Math Problem Solver

\[ \frac{1}{3} - 1 + \frac{5}{6} = \frac{1}{6} = 0.1\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{3}\), \(\frac{-1}{1}\), and \(\frac{5}{6}\) is \(6\). \[ \begin{aligned} \frac{1}{3} - 1 + \frac{5}{6} &= \frac{1 \cdot 2}{3 \cdot 2} + \frac{-1 \cdot 6}{1 \cdot 6} + \frac{5 \cdot 1}{6 \cdot 1} \\ &= \frac{2 + -6 + 5}{6} \\ &= \frac{1}{6} \end{aligned} \]