Math Problem Solver

\[ \frac{3}{6} - \frac{5}{3} + \frac{3}{9} - \frac{8}{8} = - \frac{11}{6} = -1.8\overline{3} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{3}{6}\), \(\frac{-5}{3}\), \(\frac{3}{9}\), and \(\frac{-8}{8}\) is \(72\). \[ \begin{aligned} \frac{3}{6} - \frac{5}{3} + \frac{3}{9} - \frac{8}{8} &= \frac{3 \cdot 12}{6 \cdot 12} + \frac{-5 \cdot 24}{3 \cdot 24} + \frac{3 \cdot 8}{9 \cdot 8} + \frac{-8 \cdot 9}{8 \cdot 9} \\ &= \frac{36 + -120 + 24 + -72}{72} \\ &= \frac{-132}{72} \\&= - \frac{11}{6} \end{aligned} \]