Math Problem Solver

\[ \frac{13}{2} + \frac{-2}{13} = \frac{165}{26} = 6.3\overline{461538} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{13}{2}\) and \(\frac{-2}{13}\) is \(26\). \[ \begin{aligned} \frac{13}{2} + \frac{-2}{13} &= \frac{13 \cdot 13}{2 \cdot 13} + \frac{-2 \cdot 2}{13 \cdot 2} \\ &= \frac{169 + -4}{26} \\ &= \frac{165}{26} \end{aligned} \]