Free Grade 3 Working with Operations with Rationals Lessons
Free Grade 3 lessons for Working with Operations with Rationals: 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 working with operations with rationals
Explain working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with operations with rationals
Calculate working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with operations with rationals
Compare working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with operations with rationals
Justify working with operations with rationals 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 Operations with Rationals 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 50:30.[1]
- 2.Simplify the ratio 8:16.[1]
- 3.Simplify the ratio 24:18.[1]
- 4.Simplify the ratio 24:36.[1]
- 5.Share 54 in the ratio 2:4.[2]
- 6.Share 40 in the ratio 2:6.[2]
- 7.Share 77 in the ratio 4:3.[2]
- 8.Share 28 in the ratio 3:1.[2]
- 9.Share 36 in the ratio 2:4.[3]
- 10.Share 72 in the ratio 5:3.[3]
- 11.Share 81 in the ratio 5:4.[3]
- 12.Share 18 in the ratio 5:4.[3]
Show answers and working
1. 5:3
HCF of 50 and 30 is 10. Divide both parts by it: 5:3.
2. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
3. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
4. 2:3
HCF of 24 and 36 is 12. Divide both parts by it: 2:3.
5. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
6. 10 and 30
Total parts: 2 + 6 = 8. One part: 40 ÷ 8 = 5. 2 × 5 = 10, 6 × 5 = 30.
7. 44 and 33
Total parts: 4 + 3 = 7. One part: 77 ÷ 7 = 11. 4 × 11 = 44, 3 × 11 = 33.
8. 21 and 7
Total parts: 3 + 1 = 4. One part: 28 ÷ 4 = 7. 3 × 7 = 21, 1 × 7 = 7.
9. 12 and 24
Total parts: 2 + 4 = 6. One part: 36 ÷ 6 = 6. 2 × 6 = 12, 4 × 6 = 24.
10. 45 and 27
Total parts: 5 + 3 = 8. One part: 72 ÷ 8 = 9. 5 × 9 = 45, 3 × 9 = 27.
11. 45 and 36
Total parts: 5 + 4 = 9. One part: 81 ÷ 9 = 9. 5 × 9 = 45, 4 × 9 = 36.
12. 10 and 8
Total parts: 5 + 4 = 9. One part: 18 ÷ 9 = 2. 5 × 2 = 10, 4 × 2 = 8.
Worked examples
Simplify the ratio 60:48.
- HCF of 60 and 48 is 12.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 21 in the ratio 2:5.
- Total parts: 2 + 5 = 7.
- One part: 21 ÷ 7 = 3.
- 2 × 3 = 6, 5 × 3 = 15.
- Answer: 6 and 15
Share 77 in the ratio 5:2.
- Total parts: 5 + 2 = 7.
- One part: 77 ÷ 7 = 11.
- 5 × 11 = 55, 2 × 11 = 22.
- Answer: 55 and 22
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 Working with Operations with Rationals 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 Operations with Rationals, Rational Number Line. 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 Operations with Rationals?
- Move on to Operations with Rationals in Context, Defining Rational Numbers, Rational Number Line, which build directly on this idea.
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