Free Grade 3 Introducing Simplifying Surds Worksheets
Free Grade 3 worksheets for Introducing 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing simplifying surds
Identify introducing simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing simplifying surds
Explain introducing simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing simplifying surds
Calculate introducing simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing simplifying surds
Compare introducing 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 Introducing 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 24:18.[1]
- 2.Simplify the ratio 32:8.[1]
- 3.Simplify the ratio 48:36.[1]
- 4.Simplify the ratio 24:60.[1]
- 5.Share 12 in the ratio 4:2.[2]
- 6.Share 54 in the ratio 3:3.[2]
- 7.Share 14 in the ratio 5:2.[2]
- 8.Share 22 in the ratio 1:1.[2]
- 9.Share 99 in the ratio 2:7.[3]
- 10.Share 72 in the ratio 3:3.[3]
- 11.Share 9 in the ratio 1:2.[3]
- 12.Share 18 in the ratio 4:5.[3]
Show answers and working
1. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
2. 4:1
HCF of 32 and 8 is 8. Divide both parts by it: 4:1.
3. 4:3
HCF of 48 and 36 is 12. Divide both parts by it: 4:3.
4. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
5. 8 and 4
Total parts: 4 + 2 = 6. One part: 12 ÷ 6 = 2. 4 × 2 = 8, 2 × 2 = 4.
6. 27 and 27
Total parts: 3 + 3 = 6. One part: 54 ÷ 6 = 9. 3 × 9 = 27, 3 × 9 = 27.
7. 10 and 4
Total parts: 5 + 2 = 7. One part: 14 ÷ 7 = 2. 5 × 2 = 10, 2 × 2 = 4.
8. 11 and 11
Total parts: 1 + 1 = 2. One part: 22 ÷ 2 = 11. 1 × 11 = 11, 1 × 11 = 11.
9. 22 and 77
Total parts: 2 + 7 = 9. One part: 99 ÷ 9 = 11. 2 × 11 = 22, 7 × 11 = 77.
10. 36 and 36
Total parts: 3 + 3 = 6. One part: 72 ÷ 6 = 12. 3 × 12 = 36, 3 × 12 = 36.
11. 3 and 6
Total parts: 1 + 2 = 3. One part: 9 ÷ 3 = 3. 1 × 3 = 3, 2 × 3 = 6.
12. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
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 36 in the ratio 2:2.
- Total parts: 2 + 2 = 4.
- One part: 36 ÷ 4 = 9.
- 2 × 9 = 18, 2 × 9 = 18.
- Answer: 18 and 18
Share 25 in the ratio 4:1.
- Total parts: 4 + 1 = 5.
- One part: 25 ÷ 5 = 5.
- 4 × 5 = 20, 1 × 5 = 5.
- Answer: 20 and 5
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 Introducing 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. 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 Introducing Simplifying Surds?
- Move on to Working with Simplifying Surds, Simplifying Surds in Context, Surds, Pi as an Irrational, which build directly on this idea.
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