Math Problem Solver

\[ \frac{5}{18} + \frac{11}{9} - \frac{3}{2} + \frac{5}{6} = \frac{5}{6} = 0.8\overline{3} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{18}\), \(\frac{11}{9}\), \(\frac{-3}{2}\), and \(\frac{5}{6}\) is \(18\). \[ \begin{aligned} \frac{5}{18} + \frac{11}{9} - \frac{3}{2} + \frac{5}{6} &= \frac{5 \cdot 1}{18 \cdot 1} + \frac{11 \cdot 2}{9 \cdot 2} + \frac{-3 \cdot 9}{2 \cdot 9} + \frac{5 \cdot 3}{6 \cdot 3} \\ &= \frac{5 + 22 + -27 + 15}{18} \\ &= \frac{15}{18} \\&= \frac{5}{6} \end{aligned} \]