Let's solve the given problem step by step.

The expression to solve is:

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

Step 1: Convert the mixed number to an improper fraction.

The mixed number $5 \frac{4}{5}$ can be converted to an improper fraction by multiplying the whole number (5) by the denominator (5) and adding the numerator (4):

$5 \frac{4}{5} = \frac{5 \times 5 + 4}{5} = \frac{25 + 4}{5} = \frac{29}{5}$

Step 2: Set up the division of fractions.

Now we have:

$\frac{29}{5} \div \frac{1}{2}$

To divide fractions, multiply by the reciprocal of the second fraction:

$\frac{29}{5} \times \frac{2}{1} = \frac{29 \times 2}{5 \times 1} = \frac{58}{5}$

Step 3: Convert the improper fraction to a mixed number.

Now, convert $\frac{58}{5}$ to a mixed number. Divide 58 by 5:

$58 \div 5 = 11 \text{ with a remainder of } 3$

Thus, $\frac{58}{5} = 11 \frac{3}{5}$.

Final Answer:

The answer in mixed number form is:

$11 \frac{3}{5}$

Would you like more details on any of the steps?

Here are 5 related questions:

1. How do you multiply fractions?
2. How do you convert an improper fraction to a mixed number?
3. What is the general method for dividing fractions?
4. Can you explain how to add and subtract mixed numbers?
5. How would the answer change if the divisor were $\frac{1}{3}$ instead of $\frac{1}{2}$?

Tip: When dividing fractions, remember to always multiply by the reciprocal of the divisor!