Free Grade 3 Simplifying Surds Worksheets
Free Grade 3 worksheets for Simplifying 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
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain simplifying surds
Explain simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate simplifying surds
Calculate simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare simplifying surds
Compare simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify simplifying surds
Justify simplifying 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 Simplifying 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 20:20.[1]
- 2.Simplify the ratio 24:24.[1]
- 3.Simplify the ratio 20:10.[1]
- 4.Simplify the ratio 16:32.[1]
- 5.Share 36 in the ratio 4:2.[2]
- 6.Share 99 in the ratio 4:5.[2]
- 7.Share 33 in the ratio 1:2.[2]
- 8.Share 54 in the ratio 3:6.[2]
- 9.Share 21 in the ratio 1:2.[3]
- 10.Share 110 in the ratio 4:6.[3]
- 11.Share 70 in the ratio 5:2.[3]
- 12.Share 63 in the ratio 5:2.[3]
Show answers and working
1. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
2. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
3. 2:1
HCF of 20 and 10 is 10. Divide both parts by it: 2:1.
4. 1:2
HCF of 16 and 32 is 16. Divide both parts by it: 1:2.
5. 24 and 12
Total parts: 4 + 2 = 6. One part: 36 ÷ 6 = 6. 4 × 6 = 24, 2 × 6 = 12.
6. 44 and 55
Total parts: 4 + 5 = 9. One part: 99 ÷ 9 = 11. 4 × 11 = 44, 5 × 11 = 55.
7. 11 and 22
Total parts: 1 + 2 = 3. One part: 33 ÷ 3 = 11. 1 × 11 = 11, 2 × 11 = 22.
8. 18 and 36
Total parts: 3 + 6 = 9. One part: 54 ÷ 9 = 6. 3 × 6 = 18, 6 × 6 = 36.
9. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
10. 44 and 66
Total parts: 4 + 6 = 10. One part: 110 ÷ 10 = 11. 4 × 11 = 44, 6 × 11 = 66.
11. 50 and 20
Total parts: 5 + 2 = 7. One part: 70 ÷ 7 = 10. 5 × 10 = 50, 2 × 10 = 20.
12. 45 and 18
Total parts: 5 + 2 = 7. One part: 63 ÷ 7 = 9. 5 × 9 = 45, 2 × 9 = 18.
Worked examples
Simplify the ratio 36:48.
- HCF of 36 and 48 is 12.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 56 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 56 ÷ 7 = 8.
- 3 × 8 = 24, 4 × 8 = 32.
- Answer: 24 and 32
Share 54 in the ratio 2:7.
- Total parts: 2 + 7 = 9.
- One part: 54 ÷ 9 = 6.
- 2 × 6 = 12, 7 × 6 = 42.
- Answer: 12 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.
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Frequently asked
- Is this Grade 3 Simplifying 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 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 Simplifying Surds?
- Move on to Pi as an Irrational, Whole Numbers, Counting, Number Recognition, which build directly on this idea.
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