Math Problem Solver

\[ 10 + \frac{1}{9} + \frac{2}{3} = \frac{97}{9} = 10.\overline{7} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{10}{1}\), \(\frac{1}{9}\), and \(\frac{2}{3}\) is \(9\). \[ \begin{aligned} 10 + \frac{1}{9} + \frac{2}{3} &= \frac{10 \cdot 9}{1 \cdot 9} + \frac{1 \cdot 1}{9 \cdot 1} + \frac{2 \cdot 3}{3 \cdot 3} \\ &= \frac{90 + 1 + 6}{9} \\ &= \frac{97}{9} \end{aligned} \]