Free Grade 3 Sine Ratio Worksheets
Free Grade 3 worksheets for Sine 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
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify sine ratio
Identify sine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain sine ratio
Explain sine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate sine ratio
Calculate sine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare sine ratio
Compare sine 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 Sine 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 8:32.[1]
- 2.Simplify the ratio 10:40.[1]
- 3.Simplify the ratio 20:16.[1]
- 4.Simplify the ratio 16:32.[1]
- 5.Share 8 in the ratio 1:3.[2]
- 6.Share 42 in the ratio 5:2.[2]
- 7.Share 24 in the ratio 1:1.[2]
- 8.Share 55 in the ratio 1:4.[2]
- 9.Share 80 in the ratio 2:6.[3]
- 10.Share 36 in the ratio 5:1.[3]
- 11.Share 36 in the ratio 5:4.[3]
- 12.Share 84 in the ratio 1:6.[3]
Show answers and working
1. 1:4
HCF of 8 and 32 is 8. Divide both parts by it: 1:4.
2. 1:4
HCF of 10 and 40 is 10. Divide both parts by it: 1:4.
3. 5:4
HCF of 20 and 16 is 4. Divide both parts by it: 5:4.
4. 1:2
HCF of 16 and 32 is 16. Divide both parts by it: 1:2.
5. 2 and 6
Total parts: 1 + 3 = 4. One part: 8 ÷ 4 = 2. 1 × 2 = 2, 3 × 2 = 6.
6. 30 and 12
Total parts: 5 + 2 = 7. One part: 42 ÷ 7 = 6. 5 × 6 = 30, 2 × 6 = 12.
7. 12 and 12
Total parts: 1 + 1 = 2. One part: 24 ÷ 2 = 12. 1 × 12 = 12, 1 × 12 = 12.
8. 11 and 44
Total parts: 1 + 4 = 5. One part: 55 ÷ 5 = 11. 1 × 11 = 11, 4 × 11 = 44.
9. 20 and 60
Total parts: 2 + 6 = 8. One part: 80 ÷ 8 = 10. 2 × 10 = 20, 6 × 10 = 60.
10. 30 and 6
Total parts: 5 + 1 = 6. One part: 36 ÷ 6 = 6. 5 × 6 = 30, 1 × 6 = 6.
11. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
12. 12 and 72
Total parts: 1 + 6 = 7. One part: 84 ÷ 7 = 12. 1 × 12 = 12, 6 × 12 = 72.
Worked examples
Simplify the ratio 30:24.
- HCF of 30 and 24 is 6.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 40 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 40 ÷ 4 = 10.
- 3 × 10 = 30, 1 × 10 = 10.
- Answer: 30 and 10
Share 35 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 35 ÷ 5 = 7.
- 3 × 7 = 21, 2 × 7 = 14.
- Answer: 21 and 14
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 Sine Ratio
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Sine 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 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 Sine Ratio?
- Move on to Cosine Ratio, Tangent Ratio, Pythagoras' Theorem, Angles of Elevation, which build directly on this idea.
Related resources
Stuck on Sine Ratio? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor