Free Grade 3 Working with Operations with Rationals Flashcards
Free Grade 3 flashcards 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
Foundation
35 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 60:48.[1]
- 2.Simplify the ratio 36:48.[1]
- 3.Simplify the ratio 30:6.[1]
- 4.Simplify the ratio 30:18.[1]
- 5.Share 42 in the ratio 3:3.[2]
- 6.Share 88 in the ratio 5:3.[2]
- 7.Share 15 in the ratio 2:1.[2]
- 8.Share 64 in the ratio 4:4.[2]
- 9.Share 36 in the ratio 3:6.[3]
- 10.Share 35 in the ratio 2:3.[3]
- 11.Share 88 in the ratio 1:7.[3]
- 12.Share 80 in the ratio 5:3.[3]
Show answers and working
1. 5:4
HCF of 60 and 48 is 12. Divide both parts by it: 5:4.
2. 3:4
HCF of 36 and 48 is 12. Divide both parts by it: 3:4.
3. 5:1
HCF of 30 and 6 is 6. Divide both parts by it: 5:1.
4. 5:3
HCF of 30 and 18 is 6. Divide both parts by it: 5:3.
5. 21 and 21
Total parts: 3 + 3 = 6. One part: 42 ÷ 6 = 7. 3 × 7 = 21, 3 × 7 = 21.
6. 55 and 33
Total parts: 5 + 3 = 8. One part: 88 ÷ 8 = 11. 5 × 11 = 55, 3 × 11 = 33.
7. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
8. 32 and 32
Total parts: 4 + 4 = 8. One part: 64 ÷ 8 = 8. 4 × 8 = 32, 4 × 8 = 32.
9. 12 and 24
Total parts: 3 + 6 = 9. One part: 36 ÷ 9 = 4. 3 × 4 = 12, 6 × 4 = 24.
10. 14 and 21
Total parts: 2 + 3 = 5. One part: 35 ÷ 5 = 7. 2 × 7 = 14, 3 × 7 = 21.
11. 11 and 77
Total parts: 1 + 7 = 8. One part: 88 ÷ 8 = 11. 1 × 11 = 11, 7 × 11 = 77.
12. 50 and 30
Total parts: 5 + 3 = 8. One part: 80 ÷ 8 = 10. 5 × 10 = 50, 3 × 10 = 30.
Worked examples
Simplify the ratio 16:4.
- HCF of 16 and 4 is 4.
- Divide both parts by it: 4:1.
- Answer: 4:1
Share 10 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 10 ÷ 5 = 2.
- 3 × 2 = 6, 2 × 2 = 4.
- Answer: 6 and 4
Share 84 in the ratio 1:6.
- Total parts: 1 + 6 = 7.
- One part: 84 ÷ 7 = 12.
- 1 × 12 = 12, 6 × 12 = 72.
- Answer: 12 and 72
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 flashcards really free?
- Yes. Every flashcards 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 flashcards 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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