The letters $P$, $Q$, $R$, $S$, and $T$ represent numbers located on the number line as shown.

Which of the following expressions represents a negative number?
$\text{(A)}\ P-Q \qquad \text{(B)}\ P\cdot Q \qquad \text{(C)}\ \dfrac{S}{Q}\cdot P \qquad \text{(D)}\ \dfrac{R}{P\cdot Q} \qquad \text{(E)}\ \dfrac{S+T}{R}$
First, note that $P < Q < 0 < R < S < T$.  Thus, $P$ and $Q$ are negative, while $R$, $S$, and $T$ are positive.
Option $A$ is the difference of two numbers.  If the first number is lower than the second number, the answer will be negative.  In this case, $P < Q$, so $P - Q < 0$, and $P-Q$ is thus indeed a negative number.  So option $\boxed{A}$ is correct.
Option $B$ is the product of two negatives, which is always positive.
Option $C$ starts with the quotient of a positive and a negative.  This is negative.  But this negative quotient is then multiplied by a negative number, which gives a positive number.
Option $D$ has the product of two negatives in the denominator.  Thus, the denominator is positive.  Additionally, the numerator is (barely) positive.  A positive over a positive will be positive.
Option $E$ has the sum of two positives in the numerator.   That will be positive.  The denominator is also positive.  Again, the quotient of two positives is positive.