Free Grade 3 Introducing Definite Integrals Essentials Worksheets
Free Grade 3 worksheets 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
Foundation
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 20:4.[1]
- 2.Simplify the ratio 20:12.[1]
- 3.Simplify the ratio 60:24.[1]
- 4.Simplify the ratio 24:16.[1]
- 5.Share 48 in the ratio 5:1.[2]
- 6.Share 33 in the ratio 1:2.[2]
- 7.Share 99 in the ratio 5:4.[2]
- 8.Share 16 in the ratio 4:4.[2]
- 9.Share 45 in the ratio 2:7.[3]
- 10.Share 21 in the ratio 2:1.[3]
- 11.Share 14 in the ratio 1:1.[3]
- 12.Share 55 in the ratio 3:2.[3]
Show answers and working
1. 5:1
HCF of 20 and 4 is 4. Divide both parts by it: 5:1.
2. 5:3
HCF of 20 and 12 is 4. Divide both parts by it: 5:3.
3. 5:2
HCF of 60 and 24 is 12. Divide both parts by it: 5:2.
4. 3:2
HCF of 24 and 16 is 8. Divide both parts by it: 3:2.
5. 40 and 8
Total parts: 5 + 1 = 6. One part: 48 ÷ 6 = 8. 5 × 8 = 40, 1 × 8 = 8.
6. 11 and 22
Total parts: 1 + 2 = 3. One part: 33 ÷ 3 = 11. 1 × 11 = 11, 2 × 11 = 22.
7. 55 and 44
Total parts: 5 + 4 = 9. One part: 99 ÷ 9 = 11. 5 × 11 = 55, 4 × 11 = 44.
8. 8 and 8
Total parts: 4 + 4 = 8. One part: 16 ÷ 8 = 2. 4 × 2 = 8, 4 × 2 = 8.
9. 10 and 35
Total parts: 2 + 7 = 9. One part: 45 ÷ 9 = 5. 2 × 5 = 10, 7 × 5 = 35.
10. 14 and 7
Total parts: 2 + 1 = 3. One part: 21 ÷ 3 = 7. 2 × 7 = 14, 1 × 7 = 7.
11. 7 and 7
Total parts: 1 + 1 = 2. One part: 14 ÷ 2 = 7. 1 × 7 = 7, 1 × 7 = 7.
12. 33 and 22
Total parts: 3 + 2 = 5. One part: 55 ÷ 5 = 11. 3 × 11 = 33, 2 × 11 = 22.
Worked examples
Simplify the ratio 40:30.
- HCF of 40 and 30 is 10.
- Divide both parts by it: 4:3.
- Answer: 4:3
Share 35 in the ratio 5:2.
- Total parts: 5 + 2 = 7.
- One part: 35 ÷ 7 = 5.
- 5 × 5 = 25, 2 × 5 = 10.
- Answer: 25 and 10
Share 63 in the ratio 1:6.
- Total parts: 1 + 6 = 7.
- One part: 63 ÷ 7 = 9.
- 1 × 9 = 9, 6 × 9 = 54.
- Answer: 9 and 54
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 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 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.
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