Free Grade 3 Working with Determinants Worksheets
Free Grade 3 worksheets for Working with Determinants: 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with determinants
Identify working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with determinants
Explain working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with determinants
Calculate working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with determinants
Compare working with determinants 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 Determinants 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 6:18.[1]
- 3.Simplify the ratio 8:16.[1]
- 4.Simplify the ratio 24:12.[1]
- 5.Share 56 in the ratio 3:5.[2]
- 6.Share 96 in the ratio 2:6.[2]
- 7.Share 63 in the ratio 4:5.[2]
- 8.Share 42 in the ratio 3:3.[2]
- 9.Share 72 in the ratio 2:4.[3]
- 10.Share 24 in the ratio 4:4.[3]
- 11.Share 72 in the ratio 4:4.[3]
- 12.Share 77 in the ratio 2:5.[3]
Show answers and working
1. 2:1
HCF of 32 and 16 is 16. Divide both parts by it: 2:1.
2. 1:3
HCF of 6 and 18 is 6. Divide both parts by it: 1:3.
3. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
4. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
5. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
6. 24 and 72
Total parts: 2 + 6 = 8. One part: 96 ÷ 8 = 12. 2 × 12 = 24, 6 × 12 = 72.
7. 28 and 35
Total parts: 4 + 5 = 9. One part: 63 ÷ 9 = 7. 4 × 7 = 28, 5 × 7 = 35.
8. 21 and 21
Total parts: 3 + 3 = 6. One part: 42 ÷ 6 = 7. 3 × 7 = 21, 3 × 7 = 21.
9. 24 and 48
Total parts: 2 + 4 = 6. One part: 72 ÷ 6 = 12. 2 × 12 = 24, 4 × 12 = 48.
10. 12 and 12
Total parts: 4 + 4 = 8. One part: 24 ÷ 8 = 3. 4 × 3 = 12, 4 × 3 = 12.
11. 36 and 36
Total parts: 4 + 4 = 8. One part: 72 ÷ 8 = 9. 4 × 9 = 36, 4 × 9 = 36.
12. 22 and 55
Total parts: 2 + 5 = 7. One part: 77 ÷ 7 = 11. 2 × 11 = 22, 5 × 11 = 55.
Worked examples
Simplify the ratio 4:20.
- HCF of 4 and 20 is 4.
- Divide both parts by it: 1:5.
- Answer: 1:5
Share 88 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 88 ÷ 8 = 11.
- 4 × 11 = 44, 4 × 11 = 44.
- Answer: 44 and 44
Share 9 in the ratio 1:2.
- Total parts: 1 + 2 = 3.
- One part: 9 ÷ 3 = 3.
- 1 × 3 = 3, 2 × 3 = 6.
- Answer: 3 and 6
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 Working with Determinants
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Learn — Meet the idea.
Practice — Build fluency.
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Frequently asked
- Is this Grade 3 Working with Determinants 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 Introducing Determinants, Identity Matrix. 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 Working with Determinants?
- Move on to Determinants in Context, Matrix Addition, Matrix Multiplication, Identity Matrix, which build directly on this idea.
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