To divide the fractions \( \frac{10}{10} \) and \( \frac{3}{8} \), you can multiply the first fraction by the reciprocal of the second fraction.
So, the calculation is:
\[ \frac{10}{10} \div \frac{3}{8} = \frac{10}{10} \times \frac{8}{3} \]
Now, simplify \( \frac{10}{10} \):
\[ \frac{10}{10} = 1 \]
So the equation becomes:
\[ 1 \times \frac{8}{3} = \frac{8}{3} \]
Thus, \( \frac{10}{10} \div \frac{3}{8} = \frac{8}{3} \).