Free Grade 3 Introducing Surds Essentials Worksheets
Free Grade 3 worksheets for Introducing Surds Essentials: 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 introducing surds essentials
Explain introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing surds essentials
Calculate introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing surds essentials
Compare introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing surds essentials
Justify introducing surds essentials 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 Surds Essentials 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 32:16.[1]
- 2.Simplify the ratio 36:12.[1]
- 3.Simplify the ratio 24:24.[1]
- 4.Simplify the ratio 16:16.[1]
- 5.Share 24 in the ratio 2:6.[2]
- 6.Share 56 in the ratio 3:4.[2]
- 7.Share 81 in the ratio 3:6.[2]
- 8.Share 15 in the ratio 2:1.[2]
- 9.Share 90 in the ratio 4:5.[3]
- 10.Share 21 in the ratio 1:2.[3]
- 11.Share 33 in the ratio 4:7.[3]
- 12.Share 63 in the ratio 3:6.[3]
Show answers and working
1. 2:1
HCF of 32 and 16 is 16. Divide both parts by it: 2:1.
2. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
3. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
4. 1:1
HCF of 16 and 16 is 16. Divide both parts by it: 1:1.
5. 6 and 18
Total parts: 2 + 6 = 8. One part: 24 ÷ 8 = 3. 2 × 3 = 6, 6 × 3 = 18.
6. 24 and 32
Total parts: 3 + 4 = 7. One part: 56 ÷ 7 = 8. 3 × 8 = 24, 4 × 8 = 32.
7. 27 and 54
Total parts: 3 + 6 = 9. One part: 81 ÷ 9 = 9. 3 × 9 = 27, 6 × 9 = 54.
8. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
9. 40 and 50
Total parts: 4 + 5 = 9. One part: 90 ÷ 9 = 10. 4 × 10 = 40, 5 × 10 = 50.
10. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
11. 12 and 21
Total parts: 4 + 7 = 11. One part: 33 ÷ 11 = 3. 4 × 3 = 12, 7 × 3 = 21.
12. 21 and 42
Total parts: 3 + 6 = 9. One part: 63 ÷ 9 = 7. 3 × 7 = 21, 6 × 7 = 42.
Worked examples
Simplify the ratio 24:40.
- HCF of 24 and 40 is 8.
- Divide both parts by it: 3:5.
- Answer: 3:5
Share 66 in the ratio 3:3.
- Total parts: 3 + 3 = 6.
- One part: 66 ÷ 6 = 11.
- 3 × 11 = 33, 3 × 11 = 33.
- Answer: 33 and 33
Share 84 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 84 ÷ 7 = 12.
- 4 × 12 = 48, 3 × 12 = 36.
- Answer: 48 and 36
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 Surds Essentials worksheet really free?
- Yes. Every worksheets 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 Rational Numbers. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Surds Essentials?
- Move on to Introducing Surds Techniques, Introducing Surds Word Problems, Introducing Surds Common Errors, Working with Surds, which build directly on this idea.
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