Math worksheet for dividing mixed numbers.

Sure! Let’s solve each of these dividing mixed numbers problems step by step.

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📌 General Strategy:

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

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## ✔ Problem 1:
$ 2\frac{3}{4} \div 3\frac{1}{2} $

- Convert to improper fractions:
- $ 2\frac{3}{4} = \frac{4 \times 2 + 3}{4} = \frac{11}{4} $
- $ 3\frac{1}{2} = \frac{2 \times 3 + 1}{2} = \frac{7}{2} $

- Now divide:
$ \frac{11}{4} \div \frac{7}{2} = \frac{11}{4} \times \frac{2}{7} = \frac{22}{28} $

- Simplify:
$ \frac{22}{28} = \frac{11}{14} $

✔ Answer: $ \boxed{\frac{11}{14}} $

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## ✔ Problem 2:
$ 4\frac{2}{3} \div 3\frac{3}{4} $

- Convert:
- $ 4\frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3} $
- $ 3\frac{3}{4} = \frac{4 \times 3 + 3}{4} = \frac{15}{4} $

- Divide:
$ \frac{14}{3} \div \frac{15}{4} = \frac{14}{3} \times \frac{4}{15} = \frac{56}{45} $

- Convert to mixed number:
$ \frac{56}{45} = 1 \frac{11}{45} $

✔ Answer: $ \boxed{1\frac{11}{45}} $

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## ✔ Problem 3:
$ 2\frac{2}{5} \div 4\frac{3}{4} $

- Convert:
- $ 2\frac{2}{5} = \frac{5 \times 2 + 2}{5} = \frac{12}{5} $
- $ 4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4} $

- Divide:
$ \frac{12}{5} \div \frac{19}{4} = \frac{12}{5} \times \frac{4}{19} = \frac{48}{95} $

- Check simplification: 48 and 95 have no common factors → already simplified.

✔ Answer: $ \boxed{\frac{48}{95}} $

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## ✔ Problem 4:
$ 2\frac{1}{5} \div 4\frac{3}{4} $

- Convert:
- $ 2\frac{1}{5} = \frac{5 \times 2 + 1}{5} = \frac{11}{5} $
- $ 4\frac{3}{4} = \frac{19}{4} $ (from problem 3)

- Divide:
$ \frac{11}{5} \div \frac{19}{4} = \frac{11}{5} \times \frac{4}{19} = \frac{44}{95} $

- Already simplified.

✔ Answer: $ \boxed{\frac{44}{95}} $

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## ✔ Problem 5:
$ 2\frac{1}{2} \div 2\frac{3}{4} $

- Convert:
- $ 2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} $
- $ 2\frac{3}{4} = \frac{4 \times 2 + 3}{4} = \frac{11}{4} $

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

- Simplify:
$ \frac{20}{22} = \frac{10}{11} $

✔ Answer: $ \boxed{\frac{10}{11}} $

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## 🧾 Final Answers:

1) $ \boxed{\frac{11}{14}} $
2) $ \boxed{1\frac{11}{45}} $
3) $ \boxed{\frac{48}{95}} $
4) $ \boxed{\frac{44}{95}} $
5) $ \boxed{\frac{10}{11}} $

Let me know if you’d like to see visual models or more practice! 😊