Math Problem Solver

\[ \frac{-8}{27} - \frac{8}{9} + \frac{2}{3} = - \frac{14}{27} = -0.\overline{518} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{-8}{27}\), \(\frac{-8}{9}\), and \(\frac{2}{3}\) is \(27\). \[ \begin{aligned} \frac{-8}{27} - \frac{8}{9} + \frac{2}{3} &= \frac{-8 \cdot 1}{27 \cdot 1} + \frac{-8 \cdot 3}{9 \cdot 3} + \frac{2 \cdot 9}{3 \cdot 9} \\ &= \frac{-8 + -24 + 18}{27} \\ &= \frac{-14}{27} \end{aligned} \]