jmc

Consider a negative $b$ and a positive $c$. Then $ab$ is positive and $bc$ is negative, and hence this is not true. If we consider negative numbers for all three variables, $ac>bc$, and hence this is not true. Consider a negative $b$ and a positive $c$. Then $ab$ is positive and $ac$ is negative, hence this is not true. Subtracting $b$ from both sides gives us $a<c$ which we know is true. If $c$ is positive then $c/a$ is negative and $c/a<1$. If $c$ is negative, then $a<c<0$ which means $c/a<1$.

Thus, $\boxed{D,E}$ are always true.