Free Grade 3 Working with Tangent Ratio Lessons
Free Grade 3 lessons 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
20 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 36:12.[1]
- 2.Simplify the ratio 24:6.[1]
- 3.Simplify the ratio 40:24.[1]
- 4.Simplify the ratio 30:30.[1]
- 5.Share 88 in the ratio 3:5.[2]
- 6.Share 110 in the ratio 4:6.[2]
- 7.Share 99 in the ratio 5:4.[2]
- 8.Share 21 in the ratio 1:2.[2]
- 9.Share 42 in the ratio 4:2.[3]
- 10.Share 18 in the ratio 4:2.[3]
- 11.Share 100 in the ratio 4:6.[3]
- 12.Share 30 in the ratio 4:2.[3]
Show answers and working
1. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
2. 4:1
HCF of 24 and 6 is 6. Divide both parts by it: 4:1.
3. 5:3
HCF of 40 and 24 is 8. Divide both parts by it: 5:3.
4. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
5. 33 and 55
Total parts: 3 + 5 = 8. One part: 88 ÷ 8 = 11. 3 × 11 = 33, 5 × 11 = 55.
6. 44 and 66
Total parts: 4 + 6 = 10. One part: 110 ÷ 10 = 11. 4 × 11 = 44, 6 × 11 = 66.
7. 55 and 44
Total parts: 5 + 4 = 9. One part: 99 ÷ 9 = 11. 5 × 11 = 55, 4 × 11 = 44.
8. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
9. 28 and 14
Total parts: 4 + 2 = 6. One part: 42 ÷ 6 = 7. 4 × 7 = 28, 2 × 7 = 14.
10. 12 and 6
Total parts: 4 + 2 = 6. One part: 18 ÷ 6 = 3. 4 × 3 = 12, 2 × 3 = 6.
11. 40 and 60
Total parts: 4 + 6 = 10. One part: 100 ÷ 10 = 10. 4 × 10 = 40, 6 × 10 = 60.
12. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
Worked examples
Simplify the ratio 4:8.
- HCF of 4 and 8 is 4.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 18 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 18 ÷ 9 = 2.
- 5 × 2 = 10, 4 × 2 = 8.
- Answer: 10 and 8
Share 36 in the ratio 2:7.
- Total parts: 2 + 7 = 9.
- One part: 36 ÷ 9 = 4.
- 2 × 4 = 8, 7 × 4 = 28.
- Answer: 8 and 28
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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Frequently asked
- Is this Grade 3 Working with Tangent Ratio lesson really free?
- Yes. Every lessons 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 lesson 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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