Math worksheet for converting improper fractions to mixed numbers and vice versa.

Let's solve the problems step by step.

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Part 1: Converting Improper Fractions to Mixed Numbers

To convert an improper fraction to a mixed number:
- Divide the numerator by the denominator.
- The quotient becomes the whole number.
- The remainder becomes the numerator of the fractional part.
- The denominator stays the same.

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1) $ \frac{29}{4} $
$ 29 \div 4 = 7 $ remainder $ 1 $ → $ 7\frac{1}{4} $

2) $ \frac{13}{6} $
$ 13 \div 6 = 2 $ remainder $ 1 $ → $ 2\frac{1}{6} $

3) $ \frac{73}{9} $
$ 73 \div 9 = 8 $ remainder $ 1 $ → $ 8\frac{1}{9} $

4) $ \frac{65}{8} $
$ 65 \div 8 = 8 $ remainder $ 1 $ → $ 8\frac{1}{8} $

5) $ \frac{17}{2} $
$ 17 \div 2 = 8 $ remainder $ 1 $ → $ 8\frac{1}{2} $

6) $ \frac{5}{2} $
$ 5 \div 2 = 2 $ remainder $ 1 $ → $ 2\frac{1}{2} $

7) $ \frac{25}{4} $
$ 25 \div 4 = 6 $ remainder $ 1 $ → $ 6\frac{1}{4} $

8) $ \frac{43}{7} $
$ 43 \div 7 = 6 $ remainder $ 1 $ → $ 6\frac{1}{7} $

9) $ \frac{29}{4} $
Same as #1 → $ 7\frac{1}{4} $

10) $ \frac{73}{9} $
Same as #3 → $ 8\frac{1}{9} $

11) $ \frac{19}{3} $
$ 19 \div 3 = 6 $ remainder $ 1 $ → $ 6\frac{1}{3} $

12) $ \frac{43}{7} $
Same as #8 → $ 6\frac{1}{7} $

13) $ \frac{11}{5} $
$ 11 \div 5 = 2 $ remainder $ 1 $ → $ 2\frac{1}{5} $

14) $ \frac{91}{10} $
$ 91 \div 10 = 9 $ remainder $ 1 $ → $ 9\frac{1}{10} $

15) $ \frac{37}{6} $
$ 37 \div 6 = 6 $ remainder $ 1 $ → $ 6\frac{1}{6} $

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Part 2: Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator.
- Add the numerator.
- Place the result over the original denominator.

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1) $ 7\frac{1}{3} $
$ 7 \times 3 + 1 = 21 + 1 = 22 $ → $ \frac{22}{3} $

2) $ 7\frac{9}{10} $
$ 7 \times 10 + 9 = 70 + 9 = 79 $ → $ \frac{79}{10} $

3) $ 7\frac{3}{4} $
$ 7 \times 4 + 3 = 28 + 3 = 31 $ → $ \frac{31}{4} $

4) $ 2\frac{1}{2} $
$ 2 \times 2 + 1 = 4 + 1 = 5 $ → $ \frac{5}{2} $

5) $ 8\frac{4}{7} $
$ 8 \times 7 + 4 = 56 + 4 = 60 $ → $ \frac{60}{7} $

6) $ 2\frac{3}{5} $
$ 2 \times 5 + 3 = 10 + 3 = 13 $ → $ \frac{13}{5} $

7) $ 3\frac{5}{8} $
$ 3 \times 8 + 5 = 24 + 5 = 29 $ → $ \frac{29}{8} $

8) $ 6\frac{7}{9} $
$ 6 \times 9 + 7 = 54 + 7 = 61 $ → $ \frac{61}{9} $

9) $ 9\frac{1}{8} $
$ 9 \times 8 + 1 = 72 + 1 = 73 $ → $ \frac{73}{8} $

10) $ 6\frac{2}{5} $
$ 6 \times 5 + 2 = 30 + 2 = 32 $ → $ \frac{32}{5} $

11) $ 4\frac{1}{3} $
$ 4 \times 3 + 1 = 12 + 1 = 13 $ → $ \frac{13}{3} $

12) $ 2\frac{2}{3} $
$ 2 \times 3 + 2 = 6 + 2 = 8 $ → $ \frac{8}{3} $

13) $ 8\frac{1}{2} $
$ 8 \times 2 + 1 = 16 + 1 = 17 $ → $ \frac{17}{2} $

14) $ 4\frac{3}{10} $
$ 4 \times 10 + 3 = 40 + 3 = 43 $ → $ \frac{43}{10} $

15) $ 8\frac{4}{5} $
$ 8 \times 5 + 4 = 40 + 4 = 44 $ → $ \frac{44}{5} $

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✔ Final Answers:

#### Converting Improper Fractions to Mixed Numbers
1) $ 7\frac{1}{4} $
2) $ 2\frac{1}{6} $
3) $ 8\frac{1}{9} $
4) $ 8\frac{1}{8} $
5) $ 8\frac{1}{2} $
6) $ 2\frac{1}{2} $
7) $ 6\frac{1}{4} $
8) $ 6\frac{1}{7} $
9) $ 7\frac{1}{4} $
10) $ 8\frac{1}{9} $
11) $ 6\frac{1}{3} $
12) $ 6\frac{1}{7} $
13) $ 2\frac{1}{5} $
14) $ 9\frac{1}{10} $
15) $ 6\frac{1}{6} $

#### Converting Mixed Numbers to Improper Fractions
1) $ \frac{22}{3} $
2) $ \frac{79}{10} $
3) $ \frac{31}{4} $
4) $ \frac{5}{2} $
5) $ \frac{60}{7} $
6) $ \frac{13}{5} $
7) $ \frac{29}{8} $
8) $ \frac{61}{9} $
9) $ \frac{73}{8} $
10) $ \frac{32}{5} $
11) $ \frac{13}{3} $
12) $ \frac{8}{3} $
13) $ \frac{17}{2} $
14) $ \frac{43}{10} $
15) $ \frac{44}{5} $

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✔ All problems solved correctly. Let me know if you'd like this formatted for printing or need explanations for any specific problem!