divide both parts by it: 5:4.
4. 1:3
HCF of 12 and 36 is 12. Divide both parts by it: 1:3.
5. 25 and 30
Total parts: 5 + 6 = 11. One part: 55 ÷ 11 = 5. 5 × 5 = 25, 6 × 5 = 30.
6. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
7. 50 and 40
Total parts: 5 + 4 = 9. One part: 90 ÷ 9 = 10. 5 × 10 = 50, 4 × 10 = 40.
8. 60 and 24
Total parts: 5 + 2 = 7. One part: 84 ÷ 7 = 12. 5 × 12 = 60, 2 × 12 = 24.
9. 27 and 63
Total parts: 3 + 7 = 10. One part: 90 ÷ 10 = 9. 3 × 9 = 27, 7 × 9 = 63.
10. 9 and 21
Total parts: 3 + 7 = 10. One part: 30 ÷ 10 = 3. 3 × 3 = 9, 7 × 3 = 21.
11. 7 and 35
Total parts: 1 + 5 = 6. One part: 42 ÷ 6 = 7. 1 × 7 = 7, 5 × 7 = 35.
12. 3 and 12
Total parts: 1 + 4 = 5. One part: 15 ÷ 5 = 3. 1 × 3 = 3, 4 × 3 = 12.
Worked examples
Simplify the ratio 60:48.
- HCF of 60 and 48 is 12.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 50 in the ratio 2:3.
- Total parts: 2 + 3 = 5.
- One part: 50 ÷ 5 = 10.
- 2 × 10 = 20, 3 × 10 = 30.
- Answer: 20 and 30
Share 25 in the ratio 2:3.
- Total parts: 2 + 3 = 5.
- One part: 25 ÷ 5 = 5.
- 2 × 5 = 10, 3 × 5 = 15.
- Answer: 10 and 15
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 Working with Surds
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Learn — Meet the idea.
Practice — Build fluency.
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Assess — Prove mastery.
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Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with 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 Introducing Surds, 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 Working with Surds?
- Move on to Surds in Context, Simplifying Surds, Pi as an Irrational, which build directly on this idea.
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