Free Grade 3 Introducing Surds Quizzes
Free Grade 3 quizzes for Introducing 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing surds
Identify introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing surds
Explain introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing surds
Calculate introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing surds
Compare introducing 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 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 24:36.[1]
- 3.Simplify the ratio 8:12.[1]
- 4.Simplify the ratio 10:50.[1]
- 5.Share 28 in the ratio 1:6.[2]
- 6.Share 77 in the ratio 5:6.[2]
- 7.Share 40 in the ratio 3:1.[2]
- 8.Share 32 in the ratio 2:6.[2]
- 9.Share 12 in the ratio 5:1.[3]
- 10.Share 24 in the ratio 1:2.[3]
- 11.Share 24 in the ratio 5:1.[3]
- 12.Share 44 in the ratio 5:6.[3]
Show answers and working
1. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
2. 2:3
HCF of 24 and 36 is 12. Divide both parts by it: 2:3.
3. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
4. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
5. 4 and 24
Total parts: 1 + 6 = 7. One part: 28 ÷ 7 = 4. 1 × 4 = 4, 6 × 4 = 24.
6. 35 and 42
Total parts: 5 + 6 = 11. One part: 77 ÷ 11 = 7. 5 × 7 = 35, 6 × 7 = 42.
7. 30 and 10
Total parts: 3 + 1 = 4. One part: 40 ÷ 4 = 10. 3 × 10 = 30, 1 × 10 = 10.
8. 8 and 24
Total parts: 2 + 6 = 8. One part: 32 ÷ 8 = 4. 2 × 4 = 8, 6 × 4 = 24.
9. 10 and 2
Total parts: 5 + 1 = 6. One part: 12 ÷ 6 = 2. 5 × 2 = 10, 1 × 2 = 2.
10. 8 and 16
Total parts: 1 + 2 = 3. One part: 24 ÷ 3 = 8. 1 × 8 = 8, 2 × 8 = 16.
11. 20 and 4
Total parts: 5 + 1 = 6. One part: 24 ÷ 6 = 4. 5 × 4 = 20, 1 × 4 = 4.
12. 20 and 24
Total parts: 5 + 6 = 11. One part: 44 ÷ 11 = 4. 5 × 4 = 20, 6 × 4 = 24.
Worked examples
Simplify the ratio 48:12.
- HCF of 48 and 12 is 12.
- Divide both parts by it: 4:1.
- Answer: 4:1
Share 84 in the ratio 1:6.
- Total parts: 1 + 6 = 7.
- One part: 84 ÷ 7 = 12.
- 1 × 12 = 12, 6 × 12 = 72.
- Answer: 12 and 72
Share 66 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 66 ÷ 6 = 11.
- 1 × 11 = 11, 5 × 11 = 55.
- Answer: 11 and 55
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 Introducing Surds
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Introducing 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 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 Introducing Surds?
- Move on to Working with Surds, Surds in Context, Simplifying Surds, Pi as an Irrational, which build directly on this idea.
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