Math Problem Solver

\[ \frac{3}{2} - \frac{1}{3} - \frac{2}{5} = \frac{23}{30} = 0.7\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{3}{2}\), \(\frac{-1}{3}\), and \(\frac{-2}{5}\) is \(30\). \[ \begin{aligned} \frac{3}{2} - \frac{1}{3} - \frac{2}{5} &= \frac{3 \cdot 15}{2 \cdot 15} + \frac{-1 \cdot 10}{3 \cdot 10} + \frac{-2 \cdot 6}{5 \cdot 6} \\ &= \frac{45 + -10 + -12}{30} \\ &= \frac{23}{30} \end{aligned} \]