Math worksheet for dividing mixed numbers.

Let's solve each of these problems step by step. The task is to divide mixed numbers. To do this, we follow these steps:

Steps to Divide Mixed Numbers:

1. Convert each mixed number to an improper fraction.
2. Change the division into multiplication by flipping the second fraction (reciprocal).
3. Multiply the fractions.
4. Simplify the result and convert back to a mixed number if needed.

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Problem 1:

$$
2\frac{3}{4} \div 3\frac{1}{2}
$$

Step 1: Convert to improper fractions

- $2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$
- $3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$

Step 2: Rewrite as multiplication by reciprocal

$$
\frac{11}{4} \div \frac{7}{2} = \frac{11}{4} \times \frac{2}{7}
$$

Step 3: Multiply

$$
\frac{11 \times 2}{4 \times 7} = \frac{22}{28}
$$

Step 4: Simplify

$$
\frac{22}{28} = \frac{11}{14}
$$

✔ Answer: $\boxed{\frac{11}{14}}$

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Problem 2:

$$
4\frac{2}{3} \div 3\frac{3}{4}
$$

Step 1: Convert to improper fractions

- $4\frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}$
- $3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$

Step 2: Rewrite as multiplication

$$
\frac{14}{3} \div \frac{15}{4} = \frac{14}{3} \times \frac{4}{15}
$$

Step 3: Multiply

$$
\frac{14 \times 4}{3 \times 15} = \frac{56}{45}
$$

Step 4: Simplify and convert to mixed number

$$
\frac{56}{45} = 1\frac{11}{45}
$$

✔ Answer: $\boxed{1\frac{11}{45}}$

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Problem 3:

$$
2\frac{2}{5} \div 4\frac{3}{4}
$$

Step 1: Convert to improper fractions

- $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}$
- $4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}$

Step 2: Rewrite as multiplication

$$
\frac{12}{5} \div \frac{19}{4} = \frac{12}{5} \times \frac{4}{19}
$$

Step 3: Multiply

$$
\frac{12 \times 4}{5 \times 19} = \frac{48}{95}
$$

Step 4: Simplify?
48 and 95 have no common factors.

✔ Answer: $\boxed{\frac{48}{95}}$

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Problem 4:

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

Step 1: Convert to improper fractions

- $2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}$
- $4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}$

Step 2: Rewrite as multiplication

$$
\frac{11}{5} \div \frac{19}{4} = \frac{11}{5} \times \frac{4}{19}
$$

Step 3: Multiply

$$
\frac{11 \times 4}{5 \times 19} = \frac{44}{95}
$$

Step 4: Simplify?
44 and 95 have no common factors.

✔ Answer: $\boxed{\frac{44}{95}}$

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Problem 5:

$$
2\frac{1}{2} \div 2\frac{3}{4}
$$

Step 1: Convert to improper fractions

- $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$
- $2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

Step 2: Rewrite as multiplication

$$
\frac{5}{2} \div \frac{11}{4} = \frac{5}{2} \times \frac{4}{11}
$$

Step 3: Multiply

$$
\frac{5 \times 4}{2 \times 11} = \frac{20}{22}
$$

Step 4: Simplify

$$
\frac{20}{22} = \frac{10}{11}
$$

✔ Answer: $\boxed{\frac{10}{11}}$

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✔ Final Answers:

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

Let me know if you'd like these shown with visual models or step-by-step diagrams!