Which rational number should be added to $\dfrac{-5}{9}$ to get $\dfrac{-2}{3}$?

Let $x$ be added to $\dfrac{-5}{9}$.

$\dfrac{-5}{9} + x = \dfrac{-2}{3}\\[1em] ⇒ x = \dfrac{-2}{3} - \dfrac{-5}{9}$

LCM of 3 and 9 is 3 x 3 = 9

$\Rightarrow x = \dfrac{-2 \times 3}{3 \times 3} - \dfrac{-5 \times 1}{9 \times 1}\\[1em] \Rightarrow x = \dfrac{-6}{9} - \dfrac{-5}{9}\\[1em] \Rightarrow x = \dfrac{-6 - (-5)}{9}\\[1em] \Rightarrow x = \dfrac{-6 + 5}{9}\\[1em] \Rightarrow x = \dfrac{-1}{9}$

The number added to $\dfrac{-5}{9}$ to get $\dfrac{-2}{3}$ is $\dfrac{-1}{9}$.