Free Grade 3 Surds in Context Worksheets
Free Grade 3 worksheets for 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 surds in context
Explain surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate surds in context
Calculate surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare surds in context
Compare surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify surds in context
Justify 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 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 10:50.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 40:8.[1]
- 4.Simplify the ratio 36:60.[1]
- 5.Share 20 in the ratio 3:2.[2]
- 6.Share 15 in the ratio 2:1.[2]
- 7.Share 70 in the ratio 5:2.[2]
- 8.Share 16 in the ratio 1:1.[2]
- 9.Share 35 in the ratio 3:4.[3]
- 10.Share 36 in the ratio 3:3.[3]
- 11.Share 30 in the ratio 3:3.[3]
- 12.Share 20 in the ratio 4:1.[3]
Show answers and working
1. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 5:1
HCF of 40 and 8 is 8. Divide both parts by it: 5:1.
4. 3:5
HCF of 36 and 60 is 12. Divide both parts by it: 3:5.
5. 12 and 8
Total parts: 3 + 2 = 5. One part: 20 ÷ 5 = 4. 3 × 4 = 12, 2 × 4 = 8.
6. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
7. 50 and 20
Total parts: 5 + 2 = 7. One part: 70 ÷ 7 = 10. 5 × 10 = 50, 2 × 10 = 20.
8. 8 and 8
Total parts: 1 + 1 = 2. One part: 16 ÷ 2 = 8. 1 × 8 = 8, 1 × 8 = 8.
9. 15 and 20
Total parts: 3 + 4 = 7. One part: 35 ÷ 7 = 5. 3 × 5 = 15, 4 × 5 = 20.
10. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
11. 15 and 15
Total parts: 3 + 3 = 6. One part: 30 ÷ 6 = 5. 3 × 5 = 15, 3 × 5 = 15.
12. 16 and 4
Total parts: 4 + 1 = 5. One part: 20 ÷ 5 = 4. 4 × 4 = 16, 1 × 4 = 4.
Worked examples
Simplify the ratio 30:30.
- HCF of 30 and 30 is 30.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 24 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 24 ÷ 8 = 3.
- 5 × 3 = 15, 3 × 3 = 9.
- Answer: 15 and 9
Share 60 in the ratio 4:6.
- Total parts: 4 + 6 = 10.
- One part: 60 ÷ 10 = 6.
- 4 × 6 = 24, 6 × 6 = 36.
- Answer: 24 and 36
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 in Context
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 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 Surds, 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 Surds in Context?
- Move on to Simplifying Surds, Pi as an Irrational, which build directly on this idea.
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