Math Problem Solver

\[ \frac{-9}{10} + \frac{22}{15} = \frac{17}{30} = 0.5\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{-9}{10}\) and \(\frac{22}{15}\) is \(30\). \[ \begin{aligned} \frac{-9}{10} + \frac{22}{15} &= \frac{-9 \cdot 3}{10 \cdot 3} + \frac{22 \cdot 2}{15 \cdot 2} \\ &= \frac{-27 + 44}{30} \\ &= \frac{17}{30} \end{aligned} \]