Free Grade 3 Working with Definite Integrals Worksheets
Free Grade 3 worksheets 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
Foundation
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 24:24.[1]
- 2.Simplify the ratio 8:32.[1]
- 3.Simplify the ratio 30:40.[1]
- 4.Simplify the ratio 20:50.[1]
- 5.Share 66 in the ratio 5:6.[2]
- 6.Share 48 in the ratio 3:3.[2]
- 7.Share 84 in the ratio 3:4.[2]
- 8.Share 63 in the ratio 2:5.[2]
- 9.Share 15 in the ratio 2:1.[3]
- 10.Share 18 in the ratio 4:5.[3]
- 11.Share 80 in the ratio 5:5.[3]
- 12.Share 81 in the ratio 4:5.[3]
Show answers and working
1. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
2. 1:4
HCF of 8 and 32 is 8. Divide both parts by it: 1:4.
3. 3:4
HCF of 30 and 40 is 10. Divide both parts by it: 3:4.
4. 2:5
HCF of 20 and 50 is 10. Divide both parts by it: 2:5.
5. 30 and 36
Total parts: 5 + 6 = 11. One part: 66 ÷ 11 = 6. 5 × 6 = 30, 6 × 6 = 36.
6. 24 and 24
Total parts: 3 + 3 = 6. One part: 48 ÷ 6 = 8. 3 × 8 = 24, 3 × 8 = 24.
7. 36 and 48
Total parts: 3 + 4 = 7. One part: 84 ÷ 7 = 12. 3 × 12 = 36, 4 × 12 = 48.
8. 18 and 45
Total parts: 2 + 5 = 7. One part: 63 ÷ 7 = 9. 2 × 9 = 18, 5 × 9 = 45.
9. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
10. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
11. 40 and 40
Total parts: 5 + 5 = 10. One part: 80 ÷ 10 = 8. 5 × 8 = 40, 5 × 8 = 40.
12. 36 and 45
Total parts: 4 + 5 = 9. One part: 81 ÷ 9 = 9. 4 × 9 = 36, 5 × 9 = 45.
Worked examples
Simplify the ratio 20:4.
- HCF of 20 and 4 is 4.
- Divide both parts by it: 5:1.
- Answer: 5:1
Share 60 in the ratio 3:3.
- Total parts: 3 + 3 = 6.
- One part: 60 ÷ 6 = 10.
- 3 × 10 = 30, 3 × 10 = 30.
- Answer: 30 and 30
Share 42 in the ratio 3:3.
- Total parts: 3 + 3 = 6.
- One part: 42 ÷ 6 = 7.
- 3 × 7 = 21, 3 × 7 = 21.
- Answer: 21 and 21
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 worksheet really free?
- Yes. Every worksheets 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 worksheet 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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