Dividing Fractions With Mixed Numbers Worksheet - Free Printable

Let's solve each problem step by step. The task is to divide mixed numbers and express the answers in lowest terms, using mixed numbers when possible.

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🔧 Step-by-step Method:

To divide a mixed number by a whole number:
1. Convert the mixed number to an improper fraction.
2. Divide the improper fraction by the whole number (which is the same as multiplying by its reciprocal).
3. Simplify the result.
4. Convert back to a mixed number if needed.

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We'll go through each problem:

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#### 1. $ 2\frac{1}{4} \div 3 $

- Convert: $ 2\frac{1}{4} = \frac{9}{4} $
- Divide: $ \frac{9}{4} \div 3 = \frac{9}{4} \times \frac{1}{3} = \frac{9}{12} = \frac{3}{4} $
✔ Answer: $ \frac{3}{4} $

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#### 2. $ 1\frac{2}{6} \div 2 $

- Simplify $ 1\frac{2}{6} = 1\frac{1}{3} $
- Convert: $ 1\frac{1}{3} = \frac{4}{3} $
- Divide: $ \frac{4}{3} \div 2 = \frac{4}{3} \times \frac{1}{2} = \frac{4}{6} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $

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#### 3. $ 2\frac{2}{5} \div 4 $

- Convert: $ 2\frac{2}{5} = \frac{12}{5} $
- Divide: $ \frac{12}{5} \div 4 = \frac{12}{5} \times \frac{1}{4} = \frac{12}{20} = \frac{3}{5} $
✔ Answer: $ \frac{3}{5} $

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#### 4. $ 3\frac{1}{3} \div 2 $

- Convert: $ 3\frac{1}{3} = \frac{10}{3} $
- Divide: $ \frac{10}{3} \div 2 = \frac{10}{3} \times \frac{1}{2} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3} $
✔ Answer: $ 1\frac{2}{3} $

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#### 5. $ 1\frac{2}{3} \div 2 $

- Convert: $ 1\frac{2}{3} = \frac{5}{3} $
- Divide: $ \frac{5}{3} \div 2 = \frac{5}{3} \times \frac{1}{2} = \frac{5}{6} $
✔ Answer: $ \frac{5}{6} $

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#### 6. $ 1\frac{3}{5} \div 4 $

- Convert: $ 1\frac{3}{5} = \frac{8}{5} $
- Divide: $ \frac{8}{5} \div 4 = \frac{8}{5} \times \frac{1}{4} = \frac{8}{20} = \frac{2}{5} $
✔ Answer: $ \frac{2}{5} $

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#### 7. $ 1\frac{1}{9} \div 5 $

- Convert: $ 1\frac{1}{9} = \frac{10}{9} $
- Divide: $ \frac{10}{9} \div 5 = \frac{10}{9} \times \frac{1}{5} = \frac{10}{45} = \frac{2}{9} $
✔ Answer: $ \frac{2}{9} $

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#### 8. $ 2\frac{2}{4} \div 5 $

- Simplify: $ 2\frac{2}{4} = 2\frac{1}{2} = \frac{5}{2} $
- Divide: $ \frac{5}{2} \div 5 = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $

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#### 9. $ 2\frac{2}{8} \div 9 $

- Simplify: $ 2\frac{2}{8} = 2\frac{1}{4} = \frac{9}{4} $
- Divide: $ \frac{9}{4} \div 9 = \frac{9}{4} \times \frac{1}{9} = \frac{9}{36} = \frac{1}{4} $
✔ Answer: $ \frac{1}{4} $

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#### 10. $ 1\frac{3}{6} \div 3 $

- Simplify: $ 1\frac{3}{6} = 1\frac{1}{2} = \frac{3}{2} $
- Divide: $ \frac{3}{2} \div 3 = \frac{3}{2} \times \frac{1}{3} = \frac{3}{6} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $

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#### 11. $ 2\frac{2}{6} \div 7 $

- Simplify: $ 2\frac{2}{6} = 2\frac{1}{3} = \frac{7}{3} $
- Divide: $ \frac{7}{3} \div 7 = \frac{7}{3} \times \frac{1}{7} = \frac{7}{21} = \frac{1}{3} $
✔ Answer: $ \frac{1}{3} $

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#### 12. $ 2\frac{4}{6} \div 4 $

- Simplify: $ 2\frac{4}{6} = 2\frac{2}{3} = \frac{8}{3} $
- Divide: $ \frac{8}{3} \div 4 = \frac{8}{3} \times \frac{1}{4} = \frac{8}{12} = \frac{2}{3} $
✔ Answer: $ \frac{2}{3} $

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#### 13. $ 2\frac{2}{7} \div 4 $

- Convert: $ 2\frac{2}{7} = \frac{16}{7} $
- Divide: $ \frac{16}{7} \div 4 = \frac{16}{7} \times \frac{1}{4} = \frac{16}{28} = \frac{4}{7} $
✔ Answer: $ \frac{4}{7} $

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#### 14. $ 1\frac{1}{4} \div 5 $

- Convert: $ 1\frac{1}{4} = \frac{5}{4} $
- Divide: $ \frac{5}{4} \div 5 = \frac{5}{4} \times \frac{1}{5} = \frac{5}{20} = \frac{1}{4} $
✔ Answer: $ \frac{1}{4} $

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#### 15. $ 1\frac{2}{8} \div 2 $

- Simplify: $ 1\frac{2}{8} = 1\frac{1}{4} = \frac{5}{4} $
- Divide: $ \frac{5}{4} \div 2 = \frac{5}{4} \times \frac{1}{2} = \frac{5}{8} $
✔ Answer: $ \frac{5}{8} $

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#### 16. $ 1\frac{2}{3} \div 2 $

- Convert: $ 1\frac{2}{3} = \frac{5}{3} $
- Divide: $ \frac{5}{3} \div 2 = \frac{5}{3} \times \frac{1}{2} = \frac{5}{6} $
✔ Answer: $ \frac{5}{6} $

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#### 17. $ 4\frac{4}{5} \div 3 $

- Convert: $ 4\frac{4}{5} = \frac{24}{5} $
- Divide: $ \frac{24}{5} \div 3 = \frac{24}{5} \times \frac{1}{3} = \frac{24}{15} = \frac{8}{5} = 1\frac{3}{5} $
✔ Answer: $ 1\frac{3}{5} $

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#### 18. $ 3\frac{1}{9} \div 4 $

- Convert: $ 3\frac{1}{9} = \frac{28}{9} $
- Divide: $ \frac{28}{9} \div 4 = \frac{28}{9} \times \frac{1}{4} = \frac{28}{36} = \frac{7}{9} $
✔ Answer: $ \frac{7}{9} $

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#### 19. $ 1\frac{2}{5} \div 7 $

- Convert: $ 1\frac{2}{5} = \frac{7}{5} $
- Divide: $ \frac{7}{5} \div 7 = \frac{7}{5} \times \frac{1}{7} = \frac{7}{35} = \frac{1}{5} $
✔ Answer: $ \frac{1}{5} $

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#### 20. $ 2\frac{3}{6} \div 5 $

- Simplify: $ 2\frac{3}{6} = 2\frac{1}{2} = \frac{5}{2} $
- Divide: $ \frac{5}{2} \div 5 = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $

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#### 21. $ 2\frac{4}{8} \div 5 $

- Simplify: $ 2\frac{4}{8} = 2\frac{1}{2} = \frac{5}{2} $
- Divide: $ \frac{5}{2} \div 5 = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2} $
✔ Answer: $ \frac{1}{2} $

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#### 22. $ 4\frac{1}{2} \div 3 $

- Convert: $ 4\frac{1}{2} = \frac{9}{2} $
- Divide: $ \frac{9}{2} \div 3 = \frac{9}{2} \times \frac{1}{3} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2} $
✔ Answer: $ 1\frac{1}{2} $

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✔ Final Answers (in order):

1. $ \frac{3}{4} $
2. $ \frac{2}{3} $
3. $ \frac{3}{5} $
4. $ 1\frac{2}{3} $
5. $ \frac{5}{6} $
6. $ \frac{2}{5} $
7. $ \frac{2}{9} $
8. $ \frac{1}{2} $
9. $ \frac{1}{4} $
10. $ \frac{1}{2} $
11. $ \frac{1}{3} $
12. $ \frac{2}{3} $
13. $ \frac{4}{7} $
14. $ \frac{1}{4} $
15. $ \frac{5}{8} $
16. $ \frac{5}{6} $
17. $ 1\frac{3}{5} $
18. $ \frac{7}{9} $
19. $ \frac{1}{5} $
20. $ \frac{1}{2} $
21. $ \frac{1}{2} $
22. $ 1\frac{1}{2} $

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