Free Grade 3 Working with Definite Integrals Flashcards
Free Grade 3 flashcards for Working with Definite Integrals: 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.
- RememberIdentify working with definite integrals
Identify working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with definite integrals
Explain working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with definite integrals
Calculate working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with definite integrals
Compare working with definite integrals 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 Definite Integrals 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 8:16.[1]
- 2.Simplify the ratio 40:8.[1]
- 3.Simplify the ratio 50:20.[1]
- 4.Simplify the ratio 36:60.[1]
- 5.Share 35 in the ratio 1:6.[2]
- 6.Share 54 in the ratio 5:4.[2]
- 7.Share 48 in the ratio 2:2.[2]
- 8.Share 10 in the ratio 4:1.[2]
- 9.Share 110 in the ratio 5:6.[3]
- 10.Share 12 in the ratio 1:2.[3]
- 11.Share 132 in the ratio 4:7.[3]
- 12.Share 120 in the ratio 4:6.[3]
Show answers and working
1. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
2. 5:1
HCF of 40 and 8 is 8. Divide both parts by it: 5:1.
3. 5:2
HCF of 50 and 20 is 10. Divide both parts by it: 5:2.
4. 3:5
HCF of 36 and 60 is 12. Divide both parts by it: 3:5.
5. 5 and 30
Total parts: 1 + 6 = 7. One part: 35 ÷ 7 = 5. 1 × 5 = 5, 6 × 5 = 30.
6. 30 and 24
Total parts: 5 + 4 = 9. One part: 54 ÷ 9 = 6. 5 × 6 = 30, 4 × 6 = 24.
7. 24 and 24
Total parts: 2 + 2 = 4. One part: 48 ÷ 4 = 12. 2 × 12 = 24, 2 × 12 = 24.
8. 8 and 2
Total parts: 4 + 1 = 5. One part: 10 ÷ 5 = 2. 4 × 2 = 8, 1 × 2 = 2.
9. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
10. 4 and 8
Total parts: 1 + 2 = 3. One part: 12 ÷ 3 = 4. 1 × 4 = 4, 2 × 4 = 8.
11. 48 and 84
Total parts: 4 + 7 = 11. One part: 132 ÷ 11 = 12. 4 × 12 = 48, 7 × 12 = 84.
12. 48 and 72
Total parts: 4 + 6 = 10. One part: 120 ÷ 10 = 12. 4 × 12 = 48, 6 × 12 = 72.
Worked examples
Simplify the ratio 12:6.
- HCF of 12 and 6 is 6.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 54 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 54 ÷ 9 = 6.
- 3 × 6 = 18, 6 × 6 = 36.
- Answer: 18 and 36
Share 40 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 40 ÷ 8 = 5.
- 5 × 5 = 25, 3 × 5 = 15.
- Answer: 25 and 15
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 Definite Integrals 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 Definite Integrals, Reverse Differentiation. 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 Definite Integrals?
- Move on to Definite Integrals in Context, Reverse Differentiation, Area Under a Curve, which build directly on this idea.
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