To divide the fraction \( \frac{1}{2} \) by \( \frac{3}{8} \), you can multiply by the reciprocal of the second fraction. The reciprocal of \( \frac{3}{8} \) is \( \frac{8}{3} \).
So, the operation becomes:
\[ \frac{1}{2} \div \frac{3}{8} = \frac{1}{2} \times \frac{8}{3} \]
Now, multiply the fractions:
\[ \frac{1 \times 8}{2 \times 3} = \frac{8}{6} \]
Next, simplify \( \frac{8}{6} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{8 \div 2}{6 \div 2} = \frac{4}{3} \]
Thus, \( \frac{1}{2} \div \frac{3}{8} = \frac{4}{3} \).