Free Grade 3 Tangent Ratio Worksheets
Free Grade 3 worksheets for 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify tangent ratio
Identify tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain tangent ratio
Explain tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate tangent ratio
Calculate tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare tangent ratio
Compare 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 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 24:60.[1]
- 2.Simplify the ratio 10:30.[1]
- 3.Simplify the ratio 16:16.[1]
- 4.Simplify the ratio 40:40.[1]
- 5.Share 63 in the ratio 1:6.[2]
- 6.Share 24 in the ratio 3:3.[2]
- 7.Share 72 in the ratio 4:5.[2]
- 8.Share 6 in the ratio 1:2.[2]
- 9.Share 36 in the ratio 1:5.[3]
- 10.Share 15 in the ratio 1:2.[3]
- 11.Share 20 in the ratio 1:3.[3]
- 12.Share 24 in the ratio 3:5.[3]
Show answers and working
1. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
2. 1:3
HCF of 10 and 30 is 10. Divide both parts by it: 1:3.
3. 1:1
HCF of 16 and 16 is 16. Divide both parts by it: 1:1.
4. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
5. 9 and 54
Total parts: 1 + 6 = 7. One part: 63 ÷ 7 = 9. 1 × 9 = 9, 6 × 9 = 54.
6. 12 and 12
Total parts: 3 + 3 = 6. One part: 24 ÷ 6 = 4. 3 × 4 = 12, 3 × 4 = 12.
7. 32 and 40
Total parts: 4 + 5 = 9. One part: 72 ÷ 9 = 8. 4 × 8 = 32, 5 × 8 = 40.
8. 2 and 4
Total parts: 1 + 2 = 3. One part: 6 ÷ 3 = 2. 1 × 2 = 2, 2 × 2 = 4.
9. 6 and 30
Total parts: 1 + 5 = 6. One part: 36 ÷ 6 = 6. 1 × 6 = 6, 5 × 6 = 30.
10. 5 and 10
Total parts: 1 + 2 = 3. One part: 15 ÷ 3 = 5. 1 × 5 = 5, 2 × 5 = 10.
11. 5 and 15
Total parts: 1 + 3 = 4. One part: 20 ÷ 4 = 5. 1 × 5 = 5, 3 × 5 = 15.
12. 9 and 15
Total parts: 3 + 5 = 8. One part: 24 ÷ 8 = 3. 3 × 3 = 9, 5 × 3 = 15.
Worked examples
Simplify the ratio 8:4.
- HCF of 8 and 4 is 4.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 12 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 12 ÷ 3 = 4.
- 2 × 4 = 8, 1 × 4 = 4.
- Answer: 8 and 4
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 Tangent Ratio
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Learn — Meet the idea.
Practice — Build fluency.
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Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 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 Cosine Ratio, Sine Ratio, Coordinate Geometry. 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 Tangent Ratio?
- Move on to Pythagoras' Theorem, Angles of Elevation, Non-right-angled Trigonometry, Trigonometric Graphs, which build directly on this idea.
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