Math Problem Solver

\[ 9\frac{1}{2} + 6\frac{1}{6} = \frac{47}{3} = 15.\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{9}{1}\), \(\frac{1}{2}\), \(\frac{6}{1}\), and \(\frac{1}{6}\) is \(6\). \[ \begin{aligned} 9\frac{1}{2} + 6\frac{1}{6} &= \frac{9 \cdot 6}{1 \cdot 6} + \frac{1 \cdot 3}{2 \cdot 3} + \frac{6 \cdot 6}{1 \cdot 6} + \frac{1 \cdot 1}{6 \cdot 1} \\ &= \frac{54 + 3 + 36 + 1}{6} \\ &= \frac{94}{6} \\&= \frac{47}{3} \end{aligned} \]