Free Grade 3 Simplifying Surds Lessons
Free Grade 3 lessons 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
Stretch
25 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 50:10.[1]
- 2.Simplify the ratio 24:24.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 20:40.[1]
- 5.Share 12 in the ratio 1:1.[2]
- 6.Share 12 in the ratio 2:1.[2]
- 7.Share 64 in the ratio 2:6.[2]
- 8.Share 12 in the ratio 3:1.[2]
- 9.Share 77 in the ratio 4:3.[3]
- 10.Share 30 in the ratio 3:2.[3]
- 11.Share 33 in the ratio 5:6.[3]
- 12.Share 24 in the ratio 5:3.[3]
Show answers and working
1. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
2. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 1:2
HCF of 20 and 40 is 20. Divide both parts by it: 1:2.
5. 6 and 6
Total parts: 1 + 1 = 2. One part: 12 ÷ 2 = 6. 1 × 6 = 6, 1 × 6 = 6.
6. 8 and 4
Total parts: 2 + 1 = 3. One part: 12 ÷ 3 = 4. 2 × 4 = 8, 1 × 4 = 4.
7. 16 and 48
Total parts: 2 + 6 = 8. One part: 64 ÷ 8 = 8. 2 × 8 = 16, 6 × 8 = 48.
8. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
9. 44 and 33
Total parts: 4 + 3 = 7. One part: 77 ÷ 7 = 11. 4 × 11 = 44, 3 × 11 = 33.
10. 18 and 12
Total parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. 3 × 6 = 18, 2 × 6 = 12.
11. 15 and 18
Total parts: 5 + 6 = 11. One part: 33 ÷ 11 = 3. 5 × 3 = 15, 6 × 3 = 18.
12. 15 and 9
Total parts: 5 + 3 = 8. One part: 24 ÷ 8 = 3. 5 × 3 = 15, 3 × 3 = 9.
Worked examples
Simplify the ratio 32:32.
- HCF of 32 and 32 is 32.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 110 in the ratio 5:5.
- Total parts: 5 + 5 = 10.
- One part: 110 ÷ 10 = 11.
- 5 × 11 = 55, 5 × 11 = 55.
- Answer: 55 and 55
Share 49 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 49 ÷ 7 = 7.
- 3 × 7 = 21, 4 × 7 = 28.
- Answer: 21 and 28
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 lesson really free?
- Yes. Every lessons 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 lesson 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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