#### Answer

$\frac{4}{8}\lt\frac{5}{8}$

#### Work Step by Step

To compare the values of $\frac{1}{2}$ and $\frac{5}{8}$, you first need to find the least common denominator. To do this, you first see if the greater of the two denominators can be divided by the lesser. Since 8 can be divided by 2 to get 4, you multiply $\frac{1}{2}$ by $\frac{4}{4}$ (which is 1 expressed in fourths) to get $\frac{4}{8}$. You can compare this new fraction to $\frac{5}{8}$ since they now share a common denominator.
Since $4\lt5$, $\frac{4}{8}\lt\frac{5}{8}$.