Math Problem Solver

\[ 4\frac{2}{7} + 3\frac{11}{114} = \frac{5891}{798} = 7.3\overline{822055137844611528} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{4}{1}\), \(\frac{2}{7}\), \(\frac{3}{1}\), and \(\frac{11}{114}\) is \(798\). \[ \begin{aligned} 4\frac{2}{7} + 3\frac{11}{114} &= \frac{4 \cdot 798}{1 \cdot 798} + \frac{2 \cdot 114}{7 \cdot 114} + \frac{3 \cdot 798}{1 \cdot 798} + \frac{11 \cdot 7}{114 \cdot 7} \\ &= \frac{3192 + 228 + 2394 + 77}{798} \\ &= \frac{5891}{798} \end{aligned} \]