Math worksheet for practicing division of mixed numbers.

To solve the division of mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions.
2. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction.
3. Simplify the result if possible.

Let's solve each problem step by step.

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Problem 1: \( 3 \frac{1}{5} \div 4 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5} \)
- \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{16}{5} \div \frac{14}{3} = \frac{16}{5} \times \frac{3}{14} = \frac{16 \times 3}{5 \times 14} = \frac{48}{70} \]

#### Step 3: Simplify the result.
\[ \frac{48}{70} = \frac{24}{35} \]

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, so the answer is:
Answer: \( \frac{24}{35} \)

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Problem 3: \( 3 \frac{1}{10} \div 2 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{10} = \frac{3 \times 10 + 1}{10} = \frac{31}{10} \)
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} \)

#### Step 2: Divide the fractions.
\[ \frac{31}{10} \div \frac{5}{2} = \frac{31}{10} \times \frac{2}{5} = \frac{31 \times 2}{10 \times 5} = \frac{62}{50} \]

#### Step 3: Simplify the result.
\[ \frac{62}{50} = \frac{31}{25} \]

Answer: \( \frac{31}{25} \)

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Problem 4: \( 2 \frac{1}{2} \div 2 \frac{3}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} \)
- \( 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{5}{2} \div \frac{11}{4} = \frac{5}{2} \times \frac{4}{11} = \frac{5 \times 4}{2 \times 11} = \frac{20}{22} \]

#### Step 3: Simplify the result.
\[ \frac{20}{22} = \frac{10}{11} \]

Answer: \( \frac{10}{11} \)

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Problem 5: \( 2 \frac{2}{10} \div 3 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{2}{10} = \frac{2 \times 10 + 2}{10} = \frac{22}{10} \) (Simplify \( \frac{22}{10} \) to \( \frac{11}{5} \))
- \( 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)

#### Step 2: Divide the fractions.
\[ \frac{11}{5} \div \frac{7}{2} = \frac{11}{5} \times \frac{2}{7} = \frac{11 \times 2}{5 \times 7} = \frac{22}{35} \]

Answer: \( \frac{22}{35} \)

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Problem 6: \( 2 \frac{1}{3} \div 4 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \)
- \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{7}{3} \div \frac{14}{3} = \frac{7}{3} \times \frac{3}{14} = \frac{7 \times 3}{3 \times 14} = \frac{21}{42} \]

#### Step 3: Simplify the result.
\[ \frac{21}{42} = \frac{1}{2} \]

Answer: \( \frac{1}{2} \)

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Problem 7: \( 3 \frac{2}{4} \div 1 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{2}{4} = \frac{3 \times 4 + 2}{4} = \frac{14}{4} \) (Simplify \( \frac{14}{4} \) to \( \frac{7}{2} \))
- \( 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \)

#### Step 2: Divide the fractions.
\[ \frac{7}{2} \div \frac{3}{2} = \frac{7}{2} \times \frac{2}{3} = \frac{7 \times 2}{2 \times 3} = \frac{14}{6} \]

#### Step 3: Simplify the result.
\[ \frac{14}{6} = \frac{7}{3} \]

Answer: \( \frac{7}{3} \)

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Problem 8: \( 7 \frac{1}{2} \div 4 \frac{1}{6} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{15}{2} \)
- \( 4 \frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{25}{6} \)

#### Step 2: Divide the fractions.
\[ \frac{15}{2} \div \frac{25}{6} = \frac{15}{2} \times \frac{6}{25} = \frac{15 \times 6}{2 \times 25} = \frac{90}{50} \]

#### Step 3: Simplify the result.
\[ \frac{90}{50} = \frac{9}{5} \]

Answer: \( \frac{9}{5} \)

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Problem 9: \( 3 \frac{5}{6} \div 6 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{23}{6} \)
- \( 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{23}{6} \div \frac{20}{3} = \frac{23}{6} \times \frac{3}{20} = \frac{23 \times 3}{6 \times 20} = \frac{69}{120} \]

#### Step 3: Simplify the result.
\[ \frac{69}{120} = \frac{23}{40} \]

Answer: \( \frac{23}{40} \)

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Problem 10: \( 4 \frac{1}{5} \div 3 \frac{3}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5} \)
- \( 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{21}{5} \div \frac{15}{4} = \frac{21}{5} \times \frac{4}{15} = \frac{21 \times 4}{5 \times 15} = \frac{84}{75} \]

#### Step 3: Simplify the result.
\[ \frac{84}{75} = \frac{28}{25} \]

Answer: \( \frac{28}{25} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{24}{35} \\
2. & \frac{24}{35} \\
3. & \frac{31}{25} \\
4. & \frac{10}{11} \\
5. & \frac{22}{35} \\
6. & \frac{1}{2} \\
7. & \frac{7}{3} \\
8. & \frac{9}{5} \\
9. & \frac{23}{40} \\
10. & \frac{28}{25} \\
\end{array}
}
\]