Which rational number should be subtracted from $\dfrac{-5}{6}$ to get $\dfrac{4}{9}$ ?

Let $x$ be subtracted from $\dfrac{-5}{6}$.

$\dfrac{-5}{6} - x = \dfrac{4}{9}\\[1em] \Rightarrow x = \dfrac{-5}{6} - \dfrac{4}{9}$

LCM of 6 and 9 is 2 x 3 x 3 = 18

$\Rightarrow x = \dfrac{-5 \times 3}{6 \times 3} - \dfrac{4 \times 2}{9 \times 2}\\[1em] \Rightarrow x = \dfrac{-15}{18} - \dfrac{8}{18}\\[1em] \Rightarrow x = \dfrac{-15 - 8}{18}\\[1em] \Rightarrow x = \dfrac{-23}{18}\\[1em] \Rightarrow x = -1\dfrac{5}{18}$

The number subtracted from $\dfrac{-5}{6}$ to get $\dfrac{4}{9}$ is -$1\dfrac{5}{18}$.