Free Grade 3 Introducing Definite Integrals Worksheets
Free Grade 3 worksheets for Introducing 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing definite integrals
Identify introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing definite integrals
Explain introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing definite integrals
Calculate introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing definite integrals
Compare introducing 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 Introducing 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 36:36.[1]
- 2.Simplify the ratio 24:16.[1]
- 3.Simplify the ratio 50:40.[1]
- 4.Simplify the ratio 30:24.[1]
- 5.Share 18 in the ratio 5:4.[2]
- 6.Share 30 in the ratio 5:5.[2]
- 7.Share 40 in the ratio 2:6.[2]
- 8.Share 90 in the ratio 4:5.[2]
- 9.Share 45 in the ratio 4:1.[3]
- 10.Share 30 in the ratio 5:1.[3]
- 11.Share 24 in the ratio 2:4.[3]
- 12.Share 54 in the ratio 2:4.[3]
Show answers and working
1. 1:1
HCF of 36 and 36 is 36. Divide both parts by it: 1:1.
2. 3:2
HCF of 24 and 16 is 8. Divide both parts by it: 3:2.
3. 5:4
HCF of 50 and 40 is 10. Divide both parts by it: 5:4.
4. 5:4
HCF of 30 and 24 is 6. Divide both parts by it: 5:4.
5. 10 and 8
Total parts: 5 + 4 = 9. One part: 18 ÷ 9 = 2. 5 × 2 = 10, 4 × 2 = 8.
6. 15 and 15
Total parts: 5 + 5 = 10. One part: 30 ÷ 10 = 3. 5 × 3 = 15, 5 × 3 = 15.
7. 10 and 30
Total parts: 2 + 6 = 8. One part: 40 ÷ 8 = 5. 2 × 5 = 10, 6 × 5 = 30.
8. 40 and 50
Total parts: 4 + 5 = 9. One part: 90 ÷ 9 = 10. 4 × 10 = 40, 5 × 10 = 50.
9. 36 and 9
Total parts: 4 + 1 = 5. One part: 45 ÷ 5 = 9. 4 × 9 = 36, 1 × 9 = 9.
10. 25 and 5
Total parts: 5 + 1 = 6. One part: 30 ÷ 6 = 5. 5 × 5 = 25, 1 × 5 = 5.
11. 8 and 16
Total parts: 2 + 4 = 6. One part: 24 ÷ 6 = 4. 2 × 4 = 8, 4 × 4 = 16.
12. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
Worked examples
Simplify the ratio 12:16.
- HCF of 12 and 16 is 4.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 10 in the ratio 1:1.
- Total parts: 1 + 1 = 2.
- One part: 10 ÷ 2 = 5.
- 1 × 5 = 5, 1 × 5 = 5.
- Answer: 5 and 5
Share 36 in the ratio 2:7.
- Total parts: 2 + 7 = 9.
- One part: 36 ÷ 9 = 4.
- 2 × 4 = 8, 7 × 4 = 28.
- Answer: 8 and 28
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 Introducing 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 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 Introducing Definite Integrals?
- Move on to Working with Definite Integrals, Definite Integrals in Context, Reverse Differentiation, Area Under a Curve, which build directly on this idea.
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