Solve the Fraction Expression: 1/4 - 3/4 + 1/2 + 5/10

To solve this problem, we'll follow these steps:

• Simplify fractions if possible.
• Convert fractions to have a common denominator.
• Perform the operations in order, while considering appropriate signs.

Let's proceed step-by-step:

First, notice that $\frac{5}{10}$ simplifies to $\frac{1}{2}$, as both the numerator and denominator can be divided by 5.
Scheme now becomes:

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

Convert all fractions to have a denominator of 4:

• $\frac{1}{4}$ remains $\frac{1}{4}$.
• $\frac{3}{4}$ remains $\frac{3}{4}$.
• $\frac{1}{2}$ becomes $\frac{2}{4}$.

Our new expression is:

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

Perform the operations in left to right:

$\frac{1}{4} - \frac{3}{4} = -\frac{2}{4}$ which simplifies to $-\frac{1}{2}$

Now, combine with the next term:

$-\frac{1}{2} + \frac{2}{4} = 0$

Lastly, add the remaining term:

$0 + \frac{2}{4} = \frac{1}{2}$

Therefore, the solution to the problem is $\frac{1}{2}$.

Thus, the correct answer is $\frac{1}{2}$, and it corresponds to choice 3.