Division of mixed numbers worksheet with ten practice problems for students to solve.

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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We’ll go through each problem:

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

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

✔ Answer: $ \frac{24}{35} $

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

Wait — this is the same as #1! Probably a typo in the worksheet, but we already solved it.

✔ Answer: $ \frac{24}{35} $

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

✔ Answer: $ 1\frac{6}{25} $

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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} $
- $ \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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5. $ 2\frac{2}{10} \div 3\frac{1}{2} $

First simplify $ 2\frac{2}{10} = 2\frac{1}{5} $ (since $ \frac{2}{10} = \frac{1}{5} $)

- $ 2\frac{1}{5} = \frac{11}{5} $
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ \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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6. $ 2\frac{1}{3} \div 4\frac{2}{3} $

- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 4\frac{2}{3} = \frac{14}{3} $
- $ \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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7. $ 3\frac{2}{4} \div 1\frac{1}{2} $

Simplify $ 3\frac{2}{4} = 3\frac{1}{2} $

- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 1\frac{1}{2} = \frac{3}{2} $
- $ \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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8. $ 7\frac{1}{2} \div 4\frac{1}{6} $

- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- $ \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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9. $ 3\frac{5}{6} \div 6\frac{2}{3} $

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

✔ Answer: $ \frac{23}{40} $

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10. $ 4\frac{1}{5} \div 3\frac{3}{4} $

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

✔ Answer: $ 1\frac{3}{25} $

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✔ Final Answers:

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

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💡 Tips:
- Always convert mixed numbers first.
- Flip the second fraction when dividing.
- Simplify before multiplying if possible (to reduce work).
- Double-check simplification!

Let me know if you'd like this formatted as a printable answer key!