Math Problem Solver

\[ \frac{5}{9} + \frac{2}{7} = \frac{53}{63} = 0.\overline{841269} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{9}\) and \(\frac{2}{7}\) is \(63\). \[ \begin{aligned} \frac{5}{9} + \frac{2}{7} &= \frac{5 \cdot 7}{9 \cdot 7} + \frac{2 \cdot 9}{7 \cdot 9} \\ &= \frac{35 + 18}{63} \\ &= \frac{53}{63} \end{aligned} \]