To solve the equation \( \frac{5}{8}(x - \frac{1}{2}) = 10 \), the first step involves reversing the multiplication by the fraction \( \frac{5}{8} \).
To do this, you need to divide both sides by \( \frac{5}{8} \).
Alternatively, you can multiply both sides by its reciprocal, which is \( \frac{8}{5} \), but to directly answer your question, you should divide both sides by \( \frac{5}{8} \).
So, the number you divide both sides by is \( \frac{5}{8} \).