Math worksheet for practicing multiplication and division of mixed fractions.

Let's solve each of these problems step by step. The task involves multiplying and dividing mixed fractions, and we need to express each answer in lowest terms.

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🔧 Step-by-step Strategy:

1. Convert mixed numbers to improper fractions.
2. For division: Multiply by the reciprocal.
3. For multiplication: Multiply numerators and denominators.
4. Simplify the result to lowest terms.
5. Convert back to a mixed number if needed.

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We’ll go through each problem:

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

- Convert:
- $ 1\frac{3}{4} = \frac{7}{4} $
- $ 1\frac{1}{5} = \frac{6}{5} $
- Divide: $ \frac{7}{4} \div \frac{6}{5} = \frac{7}{4} \times \frac{5}{6} = \frac{35}{24} $
- Simplify: $ \frac{35}{24} = 1\frac{11}{24} $

✔ Answer: $ \boxed{1\frac{11}{24}} $

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

- Convert:
- $ 4\frac{1}{3} = \frac{13}{3} $
- $ 2\frac{1}{4} = \frac{9}{4} $
- Divide: $ \frac{13}{3} \div \frac{9}{4} = \frac{13}{3} \times \frac{4}{9} = \frac{52}{27} $
- Simplify: $ \frac{52}{27} = 1\frac{25}{27} $

✔ Answer: $ \boxed{1\frac{25}{27}} $

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3. $ 3\frac{1}{2} \times 1\frac{1}{10} $

- Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 1\frac{1}{10} = \frac{11}{10} $
- Multiply: $ \frac{7}{2} \times \frac{11}{10} = \frac{77}{20} $
- Simplify: $ \frac{77}{20} = 3\frac{17}{20} $

✔ Answer: $ \boxed{3\frac{17}{20}} $

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

- Convert:
- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 1\frac{3}{10} = \frac{13}{10} $
- Divide: $ \frac{3}{2} \div \frac{13}{10} = \frac{3}{2} \times \frac{10}{13} = \frac{30}{26} = \frac{15}{13} $
- Simplify: $ \frac{15}{13} = 1\frac{2}{13} $

✔ Answer: $ \boxed{1\frac{2}{13}} $

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5. $ 1\frac{3}{8} \times 1\frac{1}{4} $

- Convert:
- $ 1\frac{3}{8} = \frac{11}{8} $
- $ 1\frac{1}{4} = \frac{5}{4} $
- Multiply: $ \frac{11}{8} \times \frac{5}{4} = \frac{55}{32} $
- Simplify: $ \frac{55}{32} = 1\frac{23}{32} $

✔ Answer: $ \boxed{1\frac{23}{32}} $

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6. $ 4\frac{3}{4} \div 2\frac{3}{8} $

- Convert:
- $ 4\frac{3}{4} = \frac{19}{4} $
- $ 2\frac{3}{8} = \frac{19}{8} $
- Divide: $ \frac{19}{4} \div \frac{19}{8} = \frac{19}{4} \times \frac{8}{19} = \frac{152}{76} = 2 $

✔ Answer: $ \boxed{2} $

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7. $ 4\frac{1}{3} \div 1\frac{2}{5} $

- Convert:
- $ 4\frac{1}{3} = \frac{13}{3} $
- $ 1\frac{2}{5} = \frac{7}{5} $
- Divide: $ \frac{13}{3} \div \frac{7}{5} = \frac{13}{3} \times \frac{5}{7} = \frac{65}{21} $
- Simplify: $ \frac{65}{21} = 3\frac{2}{21} $

✔ Answer: $ \boxed{3\frac{2}{21}} $

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8. $ 1\frac{2}{3} \times 2\frac{3}{4} $

- Convert:
- $ 1\frac{2}{3} = \frac{5}{3} $
- $ 2\frac{3}{4} = \frac{11}{4} $
- Multiply: $ \frac{5}{3} \times \frac{11}{4} = \frac{55}{12} $
- Simplify: $ \frac{55}{12} = 4\frac{7}{12} $

✔ Answer: $ \boxed{4\frac{7}{12}} $

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9. $ 1\frac{1}{9} \times 2\frac{1}{8} $

- Convert:
- $ 1\frac{1}{9} = \frac{10}{9} $
- $ 2\frac{1}{8} = \frac{17}{8} $
- Multiply: $ \frac{10}{9} \times \frac{17}{8} = \frac{170}{72} $
- Simplify: $ \frac{170}{72} = \frac{85}{36} = 2\frac{13}{36} $

✔ Answer: $ \boxed{2\frac{13}{36}} $

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10. $ 7\frac{1}{2} \div 4\frac{1}{4} $

- Convert:
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 4\frac{1}{4} = \frac{17}{4} $
- Divide: $ \frac{15}{2} \div \frac{17}{4} = \frac{15}{2} \times \frac{4}{17} = \frac{60}{34} = \frac{30}{17} $
- Simplify: $ \frac{30}{17} = 1\frac{13}{17} $

✔ Answer: $ \boxed{1\frac{13}{17}} $

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11. $ 2\frac{5}{6} \div 2\frac{1}{3} $

- Convert:
- $ 2\frac{5}{6} = \frac{17}{6} $
- $ 2\frac{1}{3} = \frac{7}{3} $
- Divide: $ \frac{17}{6} \div \frac{7}{3} = \frac{17}{6} \times \frac{3}{7} = \frac{51}{42} = \frac{17}{14} $
- Simplify: $ \frac{17}{14} = 1\frac{3}{14} $

✔ Answer: $ \boxed{1\frac{3}{14}} $

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12. $ 11\frac{1}{2} \div 3\frac{1}{3} $

- Convert:
- $ 11\frac{1}{2} = \frac{23}{2} $
- $ 3\frac{1}{3} = \frac{10}{3} $
- Divide: $ \frac{23}{2} \div \frac{10}{3} = \frac{23}{2} \times \frac{3}{10} = \frac{69}{20} $
- Simplify: $ \frac{69}{20} = 3\frac{9}{20} $

✔ Answer: $ \boxed{3\frac{9}{20}} $

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13. $ 2\frac{1}{5} \times 1\frac{3}{4} $

- Convert:
- $ 2\frac{1}{5} = \frac{11}{5} $
- $ 1\frac{3}{4} = \frac{7}{4} $
- Multiply: $ \frac{11}{5} \times \frac{7}{4} = \frac{77}{20} $
- Simplify: $ \frac{77}{20} = 3\frac{17}{20} $

✔ Answer: $ \boxed{3\frac{17}{20}} $

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

- Convert:
- $ 3\frac{2}{3} = \frac{11}{3} $
- $ 2\frac{2}{5} = \frac{12}{5} $
- Divide: $ \frac{11}{3} \div \frac{12}{5} = \frac{11}{3} \times \frac{5}{12} = \frac{55}{36} $
- Simplify: $ \frac{55}{36} = 1\frac{19}{36} $

✔ Answer: $ \boxed{1\frac{19}{36}} $

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15. $ 2\frac{1}{6} \times 1\frac{1}{5} $

- Convert:
- $ 2\frac{1}{6} = \frac{13}{6} $
- $ 1\frac{1}{5} = \frac{6}{5} $
- Multiply: $ \frac{13}{6} \times \frac{6}{5} = \frac{78}{30} = \frac{13}{5} $
- Simplify: $ \frac{13}{5} = 2\frac{3}{5} $

✔ Answer: $ \boxed{2\frac{3}{5}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 1\frac{11}{24} $ |
| 2 | $ 1\frac{25}{27} $ |
| 3 | $ 3\frac{17}{20} $ |
| 4 | $ 1\frac{2}{13} $ |
| 5 | $ 1\frac{23}{32} $ |
| 6 | $ 2 $ |
| 7 | $ 3\frac{2}{21} $ |
| 8 | $ 4\frac{7}{12} $ |
| 9 | $ 2\frac{13}{36} $ |
| 10 | $ 1\frac{13}{17} $ |
| 11 | $ 1\frac{3}{14} $ |
| 12 | $ 3\frac{9}{20} $ |
| 13 | $ 3\frac{17}{20} $ |
| 14 | $ 1\frac{19}{36} $ |
| 15 | $ 2\frac{3}{5} $ |

Let me know if you'd like a printable version or explanation for any specific one!