Free Grade 3 Introducing Defining Rational Numbers Worksheets
Free Grade 3 worksheets for Introducing Defining Rational Numbers: 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing defining rational numbers
Explain introducing defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing defining rational numbers
Calculate introducing defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing defining rational numbers
Compare introducing defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing defining rational numbers
Justify introducing defining rational numbers 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 Defining Rational Numbers 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 18:18.[1]
- 2.Simplify the ratio 50:50.[1]
- 3.Simplify the ratio 16:16.[1]
- 4.Simplify the ratio 24:48.[1]
- 5.Share 36 in the ratio 3:3.[2]
- 6.Share 48 in the ratio 5:1.[2]
- 7.Share 54 in the ratio 3:6.[2]
- 8.Share 84 in the ratio 1:6.[2]
- 9.Share 70 in the ratio 5:5.[3]
- 10.Share 18 in the ratio 1:2.[3]
- 11.Share 12 in the ratio 3:3.[3]
- 12.Share 56 in the ratio 5:3.[3]
Show answers and working
1. 1:1
HCF of 18 and 18 is 18. Divide both parts by it: 1:1.
2. 1:1
HCF of 50 and 50 is 50. Divide both parts by it: 1:1.
3. 1:1
HCF of 16 and 16 is 16. Divide both parts by it: 1:1.
4. 1:2
HCF of 24 and 48 is 24. Divide both parts by it: 1:2.
5. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
6. 40 and 8
Total parts: 5 + 1 = 6. One part: 48 ÷ 6 = 8. 5 × 8 = 40, 1 × 8 = 8.
7. 18 and 36
Total parts: 3 + 6 = 9. One part: 54 ÷ 9 = 6. 3 × 6 = 18, 6 × 6 = 36.
8. 12 and 72
Total parts: 1 + 6 = 7. One part: 84 ÷ 7 = 12. 1 × 12 = 12, 6 × 12 = 72.
9. 35 and 35
Total parts: 5 + 5 = 10. One part: 70 ÷ 10 = 7. 5 × 7 = 35, 5 × 7 = 35.
10. 6 and 12
Total parts: 1 + 2 = 3. One part: 18 ÷ 3 = 6. 1 × 6 = 6, 2 × 6 = 12.
11. 6 and 6
Total parts: 3 + 3 = 6. One part: 12 ÷ 6 = 2. 3 × 2 = 6, 3 × 2 = 6.
12. 35 and 21
Total parts: 5 + 3 = 8. One part: 56 ÷ 8 = 7. 5 × 7 = 35, 3 × 7 = 21.
Worked examples
Simplify the ratio 8:32.
- HCF of 8 and 32 is 8.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 24 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 24 ÷ 4 = 6.
- 3 × 6 = 18, 1 × 6 = 6.
- Answer: 18 and 6
Share 32 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 32 ÷ 4 = 8.
- 3 × 8 = 24, 1 × 8 = 8.
- Answer: 24 and 8
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.
Every free resource for Introducing Defining Rational Numbers
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Introducing Defining Rational Numbers 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 Percentages. 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 Defining Rational Numbers?
- Move on to Working with Defining Rational Numbers, Defining Rational Numbers in Context, Rational Number Line, Operations with Rationals, which build directly on this idea.
Related resources
Stuck on Introducing Defining Rational Numbers? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor