Mixed Numbers Worksheet for Grade 5 – Convert Mixed Numbers to Improper Fractions

Let's solve the worksheet step by step.

How to Convert a Mixed Number to an Improper Fraction:

A mixed number has a whole number and a fraction, like $ 9 \frac{1}{7} $. To convert it to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to that product.
3. The result becomes the new numerator, and the denominator stays the same.

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. $ 9 \frac{1}{7} $
$ = \frac{(9 \times 7) + 1}{7} = \frac{63 + 1}{7} = \frac{64}{7} $

2. $ 3 \frac{2}{5} $
$ = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $

3. $ 7 \frac{2}{3} $
$ = \frac{(7 \times 3) + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3} $

4. $ 5 \frac{1}{6} $
$ = \frac{(5 \times 6) + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6} $

5. $ 6 \frac{4}{9} $
$ = \frac{(6 \times 9) + 4}{9} = \frac{54 + 4}{9} = \frac{58}{9} $

6. $ 4 \frac{1}{3} $
$ = \frac{(4 \times 3) + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} $

7. $ 4 \frac{6}{11} $
$ = \frac{(4 \times 11) + 6}{11} = \frac{44 + 6}{11} = \frac{50}{11} $

8. $ 7 \frac{5}{6} $
$ = \frac{(7 \times 6) + 5}{6} = \frac{42 + 5}{6} = \frac{47}{6} $

9. $ 3 \frac{4}{7} $
$ = \frac{(3 \times 7) + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7} $

10. $ 8 \frac{3}{4} $
$ = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} $

11. $ 9 \frac{8}{9} $
$ = \frac{(9 \times 9) + 8}{9} = \frac{81 + 8}{9} = \frac{89}{9} $

12. $ 7 \frac{1}{12} $
$ = \frac{(7 \times 12) + 1}{12} = \frac{84 + 1}{12} = \frac{85}{12} $

13. $ 12 \frac{7}{8} $
$ = \frac{(12 \times 8) + 7}{8} = \frac{96 + 7}{8} = \frac{103}{8} $

14. $ 6 \frac{4}{5} $
$ = \frac{(6 \times 5) + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5} $

15. $ 8 \frac{1}{12} $
$ = \frac{(8 \times 12) + 1}{12} = \frac{96 + 1}{12} = \frac{97}{12} $

16. $ 10 \frac{3}{4} $
$ = \frac{(10 \times 4) + 3}{4} = \frac{40 + 3}{4} = \frac{43}{4} $

17. $ 9 \frac{9}{12} $
First simplify $ \frac{9}{12} = \frac{3}{4} $, but since we're converting to improper fraction, keep as is:
$ = \frac{(9 \times 12) + 9}{12} = \frac{108 + 9}{12} = \frac{117}{12} $
Simplify: $ \frac{117}{12} = \frac{39}{4} $ (divided numerator and denominator by 3)

But since the question asks for improper fraction, both $ \frac{117}{12} $ and $ \frac{39}{4} $ are correct — but usually we simplify. So best answer: $ \boxed{\frac{39}{4}} $

18. $ 11 \frac{5}{6} $
$ = \frac{(11 \times 6) + 5}{6} = \frac{66 + 5}{6} = \frac{71}{6} $

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✔ Final Answers:

1. $ \frac{64}{7} $
2. $ \frac{17}{5} $
3. $ \frac{23}{3} $
4. $ \frac{31}{6} $
5. $ \frac{58}{9} $
6. $ \frac{13}{3} $
7. $ \frac{50}{11} $
8. $ \frac{47}{6} $
9. $ \frac{25}{7} $
10. $ \frac{35}{4} $
11. $ \frac{89}{9} $
12. $ \frac{85}{12} $
13. $ \frac{103}{8} $
14. $ \frac{34}{5} $
15. $ \frac{97}{12} $
16. $ \frac{43}{4} $
17. $ \frac{39}{4} $ (simplified from $ \frac{117}{12} $)
18. $ \frac{71}{6} $

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✔ All answers are now in improper fractions, and simplified where needed.

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