Free Grade 3 Working with Defining Rational Numbers Worksheets
Free Grade 3 worksheets for Working with 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
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with defining rational numbers
Explain working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with defining rational numbers
Calculate working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with defining rational numbers
Compare working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with defining rational numbers
Justify working with 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 Working with 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 16:40.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 10:50.[1]
- 4.Simplify the ratio 50:10.[1]
- 5.Share 16 in the ratio 2:6.[2]
- 6.Share 88 in the ratio 3:5.[2]
- 7.Share 80 in the ratio 5:5.[2]
- 8.Share 15 in the ratio 1:4.[2]
- 9.Share 120 in the ratio 3:7.[3]
- 10.Share 55 in the ratio 4:7.[3]
- 11.Share 54 in the ratio 2:4.[3]
- 12.Share 60 in the ratio 5:7.[3]
Show answers and working
1. 2:5
HCF of 16 and 40 is 8. Divide both parts by it: 2:5.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
4. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
5. 4 and 12
Total parts: 2 + 6 = 8. One part: 16 ÷ 8 = 2. 2 × 2 = 4, 6 × 2 = 12.
6. 33 and 55
Total parts: 3 + 5 = 8. One part: 88 ÷ 8 = 11. 3 × 11 = 33, 5 × 11 = 55.
7. 40 and 40
Total parts: 5 + 5 = 10. One part: 80 ÷ 10 = 8. 5 × 8 = 40, 5 × 8 = 40.
8. 3 and 12
Total parts: 1 + 4 = 5. One part: 15 ÷ 5 = 3. 1 × 3 = 3, 4 × 3 = 12.
9. 36 and 84
Total parts: 3 + 7 = 10. One part: 120 ÷ 10 = 12. 3 × 12 = 36, 7 × 12 = 84.
10. 20 and 35
Total parts: 4 + 7 = 11. One part: 55 ÷ 11 = 5. 4 × 5 = 20, 7 × 5 = 35.
11. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
12. 25 and 35
Total parts: 5 + 7 = 12. One part: 60 ÷ 12 = 5. 5 × 5 = 25, 7 × 5 = 35.
Worked examples
Simplify the ratio 12:20.
- HCF of 12 and 20 is 4.
- Divide both parts by it: 3:5.
- Answer: 3:5
Share 72 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 72 ÷ 8 = 9.
- 2 × 9 = 18, 6 × 9 = 54.
- Answer: 18 and 54
Share 90 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 90 ÷ 9 = 10.
- 3 × 10 = 30, 6 × 10 = 60.
- Answer: 30 and 60
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 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 Introducing Defining Rational Numbers, 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 Working with Defining Rational Numbers?
- Move on to Defining Rational Numbers in Context, Rational Number Line, Operations with Rationals, which build directly on this idea.
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