Answer
$\dfrac{5}{6}$
Work Step by Step
Make the fractions similar using their LCD of $18$ to obtain:
\begin{align*}
-1\frac{4}{9}-\left(-2\frac{5}{18}\right)&=-1\frac{8}{18}-\left(-2\frac{5}{18}\right)\\\\
&=-1\frac{8}{18}+2\frac{5}{18}
\end{align*}
Add the corresponding parts to obtain:
\begin{align*}
\require{cancel}
-1\frac{8}{18}+2\frac{5}{18}&=-\left(1+\frac{8}{18}\right)+\left(2+\frac{5}{18}\right)\\\\
&=-1-\frac{8}{18}+2+\frac{5}{18}\\\\
&=(-1+2)+\left(-\frac{8}{18}+\frac{5}{18}\right)\\\\
&=1+\left(\frac{-3}{18}\right)\\\\
&=\frac{18}{18}+\frac{-3}{18}\\\\
&=\frac{18+(-3)}{18}\\\\
&=\frac{15}{18}\\\\
&=\frac{\cancel{15}5}{\cancel{18}6}\\\\
&=\frac{5}{6}
\end{align*}
