The expression in the image is:

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

Let's break it down step by step.

Step 1: Simplify the mixed fraction

First, convert the mixed fraction $1\frac{1}{5}$ to an improper fraction.

$1\frac{1}{5} = \frac{6}{5}$

Step 2: Perform the division

Now, divide 3 by $\frac{6}{5}$:

$3 \div \frac{6}{5} = 3 \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2}$

Step 3: Add $\frac{5}{2}$ and $\frac{1}{2}$

Now, add $\frac{5}{2}$ to $\frac{1}{2}$:

$\frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3$

Final Answer:

The result of the expression is 3.

Would you like further details on any part of this? Here are 5 related questions to explore:

1. How do you convert a mixed fraction into an improper fraction?
2. What are the steps to divide fractions?
3. How do you find the least common denominator in addition of fractions?
4. Can you explain more about simplifying fractions after multiplication?
5. What happens when you multiply by the reciprocal of a fraction?

Tip: Always remember to convert mixed numbers to improper fractions when performing operations like division or multiplication!