Converting Improper Fractions to Mixed Fractions (A) - Free Printable
Educational worksheet: Converting Improper Fractions to Mixed Fractions (A). Download and print for classroom or home learning activities.
JPG
500×647
19.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1475232
⭐
Show Answer Key & Explanations
Step-by-step solution for: Converting Improper Fractions to Mixed Fractions (A)
▼
Show Answer Key & Explanations
Step-by-step solution for: Converting Improper Fractions to Mixed Fractions (A)
You're working on “Converting Fractions (A)”, which asks you to convert each improper fraction into a mixed number.
---
## ✔ What is an Improper Fraction?
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
## ✔ What is a Mixed Number?
A mixed number has two parts:
- A whole number
- A proper fraction (where numerator < denominator)
---
## 🔁 How to Convert an Improper Fraction to a Mixed Number:
1. Divide the numerator by the denominator.
2. The quotient becomes the whole number.
3. The remainder becomes the new numerator.
4. The denominator stays the same.
5. Write it as: `Whole Number + Remainder/Denominator`
> Example: Convert 32/9
> 32 ÷ 9 = 3 with remainder 5 → So, 32/9 = 3 5/9
---
## 📝 Let’s Solve All Problems Step-by-Step
I’ll go row by row and show the conversion.
---
1. 32/9 → 32 ÷ 9 = 3 R5 → 3 5/9
2. 67/12 → 67 ÷ 12 = 5 R7 → 5 7/12
3. 116/15 → 116 ÷ 15 = 7 R11 → 7 11/15
4. 34/15 → 34 ÷ 15 = 2 R4 → 2 4/15
---
5. 25/12 → 25 ÷ 12 = 2 R1 → 2 1/12
6. 41/6 → 41 ÷ 6 = 6 R5 → 6 5/6
7. 53/7 → 53 ÷ 7 = 7 R4 → 7 4/7
8. 25/4 → 25 ÷ 4 = 6 R1 → 6 1/4
---
9. 127/15 → 127 ÷ 15 = 8 R7 → 8 7/15
10. 21/8 → 21 ÷ 8 = 2 R5 → 2 5/8
11. 15/4 → 15 ÷ 4 = 3 R3 → 3 3/4
12. 33/10 → 33 ÷ 10 = 3 R3 → 3 3/10
---
13. 25/9 → 25 ÷ 9 = 2 R7 → 2 7/9
14. 38/7 → 38 ÷ 7 = 5 R3 → 5 3/7
15. 99/10 → 99 ÷ 10 = 9 R9 → 9 9/10
16. 44/5 → 44 ÷ 5 = 8 R4 → 8 4/5
---
17. 53/15 → 53 ÷ 15 = 3 R8 → 3 8/15
18. 41/8 → 41 ÷ 8 = 5 R1 → 5 1/8
19. 64/9 → 64 ÷ 9 = 7 R1 → 7 1/9
20. 57/10 → 57 ÷ 10 = 5 R7 → 5 7/10
---
21. 16/7 → 16 ÷ 7 = 2 R2 → 2 2/7
22. 56/9 → 56 ÷ 9 = 6 R2 → 6 2/9
23. 21/10 → 21 ÷ 10 = 2 R1 → 2 1/10
24. 67/8 → 67 ÷ 8 = 8 R3 → 8 3/8
---
25. 12/7 → 12 ÷ 7 = 1 R5 → 1 5/7
26. 83/12 → 83 ÷ 12 = 6 R11 → 6 11/12
27. 36/7 → 36 ÷ 7 = 5 R1 → 5 1/7
28. 19/6 → 19 ÷ 6 = 3 R1 → 3 1/6
---
29. 13/2 → 13 ÷ 2 = 6 R1 → 6 1/2
30. 22/3 → 22 ÷ 3 = 7 R1 → 7 1/3
31. 23/5 → 23 ÷ 5 = 4 R3 → 4 3/5
32. 20/7 → 20 ÷ 7 = 2 R6 → 2 6/7
---
33. 76/15 → 76 ÷ 15 = 5 R1 → 5 1/15
34. 85/9 → 85 ÷ 9 = 9 R4 → 9 4/9
35. 80/9 → 80 ÷ 9 = 8 R8 → 8 8/9
36. 41/12 → 41 ÷ 12 = 3 R5 → 3 5/12
---
37. 6/5 → 6 ÷ 5 = 1 R1 → 1 1/5
38. 107/15 → 107 ÷ 15 = 7 R2 → 7 2/15
39. 63/8 → 63 ÷ 8 = 7 R7 → 7 7/8
40. 37/5 → 37 ÷ 5 = 7 R2 → 7 2/5
---
## ✔ Final Answer Key (All 40 Problems):
```
1. 3 5/9 11. 3 3/4 21. 2 2/7 31. 4 3/5
2. 5 7/12 12. 3 3/10 22. 6 2/9 32. 2 6/7
3. 7 11/15 13. 2 7/9 23. 2 1/10 33. 5 1/15
4. 2 4/15 14. 5 3/7 24. 8 3/8 34. 9 4/9
5. 2 1/12 15. 9 9/10 25. 1 5/7 35. 8 8/9
6. 6 5/6 16. 8 4/5 26. 6 11/12 36. 3 5/12
7. 7 4/7 17. 3 8/15 27. 5 1/7 37. 1 1/5
8. 6 1/4 18. 5 1/8 28. 3 1/6 38. 7 2/15
9. 8 7/15 19. 7 1/9 29. 6 1/2 39. 7 7/8
10. 2 5/8 20. 5 7/10 30. 7 1/3 40. 7 2/5
```
---
## 💡 Tip for Checking Your Work:
To verify your answer, convert the mixed number back to an improper fraction:
> Whole × Denominator + Numerator = New Numerator, Denominator stays same.
Example: Check 3 5/9 → 3×9 + 5 = 27 + 5 = 32 → 32/9 ✔️ Correct!
---
Let me know if you want this in printable format or need help with reducing fractions too! 😊
---
## ✔ What is an Improper Fraction?
An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
## ✔ What is a Mixed Number?
A mixed number has two parts:
- A whole number
- A proper fraction (where numerator < denominator)
---
## 🔁 How to Convert an Improper Fraction to a Mixed Number:
1. Divide the numerator by the denominator.
2. The quotient becomes the whole number.
3. The remainder becomes the new numerator.
4. The denominator stays the same.
5. Write it as: `Whole Number + Remainder/Denominator`
> Example: Convert 32/9
> 32 ÷ 9 = 3 with remainder 5 → So, 32/9 = 3 5/9
---
## 📝 Let’s Solve All Problems Step-by-Step
I’ll go row by row and show the conversion.
---
Row 1:
1. 32/9 → 32 ÷ 9 = 3 R5 → 3 5/9
2. 67/12 → 67 ÷ 12 = 5 R7 → 5 7/12
3. 116/15 → 116 ÷ 15 = 7 R11 → 7 11/15
4. 34/15 → 34 ÷ 15 = 2 R4 → 2 4/15
---
Row 2:
5. 25/12 → 25 ÷ 12 = 2 R1 → 2 1/12
6. 41/6 → 41 ÷ 6 = 6 R5 → 6 5/6
7. 53/7 → 53 ÷ 7 = 7 R4 → 7 4/7
8. 25/4 → 25 ÷ 4 = 6 R1 → 6 1/4
---
Row 3:
9. 127/15 → 127 ÷ 15 = 8 R7 → 8 7/15
10. 21/8 → 21 ÷ 8 = 2 R5 → 2 5/8
11. 15/4 → 15 ÷ 4 = 3 R3 → 3 3/4
12. 33/10 → 33 ÷ 10 = 3 R3 → 3 3/10
---
Row 4:
13. 25/9 → 25 ÷ 9 = 2 R7 → 2 7/9
14. 38/7 → 38 ÷ 7 = 5 R3 → 5 3/7
15. 99/10 → 99 ÷ 10 = 9 R9 → 9 9/10
16. 44/5 → 44 ÷ 5 = 8 R4 → 8 4/5
---
Row 5:
17. 53/15 → 53 ÷ 15 = 3 R8 → 3 8/15
18. 41/8 → 41 ÷ 8 = 5 R1 → 5 1/8
19. 64/9 → 64 ÷ 9 = 7 R1 → 7 1/9
20. 57/10 → 57 ÷ 10 = 5 R7 → 5 7/10
---
Row 6:
21. 16/7 → 16 ÷ 7 = 2 R2 → 2 2/7
22. 56/9 → 56 ÷ 9 = 6 R2 → 6 2/9
23. 21/10 → 21 ÷ 10 = 2 R1 → 2 1/10
24. 67/8 → 67 ÷ 8 = 8 R3 → 8 3/8
---
Row 7:
25. 12/7 → 12 ÷ 7 = 1 R5 → 1 5/7
26. 83/12 → 83 ÷ 12 = 6 R11 → 6 11/12
27. 36/7 → 36 ÷ 7 = 5 R1 → 5 1/7
28. 19/6 → 19 ÷ 6 = 3 R1 → 3 1/6
---
Row 8:
29. 13/2 → 13 ÷ 2 = 6 R1 → 6 1/2
30. 22/3 → 22 ÷ 3 = 7 R1 → 7 1/3
31. 23/5 → 23 ÷ 5 = 4 R3 → 4 3/5
32. 20/7 → 20 ÷ 7 = 2 R6 → 2 6/7
---
Row 9:
33. 76/15 → 76 ÷ 15 = 5 R1 → 5 1/15
34. 85/9 → 85 ÷ 9 = 9 R4 → 9 4/9
35. 80/9 → 80 ÷ 9 = 8 R8 → 8 8/9
36. 41/12 → 41 ÷ 12 = 3 R5 → 3 5/12
---
Row 10:
37. 6/5 → 6 ÷ 5 = 1 R1 → 1 1/5
38. 107/15 → 107 ÷ 15 = 7 R2 → 7 2/15
39. 63/8 → 63 ÷ 8 = 7 R7 → 7 7/8
40. 37/5 → 37 ÷ 5 = 7 R2 → 7 2/5
---
## ✔ Final Answer Key (All 40 Problems):
```
1. 3 5/9 11. 3 3/4 21. 2 2/7 31. 4 3/5
2. 5 7/12 12. 3 3/10 22. 6 2/9 32. 2 6/7
3. 7 11/15 13. 2 7/9 23. 2 1/10 33. 5 1/15
4. 2 4/15 14. 5 3/7 24. 8 3/8 34. 9 4/9
5. 2 1/12 15. 9 9/10 25. 1 5/7 35. 8 8/9
6. 6 5/6 16. 8 4/5 26. 6 11/12 36. 3 5/12
7. 7 4/7 17. 3 8/15 27. 5 1/7 37. 1 1/5
8. 6 1/4 18. 5 1/8 28. 3 1/6 38. 7 2/15
9. 8 7/15 19. 7 1/9 29. 6 1/2 39. 7 7/8
10. 2 5/8 20. 5 7/10 30. 7 1/3 40. 7 2/5
```
---
## 💡 Tip for Checking Your Work:
To verify your answer, convert the mixed number back to an improper fraction:
> Whole × Denominator + Numerator = New Numerator, Denominator stays same.
Example: Check 3 5/9 → 3×9 + 5 = 27 + 5 = 32 → 32/9 ✔️ Correct!
---
Let me know if you want this in printable format or need help with reducing fractions too! 😊
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed numbers.
