Free Grade 3 Introducing Simplifying Ratios Lessons
Free Grade 3 lessons for Introducing Simplifying Ratios: 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 introducing simplifying ratios
Explain introducing simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing simplifying ratios
Calculate introducing simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing simplifying ratios
Compare introducing simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing simplifying ratios
Justify introducing simplifying ratios 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 Simplifying Ratios 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 4:16.[1]
- 2.Simplify the ratio 32:24.[1]
- 3.Simplify the ratio 24:30.[1]
- 4.Simplify the ratio 30:20.[1]
- 5.Share 15 in the ratio 4:1.[2]
- 6.Share 36 in the ratio 2:4.[2]
- 7.Share 21 in the ratio 1:6.[2]
- 8.Share 12 in the ratio 1:5.[2]
- 9.Share 44 in the ratio 5:6.[3]
- 10.Share 18 in the ratio 4:5.[3]
- 11.Share 25 in the ratio 4:1.[3]
- 12.Share 25 in the ratio 3:2.[3]
Show answers and working
1. 1:4
HCF of 4 and 16 is 4. Divide both parts by it: 1:4.
2. 4:3
HCF of 32 and 24 is 8. Divide both parts by it: 4:3.
3. 4:5
HCF of 24 and 30 is 6. Divide both parts by it: 4:5.
4. 3:2
HCF of 30 and 20 is 10. Divide both parts by it: 3:2.
5. 12 and 3
Total parts: 4 + 1 = 5. One part: 15 ÷ 5 = 3. 4 × 3 = 12, 1 × 3 = 3.
6. 12 and 24
Total parts: 2 + 4 = 6. One part: 36 ÷ 6 = 6. 2 × 6 = 12, 4 × 6 = 24.
7. 3 and 18
Total parts: 1 + 6 = 7. One part: 21 ÷ 7 = 3. 1 × 3 = 3, 6 × 3 = 18.
8. 2 and 10
Total parts: 1 + 5 = 6. One part: 12 ÷ 6 = 2. 1 × 2 = 2, 5 × 2 = 10.
9. 20 and 24
Total parts: 5 + 6 = 11. One part: 44 ÷ 11 = 4. 5 × 4 = 20, 6 × 4 = 24.
10. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
11. 20 and 5
Total parts: 4 + 1 = 5. One part: 25 ÷ 5 = 5. 4 × 5 = 20, 1 × 5 = 5.
12. 15 and 10
Total parts: 3 + 2 = 5. One part: 25 ÷ 5 = 5. 3 × 5 = 15, 2 × 5 = 10.
Worked examples
Simplify the ratio 12:24.
- HCF of 12 and 24 is 12.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 40 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 40 ÷ 5 = 8.
- 3 × 8 = 24, 2 × 8 = 16.
- Answer: 24 and 16
Share 42 in the ratio 5:2.
- Total parts: 5 + 2 = 7.
- One part: 42 ÷ 7 = 6.
- 5 × 6 = 30, 2 × 6 = 12.
- Answer: 30 and 12
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.
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Frequently asked
- Is this Grade 3 Introducing Simplifying Ratios 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 Writing Ratios. 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 Introducing Simplifying Ratios?
- Move on to Working with Simplifying Ratios, Simplifying Ratios in Context, Writing Ratios, Sharing in a Ratio, which build directly on this idea.
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