Division of Mixed Numbers worksheet with 10 practice problems for students to solve.

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

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

#### Step 2: Divide the fractions.
\[ \frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10} = 2 \]

#### Answer:
\[ \boxed{2} \]

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Problem 2: \( 1 \frac{1}{5} \div 1 \frac{4}{6} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5} \)
- \( 1 \frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6} \) (Simplify \( \frac{10}{6} \) to \( \frac{5}{3} \))

#### Step 2: Divide the fractions.
\[ \frac{6}{5} \div \frac{5}{3} = \frac{6}{5} \times \frac{3}{5} = \frac{6 \times 3}{5 \times 5} = \frac{18}{25} \]

#### Answer:
\[ \boxed{\frac{18}{25}} \]

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4} \)
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{17}{4} \div \frac{7}{3} = \frac{17}{4} \times \frac{3}{7} = \frac{17 \times 3}{4 \times 7} = \frac{51}{28} \]

#### Answer:
\[ \boxed{\frac{51}{28}} \]

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Problem 4: \( 5 \frac{2}{7} \div 1 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 5 \frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{37}{7} \)
- \( 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \)

#### Step 2: Divide the fractions.
\[ \frac{37}{7} \div \frac{3}{2} = \frac{37}{7} \times \frac{2}{3} = \frac{37 \times 2}{7 \times 3} = \frac{74}{21} \]

#### Answer:
\[ \boxed{\frac{74}{21}} \]

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Problem 5: \( 3 \frac{1}{3} \div 1 \frac{8}{9} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} \)
- \( 1 \frac{8}{9} = \frac{1 \times 9 + 8}{9} = \frac{17}{9} \)

#### Step 2: Divide the fractions.
\[ \frac{10}{3} \div \frac{17}{9} = \frac{10}{3} \times \frac{9}{17} = \frac{10 \times 9}{3 \times 17} = \frac{90}{51} = \frac{30}{17} \]

#### Answer:
\[ \boxed{\frac{30}{17}} \]

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Problem 6: \( 7 \frac{1}{6} \div 1 \frac{3}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 7 \frac{1}{6} = \frac{7 \times 6 + 1}{6} = \frac{43}{6} \)
- \( 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{43}{6} \div \frac{7}{4} = \frac{43}{6} \times \frac{4}{7} = \frac{43 \times 4}{6 \times 7} = \frac{172}{42} = \frac{86}{21} \]

#### Answer:
\[ \boxed{\frac{86}{21}} \]

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Problem 7: \( 3 \frac{1}{5} \div 4 \frac{2}{3} \)

#### 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.
\[ \frac{16}{5} \div \frac{14}{3} = \frac{16}{5} \times \frac{3}{14} = \frac{16 \times 3}{5 \times 14} = \frac{48}{70} = \frac{24}{35} \]

#### Answer:
\[ \boxed{\frac{24}{35}} \]

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Problem 8: \( 10 \frac{1}{2} \div 1 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 10 \frac{1}{2} = \frac{10 \times 2 + 1}{2} = \frac{21}{2} \)
- \( 1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{21}{2} \div \frac{5}{3} = \frac{21}{2} \times \frac{3}{5} = \frac{21 \times 3}{2 \times 5} = \frac{63}{10} \]

#### Answer:
\[ \boxed{\frac{63}{10}} \]

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Problem 9: \( 2 \frac{4}{10} \div 6 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{4}{10} = \frac{2 \times 10 + 4}{10} = \frac{24}{10} \) (Simplify \( \frac{24}{10} \) to \( \frac{12}{5} \))
- \( 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3} \)

#### Step 2: Divide the fractions.
\[ \frac{12}{5} \div \frac{20}{3} = \frac{12}{5} \times \frac{3}{20} = \frac{12 \times 3}{5 \times 20} = \frac{36}{100} = \frac{9}{25} \]

#### Answer:
\[ \boxed{\frac{9}{25}} \]

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Problem 10: \( 10 \frac{1}{2} \div 1 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 10 \frac{1}{2} = \frac{10 \times 2 + 1}{2} = \frac{21}{2} \)
- \( 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{21}{2} \div \frac{5}{4} = \frac{21}{2} \times \frac{4}{5} = \frac{21 \times 4}{2 \times 5} = \frac{84}{10} = \frac{42}{5} \]

#### Answer:
\[ \boxed{\frac{42}{5}} \]

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Final Answers:

1. \( \boxed{2} \)
2. \( \boxed{\frac{18}{25}} \)
3. \( \boxed{\frac{51}{28}} \)
4. \( \boxed{\frac{74}{21}} \)
5. \( \boxed{\frac{30}{17}} \)
6. \( \boxed{\frac{86}{21}} \)
7. \( \boxed{\frac{24}{35}} \)
8. \( \boxed{\frac{63}{10}} \)
9. \( \boxed{\frac{9}{25}} \)
10. \( \boxed{\frac{42}{5}} \)