To add the fractions \( \frac{1}{2} \) and \( \frac{3}{4} \), we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4.
Now, we convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \]
Now, we can add \( \frac{2}{4} \) and \( \frac{3}{4} \):
\[ \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4} \]
So, \( \frac{1}{2} + \frac{3}{4} = \frac{5}{4} \) or \( 1 \frac{1}{4} \) as a mixed number.