To perform the operation \( \frac{1}{2} \div \frac{3}{4} \), we can rewrite the division of fractions as multiplication by the reciprocal.
So,
\[ \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} \]
Now, we multiply the fractions:
\[ \frac{1 \times 4}{2 \times 3} = \frac{4}{6} \]
Next, we simplify the fraction \( \frac{4}{6} \) by dividing both the numerator and denominator by their greatest common divisor, which is 2:
\[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \]
Thus, the simplified answer is
\[ \frac{2}{3} \]