To divide fractions, you can multiply by the reciprocal of the second fraction.
So, to solve \( \frac{1}{2} \div \frac{2}{3} \), you multiply \( \frac{1}{2} \) by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[ \frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} \]
Now, multiply the numerators and the denominators:
\[ \frac{1 \times 3}{2 \times 2} = \frac{3}{4} \]
Therefore, \( \frac{1}{2} \div \frac{2}{3} = \frac{3}{4} \).