Which one of the following expressions is correct?

To compare the fractions, let us convert each of them into their decimal equivalents:
1. $-\frac{3}{4}=-0.7500$
2. $-\frac{7}{16}=-0.4375$
3. $\frac{5}{-12}=-0.4167$
4. $\frac{9}{-24}=-\frac{3}{8}=-0.3750$

Arranging these negative values in ascending order (from the smallest value to the largest value):

$$-0.7500<-0.4375<-0.4167<-0.3750$$

Substituting the original fractions back:

$$-\frac{3}{4}<-\frac{7}{16}<\frac{5}{-12}<\frac{9}{-24}$$

This matches the sequence provided in Option A.