Least common denominator of the numbers in the list $-\frac{5}{9},-\frac{4}{3},\frac{7}{12}$ is $36$. Convert numbers in the list to fractions with denominator $36$.
$$-\frac{20}{36},-\frac{48}{36},\frac{21}{36}$$
To sort the list, start from a single element $-\frac{20}{36}$.
$$-\frac{20}{36}$$
Insert $-\frac{48}{36}$ to the appropriate location in the new list.
$$-\frac{48}{36},-\frac{20}{36}$$
Insert $\frac{21}{36}$ to the appropriate location in the new list.
$$-\frac{48}{36},-\frac{20}{36},\frac{21}{36}$$
Replace the obtained fractions with the initial values.