Free Grade 3 Simplifying Surds Flashcards
Free Grade 3 flashcards 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 60:12.[1]
- 2.Simplify the ratio 12:60.[1]
- 3.Simplify the ratio 12:6.[1]
- 4.Simplify the ratio 4:4.[1]
- 5.Share 25 in the ratio 1:4.[2]
- 6.Share 24 in the ratio 4:2.[2]
- 7.Share 56 in the ratio 3:5.[2]
- 8.Share 30 in the ratio 4:2.[2]
- 9.Share 54 in the ratio 2:4.[3]
- 10.Share 44 in the ratio 1:3.[3]
- 11.Share 66 in the ratio 2:4.[3]
- 12.Share 55 in the ratio 3:2.[3]
Show answers and working
1. 5:1
HCF of 60 and 12 is 12. Divide both parts by it: 5:1.
2. 1:5
HCF of 12 and 60 is 12. Divide both parts by it: 1:5.
3. 2:1
HCF of 12 and 6 is 6. Divide both parts by it: 2:1.
4. 1:1
HCF of 4 and 4 is 4. Divide both parts by it: 1:1.
5. 5 and 20
Total parts: 1 + 4 = 5. One part: 25 ÷ 5 = 5. 1 × 5 = 5, 4 × 5 = 20.
6. 16 and 8
Total parts: 4 + 2 = 6. One part: 24 ÷ 6 = 4. 4 × 4 = 16, 2 × 4 = 8.
7. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
8. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
9. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
10. 11 and 33
Total parts: 1 + 3 = 4. One part: 44 ÷ 4 = 11. 1 × 11 = 11, 3 × 11 = 33.
11. 22 and 44
Total parts: 2 + 4 = 6. One part: 66 ÷ 6 = 11. 2 × 11 = 22, 4 × 11 = 44.
12. 33 and 22
Total parts: 3 + 2 = 5. One part: 55 ÷ 5 = 11. 3 × 11 = 33, 2 × 11 = 22.
Worked examples
Simplify the ratio 20:20.
- HCF of 20 and 20 is 20.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 36 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 36 ÷ 9 = 4.
- 3 × 4 = 12, 6 × 4 = 24.
- Answer: 12 and 24
Share 40 in the ratio 2:3.
- Total parts: 2 + 3 = 5.
- One part: 40 ÷ 5 = 8.
- 2 × 8 = 16, 3 × 8 = 24.
- Answer: 16 and 24
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 flashcards really free?
- Yes. Every flashcards 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 flashcards 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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