Math worksheet for practicing division of mixed numbers.

Let's solve each of these division problems involving mixed numbers step by step.

🔧 Step-by-step Process:

To divide mixed numbers:
1. Convert each mixed number to an improper fraction.
2. Change the division into multiplication by flipping the second fraction (reciprocal).
3. Multiply the fractions.
4. Simplify the result and convert back to a mixed number if needed.

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Problem 1:

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

- Convert to improper fractions:
- $ 3\frac{1}{5} = \frac{16}{5} $
- $ 4\frac{2}{3} = \frac{14}{3} $
- Now divide:
$ \frac{16}{5} \div \frac{14}{3} = \frac{16}{5} \times \frac{3}{14} = \frac{48}{70} $
- Simplify:
$ \frac{48}{70} = \frac{24}{35} $

✔ Answer: $ \frac{24}{35} $

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Problem 2:

$ 3\frac{1}{5} \div 4\frac{2}{3} $
This is the same as Problem 1.

✔ Answer: $ \frac{24}{35} $

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Problem 3:

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

- Convert:
- $ 3\frac{1}{10} = \frac{31}{10} $
- $ 2\frac{1}{2} = \frac{5}{2} $
- Divide:
$ \frac{31}{10} \div \frac{5}{2} = \frac{31}{10} \times \frac{2}{5} = \frac{62}{50} $
- Simplify:
$ \frac{62}{50} = \frac{31}{25} = 1\frac{6}{25} $

✔ Answer: $ 1\frac{6}{25} $

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Problem 4:

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

- Convert:
- $ 2\frac{1}{2} = \frac{5}{2} $
- $ 2\frac{3}{4} = \frac{11}{4} $
- Divide:
$ \frac{5}{2} \div \frac{11}{4} = \frac{5}{2} \times \frac{4}{11} = \frac{20}{22} = \frac{10}{11} $

✔ Answer: $ \frac{10}{11} $

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Problem 5:

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

- Simplify $ 2\frac{2}{10} = 2\frac{1}{5} = \frac{11}{5} $
- $ 3\frac{1}{2} = \frac{7}{2} $
- Divide:
$ \frac{11}{5} \div \frac{7}{2} = \frac{11}{5} \times \frac{2}{7} = \frac{22}{35} $

✔ Answer: $ \frac{22}{35} $

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Problem 6:

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

- Convert:
- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 4\frac{2}{3} = \frac{14}{3} $
- Divide:
$ \frac{7}{3} \div \frac{14}{3} = \frac{7}{3} \times \frac{3}{14} = \frac{21}{42} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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Problem 7:

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

- Simplify $ 3\frac{2}{4} = 3\frac{1}{2} = \frac{7}{2} $
- $ 1\frac{1}{2} = \frac{3}{2} $
- Divide:
$ \frac{7}{2} \div \frac{3}{2} = \frac{7}{2} \times \frac{2}{3} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3} $

✔ Answer: $ 2\frac{1}{3} $

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Problem 8:

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

- Convert:
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- Divide:
$ \frac{15}{2} \div \frac{25}{6} = \frac{15}{2} \times \frac{6}{25} = \frac{90}{50} = \frac{9}{5} = 1\frac{4}{5} $

✔ Answer: $ 1\frac{4}{5} $

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Problem 9:

$ 3\frac{5}{6} \div 6\frac{2}{3} $

- Convert:
- $ 3\frac{5}{6} = \frac{23}{6} $
- $ 6\frac{2}{3} = \frac{20}{3} $
- Divide:
$ \frac{23}{6} \div \frac{20}{3} = \frac{23}{6} \times \frac{3}{20} = \frac{69}{120} $
- Simplify:
$ \frac{69}{120} = \frac{23}{40} $

✔ Answer: $ \frac{23}{40} $

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Problem 10:

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

- Convert:
- $ 4\frac{1}{5} = \frac{21}{5} $
- $ 3\frac{3}{4} = \frac{15}{4} $
- Divide:
$ \frac{21}{5} \div \frac{15}{4} = \frac{21}{5} \times \frac{4}{15} = \frac{84}{75} $
- Simplify:
$ \frac{84}{75} = \frac{28}{25} = 1\frac{3}{25} $

✔ Answer: $ 1\frac{3}{25} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{24}{35} $ |
| 2 | $ \frac{24}{35} $ |
| 3 | $ 1\frac{6}{25} $ |
| 4 | $ \frac{10}{11} $ |
| 5 | $ \frac{22}{35} $ |
| 6 | $ \frac{1}{2} $ |
| 7 | $ 2\frac{1}{3} $ |
| 8 | $ 1\frac{4}{5} $ |
| 9 | $ \frac{23}{40} $ |
| 10 | $ 1\frac{3}{25} $ |

Let me know if you'd like this in printable format or with steps shown on paper!