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