Do $\frac{4}{-9}$ and $\frac{-16}{36}$ represent the same rational number?

The correct answer is Yes, they represent the same rational number

$\frac{-16}{36}$ can be written as
$\frac{-16}{36}$ = $\frac{-16 ÷ 4}{36 ÷ 4}$ = $\frac{-4}{9}$

Since $\frac{-4}{9}$ is same as $\frac{4}{-9}$, the given numbers represent the same rational number.