Math Problem Solver

\[ \frac{3}{6} - \frac{5}{3} + \frac{3}{9} - \frac{8}{4} = - \frac{17}{6} = -2.8\overline{3} \]

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 \(\frac{-8}{4}\) is \(36\). \[ \begin{aligned} \frac{3}{6} - \frac{5}{3} + \frac{3}{9} - \frac{8}{4} &= \frac{3 \cdot 6}{6 \cdot 6} + \frac{-5 \cdot 12}{3 \cdot 12} + \frac{3 \cdot 4}{9 \cdot 4} + \frac{-8 \cdot 9}{4 \cdot 9} \\ &= \frac{18 + -60 + 12 + -72}{36} \\ &= \frac{-102}{36} \\&= - \frac{17}{6} \end{aligned} \]