To compute \( \frac{18}{23} \div \frac{1}{2} \), you can multiply by the reciprocal of the second fraction:
\[ \frac{18}{23} \div \frac{1}{2} = \frac{18}{23} \times \frac{2}{1} \]
Now, multiply the fractions:
\[ = \frac{18 \times 2}{23 \times 1} = \frac{36}{23} \]
The fraction \( \frac{36}{23} \) is already in simplest form since 36 and 23 do not have any common factors (23 is a prime number).
Thus, the answer is:
\[ \frac{36}{23} \]