Math Problem Solver

\[ \frac{9}{2} - 12 - \frac{14}{5} + \frac{1}{3} = - \frac{299}{30} = -9.9\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{9}{2}\), \(\frac{-12}{1}\), \(\frac{-14}{5}\), and \(\frac{1}{3}\) is \(30\). \[ \begin{aligned} \frac{9}{2} - 12 - \frac{14}{5} + \frac{1}{3} &= \frac{9 \cdot 15}{2 \cdot 15} + \frac{-12 \cdot 30}{1 \cdot 30} + \frac{-14 \cdot 6}{5 \cdot 6} + \frac{1 \cdot 10}{3 \cdot 10} \\ &= \frac{135 + -360 + -84 + 10}{30} \\ &= \frac{-299}{30} \end{aligned} \]