To divide the fractions \( \frac{3}{8} \) by \( \frac{1}{4} \), you can multiply by the reciprocal of the second fraction:
\[ \frac{3}{8} \div \frac{1}{4} = \frac{3}{8} \times \frac{4}{1} \]
Now, multiply the numerators and the denominators:
\[ = \frac{3 \times 4}{8 \times 1} = \frac{12}{8} \]
Next, simplify \( \frac{12}{8} \):
\[ \frac{12}{8} = \frac{3}{2} \]
So, \( \frac{3}{8} : \frac{1}{4} = \frac{3}{2} \) or \( 1.5 \).