16) If $p, q, r$ are three real numbers, $p \times (q + r) = (p \times q) + (p \times r)$ is always true. In which cases is $p + (q \times r) = (p + q) \times (p + r)$ also true?

$\begin{array}{ll}\text { (A) If and only if } p=q=r=\frac{1}{3} \text { or } p=0 & \text { (B) if and only if } p=q=r\end{array}$

(C) never (D) if and only if $p+q+r=1$ or $p=0$

(E) if and only if $p=q=r=0$.
16) The answer is (D). Expanding the products we have $p+q r=p^{2}+p q+p r+q r$, that is $p=p(p+q+r)$, so if $p \neq 0$ it must be $p+q+r=1$.