Math Problem Solver

\[ 5\frac{6}{7} + 4\frac{1}{2} = \frac{145}{14} = 10.3\overline{571428} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{1}\), \(\frac{6}{7}\), \(\frac{4}{1}\), and \(\frac{1}{2}\) is \(14\). \[ \begin{aligned} 5\frac{6}{7} + 4\frac{1}{2} &= \frac{5 \cdot 14}{1 \cdot 14} + \frac{6 \cdot 2}{7 \cdot 2} + \frac{4 \cdot 14}{1 \cdot 14} + \frac{1 \cdot 7}{2 \cdot 7} \\ &= \frac{70 + 12 + 56 + 7}{14} \\ &= \frac{145}{14} \end{aligned} \]