Free Grade 3 Working with Simplifying Surds Quizzes
Free Grade 3 quizzes for Working with 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with simplifying surds
Identify working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with simplifying surds
Explain working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with simplifying surds
Calculate working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with simplifying surds
Compare working with 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 Working with 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 36:36.[1]
- 2.Simplify the ratio 24:60.[1]
- 3.Simplify the ratio 18:24.[1]
- 4.Simplify the ratio 40:40.[1]
- 5.Share 48 in the ratio 5:3.[2]
- 6.Share 20 in the ratio 1:4.[2]
- 7.Share 56 in the ratio 4:3.[2]
- 8.Share 15 in the ratio 3:2.[2]
- 9.Share 80 in the ratio 4:4.[3]
- 10.Share 27 in the ratio 2:1.[3]
- 11.Share 20 in the ratio 5:5.[3]
- 12.Share 56 in the ratio 5:2.[3]
Show answers and working
1. 1:1
HCF of 36 and 36 is 36. Divide both parts by it: 1:1.
2. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
3. 3:4
HCF of 18 and 24 is 6. Divide both parts by it: 3:4.
4. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
5. 30 and 18
Total parts: 5 + 3 = 8. One part: 48 ÷ 8 = 6. 5 × 6 = 30, 3 × 6 = 18.
6. 4 and 16
Total parts: 1 + 4 = 5. One part: 20 ÷ 5 = 4. 1 × 4 = 4, 4 × 4 = 16.
7. 32 and 24
Total parts: 4 + 3 = 7. One part: 56 ÷ 7 = 8. 4 × 8 = 32, 3 × 8 = 24.
8. 9 and 6
Total parts: 3 + 2 = 5. One part: 15 ÷ 5 = 3. 3 × 3 = 9, 2 × 3 = 6.
9. 40 and 40
Total parts: 4 + 4 = 8. One part: 80 ÷ 8 = 10. 4 × 10 = 40, 4 × 10 = 40.
10. 18 and 9
Total parts: 2 + 1 = 3. One part: 27 ÷ 3 = 9. 2 × 9 = 18, 1 × 9 = 9.
11. 10 and 10
Total parts: 5 + 5 = 10. One part: 20 ÷ 10 = 2. 5 × 2 = 10, 5 × 2 = 10.
12. 40 and 16
Total parts: 5 + 2 = 7. One part: 56 ÷ 7 = 8. 5 × 8 = 40, 2 × 8 = 16.
Worked examples
Simplify the ratio 24:18.
- HCF of 24 and 18 is 6.
- Divide both parts by it: 4:3.
- Answer: 4:3
Share 56 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 56 ÷ 8 = 7.
- 4 × 7 = 28, 4 × 7 = 28.
- Answer: 28 and 28
Share 55 in the ratio 4:7.
- Total parts: 4 + 7 = 11.
- One part: 55 ÷ 11 = 5.
- 4 × 5 = 20, 7 × 5 = 35.
- Answer: 20 and 35
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 Working with 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 Introducing Simplifying Surds, 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 Working with Simplifying Surds?
- Move on to Simplifying Surds in Context, Surds, Pi as an Irrational, which build directly on this idea.
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