Free Grade 3 Working with Definite Integrals Quizzes
Free Grade 3 quizzes 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
20 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 50:10.[1]
- 2.Simplify the ratio 24:12.[1]
- 3.Simplify the ratio 40:24.[1]
- 4.Simplify the ratio 20:20.[1]
- 5.Share 49 in the ratio 5:2.[2]
- 6.Share 22 in the ratio 1:1.[2]
- 7.Share 32 in the ratio 3:5.[2]
- 8.Share 50 in the ratio 1:4.[2]
- 9.Share 16 in the ratio 4:4.[3]
- 10.Share 44 in the ratio 1:3.[3]
- 11.Share 36 in the ratio 3:1.[3]
- 12.Share 18 in the ratio 3:6.[3]
Show answers and working
1. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
2. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
3. 5:3
HCF of 40 and 24 is 8. Divide both parts by it: 5:3.
4. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
5. 35 and 14
Total parts: 5 + 2 = 7. One part: 49 ÷ 7 = 7. 5 × 7 = 35, 2 × 7 = 14.
6. 11 and 11
Total parts: 1 + 1 = 2. One part: 22 ÷ 2 = 11. 1 × 11 = 11, 1 × 11 = 11.
7. 12 and 20
Total parts: 3 + 5 = 8. One part: 32 ÷ 8 = 4. 3 × 4 = 12, 5 × 4 = 20.
8. 10 and 40
Total parts: 1 + 4 = 5. One part: 50 ÷ 5 = 10. 1 × 10 = 10, 4 × 10 = 40.
9. 8 and 8
Total parts: 4 + 4 = 8. One part: 16 ÷ 8 = 2. 4 × 2 = 8, 4 × 2 = 8.
10. 11 and 33
Total parts: 1 + 3 = 4. One part: 44 ÷ 4 = 11. 1 × 11 = 11, 3 × 11 = 33.
11. 27 and 9
Total parts: 3 + 1 = 4. One part: 36 ÷ 4 = 9. 3 × 9 = 27, 1 × 9 = 9.
12. 6 and 12
Total parts: 3 + 6 = 9. One part: 18 ÷ 9 = 2. 3 × 2 = 6, 6 × 2 = 12.
Worked examples
Simplify the ratio 18:24.
- HCF of 18 and 24 is 6.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 42 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 42 ÷ 6 = 7.
- 4 × 7 = 28, 2 × 7 = 14.
- Answer: 28 and 14
Share 21 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 21 ÷ 3 = 7.
- 2 × 7 = 14, 1 × 7 = 7.
- Answer: 14 and 7
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 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 Introducing Definite Integrals, 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 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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