Free printable worksheet for practicing division of mixed numbers with step-by-step instructions.

Let's solve each of these mixed number division problems step by step, following the instructions provided:

Steps to Divide Mixed Numbers:

1. Convert mixed numbers into improper fractions.
2. Leave the first fraction as is.
3. Change the division sign to multiplication.
4. Flip (invert) the second fraction.
5. Multiply the two fractions.
6. Simplify the result.

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We'll go through each problem one by one.

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1. $ 8\frac{2}{4} \div 6\frac{2}{7} $

- Convert:
- $ 8\frac{2}{4} = \frac{34}{4} = \frac{17}{2} $ (simplify $ \frac{34}{4} $)
- $ 6\frac{2}{7} = \frac{44}{7} $
- Now: $ \frac{17}{2} \div \frac{44}{7} = \frac{17}{2} \times \frac{7}{44} = \frac{119}{88} $
- Simplify: $ \frac{119}{88} = 1\frac{31}{88} $

✔ Answer: $ 1\frac{31}{88} $

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2. $ 7\frac{8}{9} \div 2\frac{1}{5} $

- Convert:
- $ 7\frac{8}{9} = \frac{71}{9} $
- $ 2\frac{1}{5} = \frac{11}{5} $
- $ \frac{71}{9} \div \frac{11}{5} = \frac{71}{9} \times \frac{5}{11} = \frac{355}{99} $
- Simplify: $ \frac{355}{99} = 3\frac{58}{99} $

✔ Answer: $ 3\frac{58}{99} $

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3. $ 9\frac{3}{5} \div 7\frac{4}{8} $

- Note: $ 7\frac{4}{8} = 7\frac{1}{2} $
- Convert:
- $ 9\frac{3}{5} = \frac{48}{5} $
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ \frac{48}{5} \div \frac{15}{2} = \frac{48}{5} \times \frac{2}{15} = \frac{96}{75} = \frac{32}{25} $
- $ \frac{32}{25} = 1\frac{7}{25} $

✔ Answer: $ 1\frac{7}{25} $

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4. $ 9\frac{4}{5} \div 5\frac{1}{5} $

- Convert:
- $ 9\frac{4}{5} = \frac{49}{5} $
- $ 5\frac{1}{5} = \frac{26}{5} $
- $ \frac{49}{5} \div \frac{26}{5} = \frac{49}{5} \times \frac{5}{26} = \frac{49}{26} $
- $ \frac{49}{26} = 1\frac{23}{26} $

✔ Answer: $ 1\frac{23}{26} $

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5. $ 4\frac{1}{3} \div 2\frac{1}{6} $

- Convert:
- $ 4\frac{1}{3} = \frac{13}{3} $
- $ 2\frac{1}{6} = \frac{13}{6} $
- $ \frac{13}{3} \div \frac{13}{6} = \frac{13}{3} \times \frac{6}{13} = \frac{78}{39} = 2 $

✔ Answer: $ 2 $

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6. $ 7\frac{7}{9} \div 6\frac{4}{7} $

- Convert:
- $ 7\frac{7}{9} = \frac{70}{9} $
- $ 6\frac{4}{7} = \frac{46}{7} $
- $ \frac{70}{9} \div \frac{46}{7} = \frac{70}{9} \times \frac{7}{46} = \frac{490}{414} $
- Simplify: divide numerator and denominator by 2 → $ \frac{245}{207} $
- $ \frac{245}{207} = 1\frac{38}{207} $

✔ Answer: $ 1\frac{38}{207} $

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7. $ 5\frac{2}{3} \div 9\frac{1}{2} $

- Convert:
- $ 5\frac{2}{3} = \frac{17}{3} $
- $ 9\frac{1}{2} = \frac{19}{2} $
- $ \frac{17}{3} \div \frac{19}{2} = \frac{17}{3} \times \frac{2}{19} = \frac{34}{57} $
- Simplify: $ \frac{34}{57} $ → GCD is 1 → already simplified

✔ Answer: $ \frac{34}{57} $

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8. $ 6\frac{8}{9} \div 4\frac{1}{9} $

- Convert:
- $ 6\frac{8}{9} = \frac{62}{9} $
- $ 4\frac{1}{9} = \frac{37}{9} $
- $ \frac{62}{9} \div \frac{37}{9} = \frac{62}{9} \times \frac{9}{37} = \frac{62}{37} $
- $ \frac{62}{37} = 1\frac{25}{37} $

✔ Answer: $ 1\frac{25}{37} $

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9. $ 7\frac{3}{4} \div 5\frac{2}{7} $

- Convert:
- $ 7\frac{3}{4} = \frac{31}{4} $
- $ 5\frac{2}{7} = \frac{37}{7} $
- $ \frac{31}{4} \div \frac{37}{7} = \frac{31}{4} \times \frac{7}{37} = \frac{217}{148} $
- $ \frac{217}{148} = 1\frac{69}{148} $

✔ Answer: $ 1\frac{69}{148} $

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10. $ 4\frac{3}{4} \div 2\frac{1}{2} $

- Convert:
- $ 4\frac{3}{4} = \frac{19}{4} $
- $ 2\frac{1}{2} = \frac{5}{2} $
- $ \frac{19}{4} \div \frac{5}{2} = \frac{19}{4} \times \frac{2}{5} = \frac{38}{20} = \frac{19}{10} = 1\frac{9}{10} $

✔ Answer: $ 1\frac{9}{10} $

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11. $ 6\frac{7}{8} \div 2\frac{2}{3} $

- Convert:
- $ 6\frac{7}{8} = \frac{55}{8} $
- $ 2\frac{2}{3} = \frac{8}{3} $
- $ \frac{55}{8} \div \frac{8}{3} = \frac{55}{8} \times \frac{3}{8} = \frac{165}{64} $
- $ \frac{165}{64} = 2\frac{37}{64} $

✔ Answer: $ 2\frac{37}{64} $

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12. $ 6\frac{1}{3} \div 4\frac{2}{4} $

- Simplify: $ 4\frac{2}{4} = 4\frac{1}{2} = \frac{9}{2} $
- Convert:
- $ 6\frac{1}{3} = \frac{19}{3} $
- $ \frac{19}{3} \div \frac{9}{2} = \frac{19}{3} \times \frac{2}{9} = \frac{38}{27} = 1\frac{11}{27} $

✔ Answer: $ 1\frac{11}{27} $

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13. $ 6\frac{1}{2} \div 4\frac{1}{5} $

- Convert:
- $ 6\frac{1}{2} = \frac{13}{2} $
- $ 4\frac{1}{5} = \frac{21}{5} $
- $ \frac{13}{2} \div \frac{21}{5} = \frac{13}{2} \times \frac{5}{21} = \frac{65}{42} = 1\frac{23}{42} $

✔ Answer: $ 1\frac{23}{42} $

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14. $ 7\frac{2}{3} \div 5\frac{1}{3} $

- Convert:
- $ 7\frac{2}{3} = \frac{23}{3} $
- $ 5\frac{1}{3} = \frac{16}{3} $
- $ \frac{23}{3} \div \frac{16}{3} = \frac{23}{3} \times \frac{3}{16} = \frac{23}{16} = 1\frac{7}{16} $

✔ Answer: $ 1\frac{7}{16} $

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15. $ 3\frac{3}{5} \div 2\frac{1}{4} $

- Convert:
- $ 3\frac{3}{5} = \frac{18}{5} $
- $ 2\frac{1}{4} = \frac{9}{4} $
- $ \frac{18}{5} \div \frac{9}{4} = \frac{18}{5} \times \frac{4}{9} = \frac{72}{45} = \frac{8}{5} = 1\frac{3}{5} $

✔ Answer: $ 1\frac{3}{5} $

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16. $ 3\frac{1}{2} \div 3\frac{3}{4} $

- Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 3\frac{3}{4} = \frac{15}{4} $
- $ \frac{7}{2} \div \frac{15}{4} = \frac{7}{2} \times \frac{4}{15} = \frac{28}{30} = \frac{14}{15} $

✔ Answer: $ \frac{14}{15} $

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17. $ 4\frac{1}{2} \div 7\frac{1}{2} $

- Convert:
- $ 4\frac{1}{2} = \frac{9}{2} $
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ \frac{9}{2} \div \frac{15}{2} = \frac{9}{2} \times \frac{2}{15} = \frac{18}{30} = \frac{3}{5} $

✔ Answer: $ \frac{3}{5} $

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18. $ 8\frac{5}{8} \div 7\frac{1}{2} $

- Convert:
- $ 8\frac{5}{8} = \frac{69}{8} $
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ \frac{69}{8} \div \frac{15}{2} = \frac{69}{8} \times \frac{2}{15} = \frac{138}{120} = \frac{23}{20} = 1\frac{3}{20} $

✔ Answer: $ 1\frac{3}{20} $

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19. $ 7\frac{2}{3} \div 5\frac{2}{9} $

- Convert:
- $ 7\frac{2}{3} = \frac{23}{3} $
- $ 5\frac{2}{9} = \frac{47}{9} $
- $ \frac{23}{3} \div \frac{47}{9} = \frac{23}{3} \times \frac{9}{47} = \frac{207}{141} $
- Simplify: divide numerator and denominator by 3 → $ \frac{69}{47} $
- $ \frac{69}{47} = 1\frac{22}{47} $

✔ Answer: $ 1\frac{22}{47} $

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20. $ 7\frac{3}{5} \div 6\frac{5}{6} $

- Convert:
- $ 7\frac{3}{5} = \frac{38}{5} $
- $ 6\frac{5}{6} = \frac{41}{6} $
- $ \frac{38}{5} \div \frac{41}{6} = \frac{38}{5} \times \frac{6}{41} = \frac{228}{205} $
- $ \frac{228}{205} = 1\frac{23}{205} $

✔ Answer: $ 1\frac{23}{205} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ 1\frac{31}{88} $ |
| 2 | $ 3\frac{58}{99} $ |
| 3 | $ 1\frac{7}{25} $ |
| 4 | $ 1\frac{23}{26} $ |
| 5 | $ 2 $ |
| 6 | $ 1\frac{38}{207} $ |
| 7 | $ \frac{34}{57} $ |
| 8 | $ 1\frac{25}{37} $ |
| 9 | $ 1\frac{69}{148} $ |
| 10 | $ 1\frac{9}{10} $ |
| 11 | $ 2\frac{37}{64} $ |
| 12 | $ 1\frac{11}{27} $ |
| 13 | $ 1\frac{23}{42} $ |
| 14 | $ 1\frac{7}{16} $ |
| 15 | $ 1\frac{3}{5} $ |
| 16 | $ \frac{14}{15} $ |
| 17 | $ \frac{3}{5} $ |
| 18 | $ 1\frac{3}{20} $ |
| 19 | $ 1\frac{22}{47} $ |
| 20 | $ 1\frac{23}{205} $ |

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