Free Grade 3 Determinants Worksheets
Free Grade 3 worksheets for 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify determinants
Identify determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain determinants
Explain determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate determinants
Calculate determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare determinants
Compare 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 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 8:24.[1]
- 3.Simplify the ratio 24:16.[1]
- 4.Simplify the ratio 16:24.[1]
- 5.Share 88 in the ratio 2:6.[2]
- 6.Share 45 in the ratio 5:4.[2]
- 7.Share 12 in the ratio 3:1.[2]
- 8.Share 50 in the ratio 5:5.[2]
- 9.Share 40 in the ratio 1:3.[3]
- 10.Share 27 in the ratio 3:6.[3]
- 11.Share 72 in the ratio 5:4.[3]
- 12.Share 64 in the ratio 5:3.[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 8 and 24 is 8. Divide both parts by it: 1:3.
3. 3:2
HCF of 24 and 16 is 8. Divide both parts by it: 3:2.
4. 2:3
HCF of 16 and 24 is 8. Divide both parts by it: 2:3.
5. 22 and 66
Total parts: 2 + 6 = 8. One part: 88 ÷ 8 = 11. 2 × 11 = 22, 6 × 11 = 66.
6. 25 and 20
Total parts: 5 + 4 = 9. One part: 45 ÷ 9 = 5. 5 × 5 = 25, 4 × 5 = 20.
7. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
8. 25 and 25
Total parts: 5 + 5 = 10. One part: 50 ÷ 10 = 5. 5 × 5 = 25, 5 × 5 = 25.
9. 10 and 30
Total parts: 1 + 3 = 4. One part: 40 ÷ 4 = 10. 1 × 10 = 10, 3 × 10 = 30.
10. 9 and 18
Total parts: 3 + 6 = 9. One part: 27 ÷ 9 = 3. 3 × 3 = 9, 6 × 3 = 18.
11. 40 and 32
Total parts: 5 + 4 = 9. One part: 72 ÷ 9 = 8. 5 × 8 = 40, 4 × 8 = 32.
12. 40 and 24
Total parts: 5 + 3 = 8. One part: 64 ÷ 8 = 8. 5 × 8 = 40, 3 × 8 = 24.
Worked examples
Simplify the ratio 30:50.
- HCF of 30 and 50 is 10.
- Divide both parts by it: 3:5.
- Answer: 3:5
Share 28 in the ratio 2:2.
- Total parts: 2 + 2 = 4.
- One part: 28 ÷ 4 = 7.
- 2 × 7 = 14, 2 × 7 = 14.
- Answer: 14 and 14
Share 48 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 48 ÷ 8 = 6.
- 4 × 6 = 24, 4 × 6 = 24.
- Answer: 24 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 Determinants
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Frequently asked
- Is this Grade 3 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, Matrix Multiplication, Vectors. 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 Determinants?
- Move on to Inverse Matrices, which build directly on this idea.
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