Free Grade 3 Working with Tangent Ratio Worksheets
Free Grade 3 worksheets for Working with Tangent Ratio: 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
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with tangent ratio
Explain working with tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with tangent ratio
Calculate working with tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with tangent ratio
Compare working with tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with tangent ratio
Justify working with tangent ratio 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 Tangent Ratio 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 4:4.[1]
- 2.Simplify the ratio 6:6.[1]
- 3.Simplify the ratio 20:20.[1]
- 4.Simplify the ratio 50:50.[1]
- 5.Share 12 in the ratio 3:3.[2]
- 6.Share 48 in the ratio 1:5.[2]
- 7.Share 40 in the ratio 5:5.[2]
- 8.Share 54 in the ratio 4:5.[2]
- 9.Share 10 in the ratio 2:3.[3]
- 10.Share 27 in the ratio 4:5.[3]
- 11.Share 49 in the ratio 4:3.[3]
- 12.Share 35 in the ratio 4:1.[3]
Show answers and working
1. 1:1
HCF of 4 and 4 is 4. Divide both parts by it: 1:1.
2. 1:1
HCF of 6 and 6 is 6. Divide both parts by it: 1:1.
3. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
4. 1:1
HCF of 50 and 50 is 50. Divide both parts by it: 1:1.
5. 6 and 6
Total parts: 3 + 3 = 6. One part: 12 ÷ 6 = 2. 3 × 2 = 6, 3 × 2 = 6.
6. 8 and 40
Total parts: 1 + 5 = 6. One part: 48 ÷ 6 = 8. 1 × 8 = 8, 5 × 8 = 40.
7. 20 and 20
Total parts: 5 + 5 = 10. One part: 40 ÷ 10 = 4. 5 × 4 = 20, 5 × 4 = 20.
8. 24 and 30
Total parts: 4 + 5 = 9. One part: 54 ÷ 9 = 6. 4 × 6 = 24, 5 × 6 = 30.
9. 4 and 6
Total parts: 2 + 3 = 5. One part: 10 ÷ 5 = 2. 2 × 2 = 4, 3 × 2 = 6.
10. 12 and 15
Total parts: 4 + 5 = 9. One part: 27 ÷ 9 = 3. 4 × 3 = 12, 5 × 3 = 15.
11. 28 and 21
Total parts: 4 + 3 = 7. One part: 49 ÷ 7 = 7. 4 × 7 = 28, 3 × 7 = 21.
12. 28 and 7
Total parts: 4 + 1 = 5. One part: 35 ÷ 5 = 7. 4 × 7 = 28, 1 × 7 = 7.
Worked examples
Simplify the ratio 20:50.
- HCF of 20 and 50 is 10.
- Divide both parts by it: 2:5.
- Answer: 2:5
Share 16 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 16 ÷ 8 = 2.
- 4 × 2 = 8, 4 × 2 = 8.
- Answer: 8 and 8
Share 40 in the ratio 4:6.
- Total parts: 4 + 6 = 10.
- One part: 40 ÷ 10 = 4.
- 4 × 4 = 16, 6 × 4 = 24.
- Answer: 16 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 Working with Tangent Ratio
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Working with Tangent Ratio 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 Tangent Ratio, Cosine Ratio. 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 Tangent Ratio?
- Move on to Tangent Ratio in Context, Sine Ratio, Cosine Ratio, Pythagoras' Theorem, which build directly on this idea.
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