Which pair of numbers does NOT have a product equal to $36$?
$\text{(A)}\ \{-4,-9\}\qquad\text{(B)}\ \{-3,-12\}\qquad\text{(C)}\ \left\{\frac{1}{2},-72\right\}\qquad\text{(D)}\ \{ 1,36\}\qquad\text{(E)}\ \left\{\frac{3}{2},24\right\}$
Let's calculate each of the answer choices and see which one DOES NOT equal $36$.
$A$ comes out to be $-4 \times -9= 36$,
$B$ equals $-3 \times -12= 36$,
$C$ is $\frac{1}{2} \times -72= -36$,
$D$ simplifies to $1 \times 36= 36$,
and $E$ equals $\frac{3}{2} \times 24= 3 \times 12= 36$.
Thus, our answer is $\boxed{C}$.