Free Grade 3 Working with Surds Quizzes
Free Grade 3 quizzes 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
Core
25 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 40:24.[1]
- 2.Simplify the ratio 16:32.[1]
- 3.Simplify the ratio 8:12.[1]
- 4.Simplify the ratio 12:18.[1]
- 5.Share 72 in the ratio 3:3.[2]
- 6.Share 77 in the ratio 5:2.[2]
- 7.Share 35 in the ratio 1:6.[2]
- 8.Share 35 in the ratio 3:4.[2]
- 9.Share 21 in the ratio 2:1.[3]
- 10.Share 12 in the ratio 1:1.[3]
- 11.Share 60 in the ratio 3:2.[3]
- 12.Share 96 in the ratio 2:6.[3]
Show answers and working
1. 5:3
HCF of 40 and 24 is 8. Divide both parts by it: 5:3.
2. 1:2
HCF of 16 and 32 is 16. Divide both parts by it: 1:2.
3. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
4. 2:3
HCF of 12 and 18 is 6. Divide both parts by it: 2:3.
5. 36 and 36
Total parts: 3 + 3 = 6. One part: 72 ÷ 6 = 12. 3 × 12 = 36, 3 × 12 = 36.
6. 55 and 22
Total parts: 5 + 2 = 7. One part: 77 ÷ 7 = 11. 5 × 11 = 55, 2 × 11 = 22.
7. 5 and 30
Total parts: 1 + 6 = 7. One part: 35 ÷ 7 = 5. 1 × 5 = 5, 6 × 5 = 30.
8. 15 and 20
Total parts: 3 + 4 = 7. One part: 35 ÷ 7 = 5. 3 × 5 = 15, 4 × 5 = 20.
9. 14 and 7
Total parts: 2 + 1 = 3. One part: 21 ÷ 3 = 7. 2 × 7 = 14, 1 × 7 = 7.
10. 6 and 6
Total parts: 1 + 1 = 2. One part: 12 ÷ 2 = 6. 1 × 6 = 6, 1 × 6 = 6.
11. 36 and 24
Total parts: 3 + 2 = 5. One part: 60 ÷ 5 = 12. 3 × 12 = 36, 2 × 12 = 24.
12. 24 and 72
Total parts: 2 + 6 = 8. One part: 96 ÷ 8 = 12. 2 × 12 = 24, 6 × 12 = 72.
Worked examples
Simplify the ratio 30:24.
- HCF of 30 and 24 is 6.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 55 in the ratio 5:6.
- Total parts: 5 + 6 = 11.
- One part: 55 ÷ 11 = 5.
- 5 × 5 = 25, 6 × 5 = 30.
- Answer: 25 and 30
Share 24 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 24 ÷ 6 = 4.
- 4 × 4 = 16, 2 × 4 = 8.
- Answer: 16 and 8
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 quiz really free?
- Yes. Every quizzes 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 quiz 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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