To determine the fraction \( u \) that, when you divide \( \frac{3}{8} \) by \( \frac{5}{8} \), you can set up the equation:
\[ u = \frac{3/8}{5/8} \]
When dividing fractions, you multiply by the reciprocal of the divisor. Therefore:
\[ u = \frac{3}{8} \div \frac{5}{8} = \frac{3}{8} \times \frac{8}{5} \]
The \( 8 \) in the numerator and the denominator cancels out:
\[ u = \frac{3}{5} \]
Thus, the fraction \( u \) that results from dividing \( \frac{3}{8} \) by \( \frac{5}{8} \) is:
\[ u = \frac{3}{5} \]