Dividing Mixed Numbers worksheet with ten problems for practice.

To solve these problems, we need to divide mixed numbers. The standard method is:

1. Convert each mixed number to an improper fraction.
2. Multiply the first fraction by the reciprocal of the second fraction.
3. Simplify the result (reduce and/or convert back to a mixed number if needed).

Let’s solve each problem step-by-step.

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1) \( 3\frac{3}{5} \div 2\frac{1}{2} \)

- Convert:
\( 3\frac{3}{5} = \frac{18}{5} \)
\( 2\frac{1}{2} = \frac{5}{2} \)

- Divide:
\( \frac{18}{5} \div \frac{5}{2} = \frac{18}{5} \times \frac{2}{5} = \frac{36}{25} \)

- Simplify:
\( \frac{36}{25} = 1\frac{11}{25} \)

✔ Answer: \( \boxed{1\frac{11}{25}} \)

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2) \( 2\frac{7}{10} \div 3\frac{1}{3} \)

- Convert:
\( 2\frac{7}{10} = \frac{27}{10} \)
\( 3\frac{1}{3} = \frac{10}{3} \)

- Divide:
\( \frac{27}{10} \div \frac{10}{3} = \frac{27}{10} \times \frac{3}{10} = \frac{81}{100} \)

- Already simplified.

✔ Answer: \( \boxed{\frac{81}{100}} \)

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3) \( 4\frac{3}{5} \div 4\frac{1}{3} \)

- Convert:
\( 4\frac{3}{5} = \frac{23}{5} \)
\( 4\frac{1}{3} = \frac{13}{3} \)

- Divide:
\( \frac{23}{5} \div \frac{13}{3} = \frac{23}{5} \times \frac{3}{13} = \frac{69}{65} \)

- Simplify:
\( \frac{69}{65} = 1\frac{4}{65} \)

✔ Answer: \( \boxed{1\frac{4}{65}} \)

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

- Convert:
\( 4\frac{1}{2} = \frac{9}{2} \)
\( 4\frac{1}{3} = \frac{13}{3} \)

- Divide:
\( \frac{9}{2} \div \frac{13}{3} = \frac{9}{2} \times \frac{3}{13} = \frac{27}{26} \)

- Simplify:
\( \frac{27}{26} = 1\frac{1}{26} \)

✔ Answer: \( \boxed{1\frac{1}{26}} \)

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5) \( 4\frac{1}{10} \div 2\frac{1}{2} \)

- Convert:
\( 4\frac{1}{10} = \frac{41}{10} \)
\( 2\frac{1}{2} = \frac{5}{2} \)

- Divide:
\( \frac{41}{10} \div \frac{5}{2} = \frac{41}{10} \times \frac{2}{5} = \frac{82}{50} \)

- Simplify:
\( \frac{82}{50} = \frac{41}{25} = 1\frac{16}{25} \)

✔ Answer: \( \boxed{1\frac{16}{25}} \)

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6) \( 3\frac{1}{5} \div 4\frac{2}{3} \)

- Convert:
\( 3\frac{1}{5} = \frac{16}{5} \)
\( 4\frac{2}{3} = \frac{14}{3} \)

- 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: \( \boxed{\frac{24}{35}} \)

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7) \( 3\frac{3}{10} \div 3\frac{2}{3} \)

- Convert:
\( 3\frac{3}{10} = \frac{33}{10} \)
\( 3\frac{2}{3} = \frac{11}{3} \)

- Divide:
\( \frac{33}{10} \div \frac{11}{3} = \frac{33}{10} \times \frac{3}{11} = \frac{99}{110} \)

- Simplify:
\( \frac{99}{110} = \frac{9}{10} \) (divide numerator and denominator by 11)

✔ Answer: \( \boxed{\frac{9}{10}} \)

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8) \( 2\frac{9}{10} \div 3\frac{4}{5} \)

- Convert:
\( 2\frac{9}{10} = \frac{29}{10} \)
\( 3\frac{4}{5} = \frac{19}{5} \)

- Divide:
\( \frac{29}{10} \div \frac{19}{5} = \frac{29}{10} \times \frac{5}{19} = \frac{145}{190} \)

- Simplify:
\( \frac{145}{190} = \frac{29}{38} \) (divide by 5)

✔ Answer: \( \boxed{\frac{29}{38}} \)

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9) \( 4\frac{1}{5} \div 2\frac{1}{2} \)

- Convert:
\( 4\frac{1}{5} = \frac{21}{5} \)
\( 2\frac{1}{2} = \frac{5}{2} \)

- Divide:
\( \frac{21}{5} \div \frac{5}{2} = \frac{21}{5} \times \frac{2}{5} = \frac{42}{25} \)

- Simplify:
\( \frac{42}{25} = 1\frac{17}{25} \)

✔ Answer: \( \boxed{1\frac{17}{25}} \)

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10) \( 2\frac{9}{10} \div 3\frac{1}{2} \)

- Convert:
\( 2\frac{9}{10} = \frac{29}{10} \)
\( 3\frac{1}{2} = \frac{7}{2} \)

- Divide:
\( \frac{29}{10} \div \frac{7}{2} = \frac{29}{10} \times \frac{2}{7} = \frac{58}{70} \)

- Simplify:
\( \frac{58}{70} = \frac{29}{35} \) (divide by 2)

✔ Answer: \( \boxed{\frac{29}{35}} \)

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## ✔ Final Answers:

1) \( \boxed{1\frac{11}{25}} \)
2) \( \boxed{\frac{81}{100}} \)
3) \( \boxed{1\frac{4}{65}} \)
4) \( \boxed{1\frac{1}{26}} \)
5) \( \boxed{1\frac{16}{25}} \)
6) \( \boxed{\frac{24}{35}} \)
7) \( \boxed{\frac{9}{10}} \)
8) \( \boxed{\frac{29}{38}} \)
9) \( \boxed{1\frac{17}{25}} \)
10) \( \boxed{\frac{29}{35}} \)

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