Free Grade 3 Introducing Definite Integrals Essentials Quizzes
Free Grade 3 quizzes for Introducing Definite Integrals Essentials: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing definite integrals essentials
Identify introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing definite integrals essentials
Explain introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing definite integrals essentials
Calculate introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing definite integrals essentials
Compare introducing definite integrals essentials 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 Introducing Definite Integrals Essentials 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 32:40.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 20:30.[1]
- 4.Simplify the ratio 40:16.[1]
- 5.Share 21 in the ratio 1:2.[2]
- 6.Share 21 in the ratio 2:1.[2]
- 7.Share 60 in the ratio 4:6.[2]
- 8.Share 77 in the ratio 2:5.[2]
- 9.Share 56 in the ratio 3:4.[3]
- 10.Share 32 in the ratio 4:4.[3]
- 11.Share 96 in the ratio 3:5.[3]
- 12.Share 63 in the ratio 3:6.[3]
Show answers and working
1. 4:5
HCF of 32 and 40 is 8. Divide both parts by it: 4:5.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 2:3
HCF of 20 and 30 is 10. Divide both parts by it: 2:3.
4. 5:2
HCF of 40 and 16 is 8. Divide both parts by it: 5:2.
5. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
6. 14 and 7
Total parts: 2 + 1 = 3. One part: 21 ÷ 3 = 7. 2 × 7 = 14, 1 × 7 = 7.
7. 24 and 36
Total parts: 4 + 6 = 10. One part: 60 ÷ 10 = 6. 4 × 6 = 24, 6 × 6 = 36.
8. 22 and 55
Total parts: 2 + 5 = 7. One part: 77 ÷ 7 = 11. 2 × 11 = 22, 5 × 11 = 55.
9. 24 and 32
Total parts: 3 + 4 = 7. One part: 56 ÷ 7 = 8. 3 × 8 = 24, 4 × 8 = 32.
10. 16 and 16
Total parts: 4 + 4 = 8. One part: 32 ÷ 8 = 4. 4 × 4 = 16, 4 × 4 = 16.
11. 36 and 60
Total parts: 3 + 5 = 8. One part: 96 ÷ 8 = 12. 3 × 12 = 36, 5 × 12 = 60.
12. 21 and 42
Total parts: 3 + 6 = 9. One part: 63 ÷ 9 = 7. 3 × 7 = 21, 6 × 7 = 42.
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 44 in the ratio 1:3.
- Total parts: 1 + 3 = 4.
- One part: 44 ÷ 4 = 11.
- 1 × 11 = 11, 3 × 11 = 33.
- Answer: 11 and 33
Share 36 in the ratio 3:3.
- Total parts: 3 + 3 = 6.
- One part: 36 ÷ 6 = 6.
- 3 × 6 = 18, 3 × 6 = 18.
- Answer: 18 and 18
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
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Frequently asked
- Is this Grade 3 Introducing Definite Integrals Essentials quiz really free?
- Yes. Every quizzes 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 Reverse Differentiation. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Introducing Definite Integrals Essentials?
- Move on to Introducing Definite Integrals Techniques, Introducing Definite Integrals Word Problems, Introducing Definite Integrals Common Errors, Working with Definite Integrals, which build directly on this idea.
Related resources
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