Let's solve the given expression step by step:

Given expression:

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

First, let's simplify $\frac{\frac{3}{5}}{\frac{1}{5}}$:

$\frac{3}{5} \div \frac{1}{5} = \frac{3}{5} \times \frac{5}{1} = 3$

Now, substitute this back into the original expression:

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

Next, let's find a common denominator for $\frac{1}{2}$ and $\frac{3}{4}$:

The common denominator is 4.

$\frac{1}{2} = \frac{2}{4}$

So the expression becomes:

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

Combine the fractions:

$\frac{2}{4} + \frac{3}{4} = \frac{5}{4}$

Now add 3 to the sum:

$\frac{5}{4} + 3 = \frac{5}{4} + \frac{12}{4} = \frac{17}{4}$

Thus, the final simplified form of the expression is:

$\frac{17}{4}$

Would you like more details or have any questions?

Here are 5 numbered questions you might want to ask:

1. How do you find a common denominator?
2. Can you explain how to add fractions with different denominators?
3. What are some common mistakes to avoid when simplifying fractions?
4. How do you convert a fraction to a decimal?
5. Can you show how to simplify complex fractions?

Tip: Always remember to simplify complex fractions by dividing the numerator by the denominator before combining with other terms in the expression.