Math worksheet featuring division problems with mixed numbers

Of course! Let's solve each of these mixed number division problems step by step.

The general rule for dividing mixed numbers is:

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

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

Step 1: Convert to improper fractions

- $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$
- $3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$

Step 2: Multiply by the reciprocal

$\frac{12}{5} \div \frac{10}{3} = \frac{12}{5} \times \frac{3}{10} = \frac{36}{50}$

Step 3: Simplify

$\frac{36}{50} = \frac{18}{25}$ (divide numerator and denominator by 2)

✔ Answer: $\frac{18}{25}$

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Problem 2: $4\frac{1}{2} \div 4\frac{1}{2}$

This is any number divided by itself!

Answer: 1

✔ Answer: $1$

*(You can verify: $\frac{9}{2} \div \frac{9}{2} = 1$)*

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Problem 3: $4\frac{1}{3} \div 3\frac{1}{4}$

Step 1: Convert to improper fractions

- $4\frac{1}{3} = \frac{13}{3}$
- $3\frac{1}{4} = \frac{13}{4}$

Step 2: Multiply by reciprocal

$\frac{13}{3} \div \frac{13}{4} = \frac{13}{3} \times \frac{4}{13} = \frac{52}{39}$

Step 3: Simplify

$\frac{52}{39} = \frac{4}{3}$ (divide numerator and denominator by 13)

Convert to mixed number: $\frac{4}{3} = 1\frac{1}{3}$

✔ Answer: $1\frac{1}{3}$

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

Step 1: Convert to improper fractions

- $2\frac{1}{2} = \frac{5}{2}$
- $4\frac{3}{5} = \frac{23}{5}$

Step 2: Multiply by reciprocal

$\frac{5}{2} \div \frac{23}{5} = \frac{5}{2} \times \frac{5}{23} = \frac{25}{46}$

Step 3: Simplify

Already in simplest form.

✔ Answer: $\frac{25}{46}$

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

Step 1: Convert to improper fractions

- $4\frac{1}{5} = \frac{21}{5}$
- $3\frac{1}{5} = \frac{16}{5}$

Step 2: Multiply by reciprocal

$\frac{21}{5} \div \frac{16}{5} = \frac{21}{5} \times \frac{5}{16} = \frac{105}{80}$

Step 3: Simplify

$\frac{105}{80} = \frac{21}{16}$ (divide by 5)

Convert to mixed number: $\frac{21}{16} = 1\frac{5}{16}$

✔ Answer: $1\frac{5}{16}$

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Problem 6: $3\frac{2}{3} \div 2\frac{1}{2}$

Step 1: Convert to improper fractions

- $3\frac{2}{3} = \frac{11}{3}$
- $2\frac{1}{2} = \frac{5}{2}$

Step 2: Multiply by reciprocal

$\frac{11}{3} \div \frac{5}{2} = \frac{11}{3} \times \frac{2}{5} = \frac{22}{15}$

Step 3: Simplify

Convert to mixed number: $\frac{22}{15} = 1\frac{7}{15}$

✔ Answer: $1\frac{7}{15}$

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Problem 7: $4\frac{1}{3} \div 4\frac{3}{5}$

Step 1: Convert to improper fractions

- $4\frac{1}{3} = \frac{13}{3}$
- $4\frac{3}{5} = \frac{23}{5}$

Step 2: Multiply by reciprocal

$\frac{13}{3} \div \frac{23}{5} = \frac{13}{3} \times \frac{5}{23} = \frac{65}{69}$

Step 3: Simplify

Already in simplest form (no common factors).

✔ Answer: $\frac{65}{69}$

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Problem 8: $2\frac{1}{2} \div 2\frac{4}{5}$

Step 1: Convert to improper fractions

- $2\frac{1}{2} = \frac{5}{2}$
- $2\frac{4}{5} = \frac{14}{5}$

Step 2: Multiply by reciprocal

$\frac{5}{2} \div \frac{14}{5} = \frac{5}{2} \times \frac{5}{14} = \frac{25}{28}$

Step 3: Simplify

Already in simplest form.

✔ Answer: $\frac{25}{28}$

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## ✔ Final Answers:

1. $2\frac{2}{5} \div 3\frac{1}{3} = \boxed{\frac{18}{25}}$

2. $4\frac{1}{2} \div 4\frac{1}{2} = \boxed{1}$

3. $4\frac{1}{3} \div 3\frac{1}{4} = \boxed{1\frac{1}{3}}$

4. $2\frac{1}{2} \div 4\frac{3}{5} = \boxed{\frac{25}{46}}$

5. $4\frac{1}{5} \div 3\frac{1}{5} = \boxed{1\frac{5}{16}}$

6. $3\frac{2}{3} \div 2\frac{1}{2} = \boxed{1\frac{7}{15}}$

7. $4\frac{1}{3} \div 4\frac{3}{5} = \boxed{\frac{65}{69}}$

8. $2\frac{1}{2} \div 2\frac{4}{5} = \boxed{\frac{25}{28}}$

Let me know if you’d like to see any step explained further!