Free Grade 3 Simplifying Surds Quizzes
Free Grade 3 quizzes for 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
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain simplifying surds
Explain simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate simplifying surds
Calculate simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare simplifying surds
Compare simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify simplifying surds
Justify 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 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 24:8.[1]
- 2.Simplify the ratio 10:40.[1]
- 3.Simplify the ratio 48:48.[1]
- 4.Simplify the ratio 40:40.[1]
- 5.Share 54 in the ratio 5:1.[2]
- 6.Share 84 in the ratio 5:2.[2]
- 7.Share 28 in the ratio 1:6.[2]
- 8.Share 56 in the ratio 4:3.[2]
- 9.Share 55 in the ratio 4:7.[3]
- 10.Share 36 in the ratio 3:6.[3]
- 11.Share 56 in the ratio 3:4.[3]
- 12.Share 66 in the ratio 5:6.[3]
Show answers and working
1. 3:1
HCF of 24 and 8 is 8. Divide both parts by it: 3:1.
2. 1:4
HCF of 10 and 40 is 10. Divide both parts by it: 1:4.
3. 1:1
HCF of 48 and 48 is 48. Divide both parts by it: 1:1.
4. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
5. 45 and 9
Total parts: 5 + 1 = 6. One part: 54 ÷ 6 = 9. 5 × 9 = 45, 1 × 9 = 9.
6. 60 and 24
Total parts: 5 + 2 = 7. One part: 84 ÷ 7 = 12. 5 × 12 = 60, 2 × 12 = 24.
7. 4 and 24
Total parts: 1 + 6 = 7. One part: 28 ÷ 7 = 4. 1 × 4 = 4, 6 × 4 = 24.
8. 32 and 24
Total parts: 4 + 3 = 7. One part: 56 ÷ 7 = 8. 4 × 8 = 32, 3 × 8 = 24.
9. 20 and 35
Total parts: 4 + 7 = 11. One part: 55 ÷ 11 = 5. 4 × 5 = 20, 7 × 5 = 35.
10. 12 and 24
Total parts: 3 + 6 = 9. One part: 36 ÷ 9 = 4. 3 × 4 = 12, 6 × 4 = 24.
11. 24 and 32
Total parts: 3 + 4 = 7. One part: 56 ÷ 7 = 8. 3 × 8 = 24, 4 × 8 = 32.
12. 30 and 36
Total parts: 5 + 6 = 11. One part: 66 ÷ 11 = 6. 5 × 6 = 30, 6 × 6 = 36.
Worked examples
Simplify the ratio 12:6.
- HCF of 12 and 6 is 6.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 36 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 36 ÷ 9 = 4.
- 5 × 4 = 20, 4 × 4 = 16.
- Answer: 20 and 16
Share 35 in the ratio 4:1.
- Total parts: 4 + 1 = 5.
- One part: 35 ÷ 5 = 7.
- 4 × 7 = 28, 1 × 7 = 7.
- Answer: 28 and 7
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 Simplifying Surds
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Frequently asked
- Is this Grade 3 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, 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 Simplifying Surds?
- Move on to Pi as an Irrational, Whole Numbers, Counting, Number Recognition, which build directly on this idea.
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