Math Problem Solver

\[ \frac{5}{8} + \frac{3}{40} + \frac{7}{10} + \frac{5}{6} = \frac{67}{30} = 2.2\overline{3} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{8}\), \(\frac{3}{40}\), \(\frac{7}{10}\), and \(\frac{5}{6}\) is \(120\). \[ \begin{aligned} \frac{5}{8} + \frac{3}{40} + \frac{7}{10} + \frac{5}{6} &= \frac{5 \cdot 15}{8 \cdot 15} + \frac{3 \cdot 3}{40 \cdot 3} + \frac{7 \cdot 12}{10 \cdot 12} + \frac{5 \cdot 20}{6 \cdot 20} \\ &= \frac{75 + 9 + 84 + 100}{120} \\ &= \frac{268}{120} \\&= \frac{67}{30} \end{aligned} \]