To solve the equation \( \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} \), we first need to convert \( \frac{1}{2} \) to a fraction with a common denominator of 4.
We know that: \[ \frac{1}{2} = \frac{2}{4} \]
Now, substituting back into the equation: \[ \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} \]
Adding the fractions on the right side: \[ \frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4} \]
Therefore: \[ \frac{1}{4} + \frac{1}{2} = \frac{3}{4} \]
So, the answer is: \[ \frac{3}{4} \]