To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of \( \frac{2}{3} \) is \( \frac{3}{2} \).
So, you can rewrite the division as:
\[ \frac{1}{4} \div \frac{2}{3} = \frac{1}{4} \times \frac{3}{2} \]
Now, multiply the fractions:
\[ \frac{1 \times 3}{4 \times 2} = \frac{3}{8} \]
Thus, \( \frac{1}{4} \div \frac{2}{3} = \frac{3}{8} \).