Free Grade 3 Working with Simplifying Ratios Lessons
Free Grade 3 lessons for Working with 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with simplifying ratios
Explain working with simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with simplifying ratios
Calculate working with simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with simplifying ratios
Compare working with simplifying ratios accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with simplifying ratios
Justify working with 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 Working with 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 24:40.[1]
- 2.Simplify the ratio 12:4.[1]
- 3.Simplify the ratio 4:12.[1]
- 4.Simplify the ratio 8:16.[1]
- 5.Share 14 in the ratio 1:6.[2]
- 6.Share 40 in the ratio 4:1.[2]
- 7.Share 25 in the ratio 1:4.[2]
- 8.Share 55 in the ratio 2:3.[2]
- 9.Share 108 in the ratio 5:4.[3]
- 10.Share 27 in the ratio 3:6.[3]
- 11.Share 70 in the ratio 2:5.[3]
- 12.Share 88 in the ratio 3:5.[3]
Show answers and working
1. 3:5
HCF of 24 and 40 is 8. Divide both parts by it: 3:5.
2. 3:1
HCF of 12 and 4 is 4. Divide both parts by it: 3:1.
3. 1:3
HCF of 4 and 12 is 4. Divide both parts by it: 1:3.
4. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
5. 2 and 12
Total parts: 1 + 6 = 7. One part: 14 ÷ 7 = 2. 1 × 2 = 2, 6 × 2 = 12.
6. 32 and 8
Total parts: 4 + 1 = 5. One part: 40 ÷ 5 = 8. 4 × 8 = 32, 1 × 8 = 8.
7. 5 and 20
Total parts: 1 + 4 = 5. One part: 25 ÷ 5 = 5. 1 × 5 = 5, 4 × 5 = 20.
8. 22 and 33
Total parts: 2 + 3 = 5. One part: 55 ÷ 5 = 11. 2 × 11 = 22, 3 × 11 = 33.
9. 60 and 48
Total parts: 5 + 4 = 9. One part: 108 ÷ 9 = 12. 5 × 12 = 60, 4 × 12 = 48.
10. 9 and 18
Total parts: 3 + 6 = 9. One part: 27 ÷ 9 = 3. 3 × 3 = 9, 6 × 3 = 18.
11. 20 and 50
Total parts: 2 + 5 = 7. One part: 70 ÷ 7 = 10. 2 × 10 = 20, 5 × 10 = 50.
12. 33 and 55
Total parts: 3 + 5 = 8. One part: 88 ÷ 8 = 11. 3 × 11 = 33, 5 × 11 = 55.
Worked examples
Simplify the ratio 40:50.
- HCF of 40 and 50 is 10.
- Divide both parts by it: 4:5.
- Answer: 4:5
Share 28 in the ratio 1:3.
- Total parts: 1 + 3 = 4.
- One part: 28 ÷ 4 = 7.
- 1 × 7 = 7, 3 × 7 = 21.
- Answer: 7 and 21
Share 21 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 21 ÷ 7 = 3.
- 4 × 3 = 12, 3 × 3 = 9.
- Answer: 12 and 9
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 Simplifying Ratios
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 Working with 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 Introducing Simplifying Ratios, 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 Working with Simplifying Ratios?
- Move on to Simplifying Ratios in Context, Writing Ratios, Sharing in a Ratio, Ratio Word Problems, which build directly on this idea.
Related resources
Stuck on Working with Simplifying Ratios? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor