Free Grade 3 Operations with Rationals Lessons
Free Grade 3 lessons for 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify operations with rationals
Identify operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain operations with rationals
Explain operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate operations with rationals
Calculate operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare operations with rationals
Compare 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 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 30:6.[1]
- 2.Simplify the ratio 24:24.[1]
- 3.Simplify the ratio 24:12.[1]
- 4.Simplify the ratio 20:20.[1]
- 5.Share 66 in the ratio 3:3.[2]
- 6.Share 66 in the ratio 1:5.[2]
- 7.Share 18 in the ratio 1:5.[2]
- 8.Share 33 in the ratio 5:6.[2]
- 9.Share 48 in the ratio 1:3.[3]
- 10.Share 30 in the ratio 1:2.[3]
- 11.Share 121 in the ratio 5:6.[3]
- 12.Share 6 in the ratio 1:1.[3]
Show answers and working
1. 5:1
HCF of 30 and 6 is 6. Divide both parts by it: 5:1.
2. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
3. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
4. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
5. 33 and 33
Total parts: 3 + 3 = 6. One part: 66 ÷ 6 = 11. 3 × 11 = 33, 3 × 11 = 33.
6. 11 and 55
Total parts: 1 + 5 = 6. One part: 66 ÷ 6 = 11. 1 × 11 = 11, 5 × 11 = 55.
7. 3 and 15
Total parts: 1 + 5 = 6. One part: 18 ÷ 6 = 3. 1 × 3 = 3, 5 × 3 = 15.
8. 15 and 18
Total parts: 5 + 6 = 11. One part: 33 ÷ 11 = 3. 5 × 3 = 15, 6 × 3 = 18.
9. 12 and 36
Total parts: 1 + 3 = 4. One part: 48 ÷ 4 = 12. 1 × 12 = 12, 3 × 12 = 36.
10. 10 and 20
Total parts: 1 + 2 = 3. One part: 30 ÷ 3 = 10. 1 × 10 = 10, 2 × 10 = 20.
11. 55 and 66
Total parts: 5 + 6 = 11. One part: 121 ÷ 11 = 11. 5 × 11 = 55, 6 × 11 = 66.
12. 3 and 3
Total parts: 1 + 1 = 2. One part: 6 ÷ 2 = 3. 1 × 3 = 3, 1 × 3 = 3.
Worked examples
Simplify the ratio 24:8.
- HCF of 24 and 8 is 8.
- Divide both parts by it: 3:1.
- Answer: 3:1
Share 40 in the ratio 4:6.
- Total parts: 4 + 6 = 10.
- One part: 40 ÷ 10 = 4.
- 4 × 4 = 16, 6 × 4 = 24.
- Answer: 16 and 24
Share 12 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 12 ÷ 3 = 4.
- 2 × 4 = 8, 1 × 4 = 4.
- Answer: 8 and 4
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 Operations with Rationals
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Frequently asked
- Is this Grade 3 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 Rational Number Line, Defining Rational Numbers, Percentages. 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 Operations with Rationals?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
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