Free Grade 3 Simplifying Surds in Context Worksheets
Free Grade 3 worksheets for Simplifying Surds in Context: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain simplifying surds in context
Explain simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate simplifying surds in context
Calculate simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare simplifying surds in context
Compare simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify simplifying surds in context
Justify simplifying surds in context 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 in Context 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 40:20.[1]
- 2.Simplify the ratio 60:12.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 50:50.[1]
- 5.Share 48 in the ratio 5:1.[2]
- 6.Share 49 in the ratio 2:5.[2]
- 7.Share 96 in the ratio 5:3.[2]
- 8.Share 81 in the ratio 4:5.[2]
- 9.Share 110 in the ratio 4:6.[3]
- 10.Share 24 in the ratio 2:1.[3]
- 11.Share 14 in the ratio 2:5.[3]
- 12.Share 77 in the ratio 4:3.[3]
Show answers and working
1. 2:1
HCF of 40 and 20 is 20. Divide both parts by it: 2:1.
2. 5:1
HCF of 60 and 12 is 12. Divide both parts by it: 5:1.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 1:1
HCF of 50 and 50 is 50. Divide both parts by it: 1:1.
5. 40 and 8
Total parts: 5 + 1 = 6. One part: 48 ÷ 6 = 8. 5 × 8 = 40, 1 × 8 = 8.
6. 14 and 35
Total parts: 2 + 5 = 7. One part: 49 ÷ 7 = 7. 2 × 7 = 14, 5 × 7 = 35.
7. 60 and 36
Total parts: 5 + 3 = 8. One part: 96 ÷ 8 = 12. 5 × 12 = 60, 3 × 12 = 36.
8. 36 and 45
Total parts: 4 + 5 = 9. One part: 81 ÷ 9 = 9. 4 × 9 = 36, 5 × 9 = 45.
9. 44 and 66
Total parts: 4 + 6 = 10. One part: 110 ÷ 10 = 11. 4 × 11 = 44, 6 × 11 = 66.
10. 16 and 8
Total parts: 2 + 1 = 3. One part: 24 ÷ 3 = 8. 2 × 8 = 16, 1 × 8 = 8.
11. 4 and 10
Total parts: 2 + 5 = 7. One part: 14 ÷ 7 = 2. 2 × 2 = 4, 5 × 2 = 10.
12. 44 and 33
Total parts: 4 + 3 = 7. One part: 77 ÷ 7 = 11. 4 × 11 = 44, 3 × 11 = 33.
Worked examples
Simplify the ratio 24:48.
- HCF of 24 and 48 is 24.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 44 in the ratio 2:2.
- Total parts: 2 + 2 = 4.
- One part: 44 ÷ 4 = 11.
- 2 × 11 = 22, 2 × 11 = 22.
- Answer: 22 and 22
Share 28 in the ratio 1:3.
- Total parts: 1 + 3 = 4.
- One part: 28 ÷ 4 = 7.
- 1 × 7 = 7, 3 × 7 = 21.
- Answer: 7 and 21
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 in Context 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 Working with Simplifying Surds, Introducing Simplifying Surds, 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 Simplifying Surds in Context?
- Move on to Surds, Pi as an Irrational, which build directly on this idea.
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