Free Grade 3 Introducing Mixed Numbers Lessons
Free Grade 3 lessons for Introducing Mixed Numbers: 12 real questions with a full answer key and worked solutions. A mixed number has a whole part and a fraction. An improper fraction has a numerator bigger than its denominator. Both can describe the same amount.
Free
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing mixed numbers
Explain introducing mixed numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing mixed numbers
Calculate introducing mixed numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing mixed numbers
Compare introducing mixed numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing mixed numbers
Justify introducing mixed 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 Mixed Numbers works
A mixed number has a whole part and a fraction. An improper fraction has a numerator bigger than its denominator. Both can describe the same amount.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Write 2 1/2 as an improper fraction.[1]
- 2.Write 1 1/3 as an improper fraction.[1]
- 3.Write 1 3/6 as an improper fraction.[1]
- 4.Write 1 2/7 as an improper fraction.[1]
- 5.Write 11/5 as a mixed number.[2]
- 6.Write 5/3 as a mixed number.[2]
- 7.Write 7/4 as a mixed number.[2]
- 8.Write 33/8 as a mixed number.[2]
- 9.Write 6 6/7 as an improper fraction.[3]
- 10.Write 7 1/3 as an improper fraction.[3]
- 11.Write 1 1/5 as an improper fraction.[3]
- 12.Write 7 1/2 as an improper fraction.[3]
Show answers and working
1. 5/2
2 wholes = 4/2. 4 + 1 = 5. = 5/2
2. 4/3
1 wholes = 3/3. 3 + 1 = 4. = 4/3
3. 9/6
1 wholes = 6/6. 6 + 3 = 9. = 9/6
4. 9/7
1 wholes = 7/7. 7 + 2 = 9. = 9/7
5. 2 1/5
11 ÷ 5 = 2 remainder 1. 2 wholes and 1/5 left: 2 1/5.
6. 1 2/3
5 ÷ 3 = 1 remainder 2. 1 wholes and 2/3 left: 1 2/3.
7. 1 3/4
7 ÷ 4 = 1 remainder 3. 1 wholes and 3/4 left: 1 3/4.
8. 4 1/8
33 ÷ 8 = 4 remainder 1. 4 wholes and 1/8 left: 4 1/8.
9. 48/7
6 wholes = 42/7. 42 + 6 = 48. = 48/7
10. 22/3
7 wholes = 21/3. 21 + 1 = 22. = 22/3
11. 6/5
1 wholes = 5/5. 5 + 1 = 6. = 6/5
12. 15/2
7 wholes = 14/2. 14 + 1 = 15. = 15/2
Worked examples
Write 1 5/8 as an improper fraction.
- 1 wholes = 8/8.
- 8 + 5 = 13.
- = 13/8
- Answer: 13/8
Write 13/8 as a mixed number.
- 13 ÷ 8 = 1 remainder 5.
- 1 wholes and 5/8 left: 1 5/8.
- Answer: 1 5/8
Write 2 3/9 as an improper fraction.
- 2 wholes = 18/9.
- 18 + 3 = 21.
- = 21/9
- Answer: 21/9
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Multiplies the whole number by the numerator.
Correction: Multiply the whole by the denominator, then add the numerator.
Ignores the remainder when converting back.
Correction: The remainder becomes the new numerator.
Teacher tips
- · Draw the wholes as full circles before converting.
Parent tips
- · Count halves of oranges: 5 halves = 2 1/2 oranges.
Real-life applications
- · 2 1/2 pizzas, 1 3/4 hours.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Introducing Mixed Numbers
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Frequently asked
- Is this Grade 3 Introducing Mixed Numbers lesson really free?
- Yes. Every lessons 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 Improper Fractions. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Mixed Numbers?
- Move on to Working with Mixed Numbers, Mixed Numbers in Context, Introduction to Fractions, Parts of a Fraction, which build directly on this idea.
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