Free Grade 3 Introducing Cosine Ratio Worksheets
Free Grade 3 worksheets for Introducing Cosine 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing cosine ratio
Explain introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing cosine ratio
Calculate introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing cosine ratio
Compare introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing cosine ratio
Justify introducing cosine 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 Introducing Cosine 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 10:50.[1]
- 2.Simplify the ratio 32:8.[1]
- 3.Simplify the ratio 50:20.[1]
- 4.Simplify the ratio 24:60.[1]
- 5.Share 18 in the ratio 4:5.[2]
- 6.Share 30 in the ratio 3:2.[2]
- 7.Share 60 in the ratio 4:2.[2]
- 8.Share 48 in the ratio 1:5.[2]
- 9.Share 33 in the ratio 5:6.[3]
- 10.Share 40 in the ratio 1:3.[3]
- 11.Share 28 in the ratio 3:4.[3]
- 12.Share 33 in the ratio 1:2.[3]
Show answers and working
1. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
2. 4:1
HCF of 32 and 8 is 8. Divide both parts by it: 4:1.
3. 5:2
HCF of 50 and 20 is 10. Divide both parts by it: 5:2.
4. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
5. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
6. 18 and 12
Total parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. 3 × 6 = 18, 2 × 6 = 12.
7. 40 and 20
Total parts: 4 + 2 = 6. One part: 60 ÷ 6 = 10. 4 × 10 = 40, 2 × 10 = 20.
8. 8 and 40
Total parts: 1 + 5 = 6. One part: 48 ÷ 6 = 8. 1 × 8 = 8, 5 × 8 = 40.
9. 15 and 18
Total parts: 5 + 6 = 11. One part: 33 ÷ 11 = 3. 5 × 3 = 15, 6 × 3 = 18.
10. 10 and 30
Total parts: 1 + 3 = 4. One part: 40 ÷ 4 = 10. 1 × 10 = 10, 3 × 10 = 30.
11. 12 and 16
Total parts: 3 + 4 = 7. One part: 28 ÷ 7 = 4. 3 × 4 = 12, 4 × 4 = 16.
12. 11 and 22
Total parts: 1 + 2 = 3. One part: 33 ÷ 3 = 11. 1 × 11 = 11, 2 × 11 = 22.
Worked examples
Simplify the ratio 40:20.
- HCF of 40 and 20 is 20.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 108 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 108 ÷ 9 = 12.
- 5 × 12 = 60, 4 × 12 = 48.
- Answer: 60 and 48
Share 12 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 12 ÷ 6 = 2.
- 1 × 2 = 2, 5 × 2 = 10.
- Answer: 2 and 10
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 Introducing Cosine Ratio
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Frequently asked
- Is this Grade 3 Introducing Cosine 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 Sine 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 Introducing Cosine Ratio?
- Move on to Working with Cosine Ratio, Cosine Ratio in Context, Sine Ratio, Tangent Ratio, which build directly on this idea.
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