Free Grade 3 Defining Rational Numbers Worksheets
Free Grade 3 worksheets for 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain defining rational numbers
Explain defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate defining rational numbers
Calculate defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare defining rational numbers
Compare defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify defining rational numbers
Justify 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 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 24:18.[1]
- 2.Simplify the ratio 24:48.[1]
- 3.Simplify the ratio 40:40.[1]
- 4.Simplify the ratio 8:4.[1]
- 5.Share 25 in the ratio 2:3.[2]
- 6.Share 40 in the ratio 1:3.[2]
- 7.Share 36 in the ratio 1:3.[2]
- 8.Share 42 in the ratio 4:2.[2]
- 9.Share 20 in the ratio 5:5.[3]
- 10.Share 33 in the ratio 1:2.[3]
- 11.Share 27 in the ratio 2:7.[3]
- 12.Share 88 in the ratio 3:5.[3]
Show answers and working
1. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
2. 1:2
HCF of 24 and 48 is 24. Divide both parts by it: 1:2.
3. 1:1
HCF of 40 and 40 is 40. Divide both parts by it: 1:1.
4. 2:1
HCF of 8 and 4 is 4. Divide both parts by it: 2:1.
5. 10 and 15
Total parts: 2 + 3 = 5. One part: 25 ÷ 5 = 5. 2 × 5 = 10, 3 × 5 = 15.
6. 10 and 30
Total parts: 1 + 3 = 4. One part: 40 ÷ 4 = 10. 1 × 10 = 10, 3 × 10 = 30.
7. 9 and 27
Total parts: 1 + 3 = 4. One part: 36 ÷ 4 = 9. 1 × 9 = 9, 3 × 9 = 27.
8. 28 and 14
Total parts: 4 + 2 = 6. One part: 42 ÷ 6 = 7. 4 × 7 = 28, 2 × 7 = 14.
9. 10 and 10
Total parts: 5 + 5 = 10. One part: 20 ÷ 10 = 2. 5 × 2 = 10, 5 × 2 = 10.
10. 11 and 22
Total parts: 1 + 2 = 3. One part: 33 ÷ 3 = 11. 1 × 11 = 11, 2 × 11 = 22.
11. 6 and 21
Total parts: 2 + 7 = 9. One part: 27 ÷ 9 = 3. 2 × 3 = 6, 7 × 3 = 21.
12. 33 and 55
Total parts: 3 + 5 = 8. One part: 88 ÷ 8 = 11. 3 × 11 = 33, 5 × 11 = 55.
Worked examples
Simplify the ratio 60:36.
- HCF of 60 and 36 is 12.
- Divide both parts by it: 5:3.
- Answer: 5:3
Share 20 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 20 ÷ 5 = 4.
- 3 × 4 = 12, 2 × 4 = 8.
- Answer: 12 and 8
Share 28 in the ratio 2:5.
- Total parts: 2 + 5 = 7.
- One part: 28 ÷ 7 = 4.
- 2 × 4 = 8, 5 × 4 = 20.
- Answer: 8 and 20
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 Defining Rational Numbers
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Frequently asked
- Is this Grade 3 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 Defining Rational Numbers?
- Move on to Rational Number Line, Operations with Rationals, Whole Numbers, Counting, which build directly on this idea.
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