Practice worksheet for converting between improper fractions and mixed numbers, featuring eight problems in each section.

Let's solve each problem step by step.

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A) Convert each improper fraction to a mixed number

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 new numerator.
- The denominator stays the same.

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1) $ \frac{9}{5} $

- $ 9 \div 5 = 1 $ remainder $ 4 $
- So, $ \frac{9}{5} = 1 \frac{4}{5} $

✔ Answer: $ 1 \frac{4}{5} $

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2) $ \frac{53}{12} $

- $ 53 \div 12 = 4 $ remainder $ 5 $ (since $ 12 \times 4 = 48 $, $ 53 - 48 = 5 $)
- So, $ \frac{53}{12} = 4 \frac{5}{12} $

✔ Answer: $ 4 \frac{5}{12} $

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3) $ \frac{10}{3} $

- $ 10 \div 3 = 3 $ remainder $ 1 $
- So, $ \frac{10}{3} = 3 \frac{1}{3} $

✔ Answer: $ 3 \frac{1}{3} $

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4) $ \frac{8}{7} $

- $ 8 \div 7 = 1 $ remainder $ 1 $
- So, $ \frac{8}{7} = 1 \frac{1}{7} $

✔ Answer: $ 1 \frac{1}{7} $

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5) $ \frac{65}{11} $

- $ 65 \div 11 = 5 $ remainder $ 10 $ (since $ 11 \times 5 = 55 $, $ 65 - 55 = 10 $)
- So, $ \frac{65}{11} = 5 \frac{10}{11} $

✔ Answer: $ 5 \frac{10}{11} $

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6) $ \frac{31}{4} $

- $ 31 \div 4 = 7 $ remainder $ 3 $ (since $ 4 \times 7 = 28 $, $ 31 - 28 = 3 $)
- So, $ \frac{31}{4} = 7 \frac{3}{4} $

✔ Answer: $ 7 \frac{3}{4} $

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7) $ \frac{29}{6} $

- $ 29 \div 6 = 4 $ remainder $ 5 $ (since $ 6 \times 4 = 24 $, $ 29 - 24 = 5 $)
- So, $ \frac{29}{6} = 4 \frac{5}{6} $

✔ Answer: $ 4 \frac{5}{6} $

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8) $ \frac{74}{9} $

- $ 74 \div 9 = 8 $ remainder $ 2 $ (since $ 9 \times 8 = 72 $, $ 74 - 72 = 2 $)
- So, $ \frac{74}{9} = 8 \frac{2}{9} $

✔ Answer: $ 8 \frac{2}{9} $

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B) Rewrite each mixed number as an improper fraction

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) $ 9 \frac{3}{10} $

- $ 9 \times 10 = 90 $
- $ 90 + 3 = 93 $
- So, $ \frac{93}{10} $

✔ Answer: $ \frac{93}{10} $

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2) $ 7 \frac{1}{2} $

- $ 7 \times 2 = 14 $
- $ 14 + 1 = 15 $
- So, $ \frac{15}{2} $

✔ Answer: $ \frac{15}{2} $

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3) $ 1 \frac{1}{6} $

- $ 1 \times 6 = 6 $
- $ 6 + 1 = 7 $
- So, $ \frac{7}{6} $

✔ Answer: $ \frac{7}{6} $

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4) $ 2 \frac{6}{11} $

- $ 2 \times 11 = 22 $
- $ 22 + 6 = 28 $
- So, $ \frac{28}{11} $

✔ Answer: $ \frac{28}{11} $

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5) $ 4 \frac{5}{8} $

- $ 4 \times 8 = 32 $
- $ 32 + 5 = 37 $
- So, $ \frac{37}{8} $

✔ Answer: $ \frac{37}{8} $

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6) $ 1 \frac{3}{5} $

- $ 1 \times 5 = 5 $
- $ 5 + 3 = 8 $
- So, $ \frac{8}{5} $

✔ Answer: $ \frac{8}{5} $

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7) $ 6 \frac{2}{7} $

- $ 6 \times 7 = 42 $
- $ 42 + 2 = 44 $
- So, $ \frac{44}{7} $

✔ Answer: $ \frac{44}{7} $

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8) $ 5 \frac{8}{9} $

- $ 5 \times 9 = 45 $
- $ 45 + 8 = 53 $
- So, $ \frac{53}{9} $

✔ Answer: $ \frac{53}{9} $

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✔ Final Answers:

#### A) Improper Fractions → Mixed Numbers
1) $ 1 \frac{4}{5} $
2) $ 4 \frac{5}{12} $
3) $ 3 \frac{1}{3} $
4) $ 1 \frac{1}{7} $
5) $ 5 \frac{10}{11} $
6) $ 7 \frac{3}{4} $
7) $ 4 \frac{5}{6} $
8) $ 8 \frac{2}{9} $

#### B) Mixed Numbers → Improper Fractions
1) $ \frac{93}{10} $
2) $ \frac{15}{2} $
3) $ \frac{7}{6} $
4) $ \frac{28}{11} $
5) $ \frac{37}{8} $
6) $ \frac{8}{5} $
7) $ \frac{44}{7} $
8) $ \frac{53}{9} $

Let me know if you'd like these explained visually or with diagrams!