Free Grade 3 Introducing Determinants Worksheets
Free Grade 3 worksheets for Introducing 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing determinants
Identify introducing determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing determinants
Explain introducing determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing determinants
Calculate introducing determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing determinants
Compare introducing 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 Introducing 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 24:12.[1]
- 2.Simplify the ratio 4:12.[1]
- 3.Simplify the ratio 24:40.[1]
- 4.Simplify the ratio 50:10.[1]
- 5.Share 55 in the ratio 4:1.[2]
- 6.Share 66 in the ratio 3:3.[2]
- 7.Share 48 in the ratio 5:3.[2]
- 8.Share 60 in the ratio 4:6.[2]
- 9.Share 15 in the ratio 2:1.[3]
- 10.Share 80 in the ratio 5:3.[3]
- 11.Share 81 in the ratio 4:5.[3]
- 12.Share 40 in the ratio 3:2.[3]
Show answers and working
1. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
2. 1:3
HCF of 4 and 12 is 4. Divide both parts by it: 1:3.
3. 3:5
HCF of 24 and 40 is 8. Divide both parts by it: 3:5.
4. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
5. 44 and 11
Total parts: 4 + 1 = 5. One part: 55 ÷ 5 = 11. 4 × 11 = 44, 1 × 11 = 11.
6. 33 and 33
Total parts: 3 + 3 = 6. One part: 66 ÷ 6 = 11. 3 × 11 = 33, 3 × 11 = 33.
7. 30 and 18
Total parts: 5 + 3 = 8. One part: 48 ÷ 8 = 6. 5 × 6 = 30, 3 × 6 = 18.
8. 24 and 36
Total parts: 4 + 6 = 10. One part: 60 ÷ 10 = 6. 4 × 6 = 24, 6 × 6 = 36.
9. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
10. 50 and 30
Total parts: 5 + 3 = 8. One part: 80 ÷ 8 = 10. 5 × 10 = 50, 3 × 10 = 30.
11. 36 and 45
Total parts: 4 + 5 = 9. One part: 81 ÷ 9 = 9. 4 × 9 = 36, 5 × 9 = 45.
12. 24 and 16
Total parts: 3 + 2 = 5. One part: 40 ÷ 5 = 8. 3 × 8 = 24, 2 × 8 = 16.
Worked examples
Simplify the ratio 4:16.
- HCF of 4 and 16 is 4.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 77 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 77 ÷ 7 = 11.
- 3 × 11 = 33, 4 × 11 = 44.
- Answer: 33 and 44
Share 40 in the ratio 4:1.
- Total parts: 4 + 1 = 5.
- One part: 40 ÷ 5 = 8.
- 4 × 8 = 32, 1 × 8 = 8.
- Answer: 32 and 8
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 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 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 Introducing Determinants?
- Move on to Working with Determinants, Determinants in Context, Matrix Addition, Matrix Multiplication, which build directly on this idea.
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