To compute \( \frac{1}{2} \div \frac{2}{3} \), you can multiply by the reciprocal of \( \frac{2}{3} \):
\[ \frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} \]
Now, multiply the numerators and the denominators:
\[ \frac{1 \times 3}{2 \times 2} = \frac{3}{4} \]
The fraction \( \frac{3}{4} \) is already in its simplest form.
So, the answer is:
\[ \frac{3}{4} \]