Math Problem Solver

\[ \frac{1}{4} + \frac{5}{8} - \frac{5}{2} - 2 + \frac{2}{3} + 7 = \frac{97}{24} = 4.041\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{4}\), \(\frac{5}{8}\), \(\frac{-5}{2}\), \(\frac{-2}{1}\), \(\frac{2}{3}\), and \(\frac{7}{1}\) is \(24\). \[ \begin{aligned} \frac{1}{4} + \frac{5}{8} - \frac{5}{2} - 2 + \frac{2}{3} + 7 &= \frac{1 \cdot 6}{4 \cdot 6} + \frac{5 \cdot 3}{8 \cdot 3} + \frac{-5 \cdot 12}{2 \cdot 12} + \frac{-2 \cdot 24}{1 \cdot 24} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{7 \cdot 24}{1 \cdot 24} \\ &= \frac{6 + 15 + -60 + -48 + 16 + 168}{24} \\ &= \frac{97}{24} \end{aligned} \]