Free Grade 3 Introducing Simplifying Surds Quizzes
Free Grade 3 quizzes 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
Stretch
30 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 24:12.[1]
- 2.Simplify the ratio 6:24.[1]
- 3.Simplify the ratio 32:8.[1]
- 4.Simplify the ratio 8:12.[1]
- 5.Share 21 in the ratio 3:4.[2]
- 6.Share 36 in the ratio 3:1.[2]
- 7.Share 33 in the ratio 2:1.[2]
- 8.Share 54 in the ratio 5:4.[2]
- 9.Share 45 in the ratio 3:2.[3]
- 10.Share 20 in the ratio 5:5.[3]
- 11.Share 55 in the ratio 3:2.[3]
- 12.Share 108 in the ratio 4:5.[3]
Show answers and working
1. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
2. 1:4
HCF of 6 and 24 is 6. Divide both parts by it: 1:4.
3. 4:1
HCF of 32 and 8 is 8. Divide both parts by it: 4:1.
4. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
5. 9 and 12
Total parts: 3 + 4 = 7. One part: 21 ÷ 7 = 3. 3 × 3 = 9, 4 × 3 = 12.
6. 27 and 9
Total parts: 3 + 1 = 4. One part: 36 ÷ 4 = 9. 3 × 9 = 27, 1 × 9 = 9.
7. 22 and 11
Total parts: 2 + 1 = 3. One part: 33 ÷ 3 = 11. 2 × 11 = 22, 1 × 11 = 11.
8. 30 and 24
Total parts: 5 + 4 = 9. One part: 54 ÷ 9 = 6. 5 × 6 = 30, 4 × 6 = 24.
9. 27 and 18
Total parts: 3 + 2 = 5. One part: 45 ÷ 5 = 9. 3 × 9 = 27, 2 × 9 = 18.
10. 10 and 10
Total parts: 5 + 5 = 10. One part: 20 ÷ 10 = 2. 5 × 2 = 10, 5 × 2 = 10.
11. 33 and 22
Total parts: 3 + 2 = 5. One part: 55 ÷ 5 = 11. 3 × 11 = 33, 2 × 11 = 22.
12. 48 and 60
Total parts: 4 + 5 = 9. One part: 108 ÷ 9 = 12. 4 × 12 = 48, 5 × 12 = 60.
Worked examples
Simplify the ratio 60:24.
- HCF of 60 and 24 is 12.
- Divide both parts by it: 5:2.
- Answer: 5:2
Share 54 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 54 ÷ 6 = 9.
- 4 × 9 = 36, 2 × 9 = 18.
- Answer: 36 and 18
Share 56 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 56 ÷ 7 = 8.
- 3 × 8 = 24, 4 × 8 = 32.
- Answer: 24 and 32
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 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 Surds. 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 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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