Math Problem Solver

\[ \frac{1}{2} + \frac{4}{5} + \frac{6}{7} = \frac{151}{70} = 2.1\overline{571428} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{2}\), \(\frac{4}{5}\), and \(\frac{6}{7}\) is \(70\). \[ \begin{aligned} \frac{1}{2} + \frac{4}{5} + \frac{6}{7} &= \frac{1 \cdot 35}{2 \cdot 35} + \frac{4 \cdot 14}{5 \cdot 14} + \frac{6 \cdot 10}{7 \cdot 10} \\ &= \frac{35 + 56 + 60}{70} \\ &= \frac{151}{70} \end{aligned} \]