Grade 5 worksheet for converting mixed numbers to improper fractions.

Let's solve the worksheet step by step. The task is to convert mixed numbers to improper fractions.

🔷 How to Convert a Mixed Number to an Improper Fraction:

A mixed number has the form:
Whole number + Fraction (e.g., $ 7 \frac{3}{5} $)

To convert it to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to that product.
3. Place the result over the original denominator.

Formula:
$$
\text{Improper Fraction} = \frac{(Whole \times Denominator) + Numerator}{Denominator}
$$

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Now, let’s solve each problem:

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1. $ 7 \frac{3}{5} = \frac{(7 \times 5) + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5} $

2. $ 6 \frac{5}{6} = \frac{(6 \times 6) + 5}{6} = \frac{36 + 5}{6} = \frac{41}{6} $

3. $ 9 \frac{2}{9} = \frac{(9 \times 9) + 2}{9} = \frac{81 + 2}{9} = \frac{83}{9} $

4. $ 2 \frac{2}{4} = \frac{(2 \times 4) + 2}{4} = \frac{8 + 2}{4} = \frac{10}{4} $ → Simplify: $ \frac{5}{2} $

*(Note: You can simplify $ \frac{10}{4} $ to $ \frac{5}{2} $, but if not required, $ \frac{10}{4} $ is acceptable.)*

5. $ 6 \frac{1}{9} = \frac{(6 \times 9) + 1}{9} = \frac{54 + 1}{9} = \frac{55}{9} $

6. $ 5 \frac{5}{7} = \frac{(5 \times 7) + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7} $

7. $ 3 \frac{1}{8} = \frac{(3 \times 8) + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8} $

8. $ 8 \frac{1}{12} = \frac{(8 \times 12) + 1}{12} = \frac{96 + 1}{12} = \frac{97}{12} $

9. $ 6 \frac{1}{4} = \frac{(6 \times 4) + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} $

10. $ 4 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} $

11. $ 8 \frac{1}{12} = \frac{(8 \times 12) + 1}{12} = \frac{96 + 1}{12} = \frac{97}{12} $

12. $ 9 \frac{6}{8} = \frac{(9 \times 8) + 6}{8} = \frac{72 + 6}{8} = \frac{78}{8} $ → Simplify: $ \frac{39}{4} $

13. $ 5 \frac{8}{11} = \frac{(5 \times 11) + 8}{11} = \frac{55 + 8}{11} = \frac{63}{11} $

14. $ 3 \frac{6}{9} = \frac{(3 \times 9) + 6}{9} = \frac{27 + 6}{9} = \frac{33}{9} $ → Simplify: $ \frac{11}{3} $

15. $ 5 \frac{10}{11} = \frac{(5 \times 11) + 10}{11} = \frac{55 + 10}{11} = \frac{65}{11} $

16. $ 6 \frac{6}{5} = \frac{(6 \times 5) + 6}{5} = \frac{30 + 6}{5} = \frac{36}{5} $

17. $ 9 \frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2} $

18. $ 7 \frac{8}{10} = \frac{(7 \times 10) + 8}{10} = \frac{70 + 8}{10} = \frac{78}{10} $ → Simplify: $ \frac{39}{5} $

19. $ 5 \frac{1}{5} = \frac{(5 \times 5) + 1}{5} = \frac{25 + 1}{5} = \frac{26}{5} $

20. $ 8 \frac{5}{10} = \frac{(8 \times 10) + 5}{10} = \frac{80 + 5}{10} = \frac{85}{10} $ → Simplify: $ \frac{17}{2} $

21. $ 8 \frac{3}{4} = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} $

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✔ Final Answers (Simplified where possible):

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{38}{5} $ |
| 2 | $ \frac{41}{6} $ |
| 3 | $ \frac{83}{9} $ |
| 4 | $ \frac{10}{4} $ or $ \frac{5}{2} $ |
| 5 | $ \frac{55}{9} $ |
| 6 | $ \frac{40}{7} $ |
| 7 | $ \frac{25}{8} $ |
| 8 | $ \frac{97}{12} $ |
| 9 | $ \frac{25}{4} $ |
| 10 | $ \frac{19}{4} $ |
| 11 | $ \frac{97}{12} $ |
| 12 | $ \frac{78}{8} $ or $ \frac{39}{4} $ |
| 13 | $ \frac{63}{11} $ |
| 14 | $ \frac{33}{9} $ or $ \frac{11}{3} $ |
| 15 | $ \frac{65}{11} $ |
| 16 | $ \frac{36}{5} $ |
| 17 | $ \frac{19}{2} $ |
| 18 | $ \frac{78}{10} $ or $ \frac{39}{5} $ |
| 19 | $ \frac{26}{5} $ |
| 20 | $ \frac{85}{10} $ or $ \frac{17}{2} $ |
| 21 | $ \frac{35}{4} $ |

> 💡 Tip: Always check if the resulting improper fraction can be simplified (reduce numerator and denominator by GCF).

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