(1-7/2)(1/2-4/5)-3/5/(-2/5+2/3)

asked by guest
on Sep 24, 2024 at 1:29 pm



You asked:

Evaluate the expression: \(\left(1 - \frac{7}{2}\right) \cdot \left(\frac{1}{2} - \frac{4}{5}\right) - \frac{\frac{3}{5}}{\frac{-2}{5} + \frac{2}{3}}\)

MathBot Answer:

\[\left(1 - \frac{7}{2}\right) \cdot \left(\frac{1}{2} - \frac{4}{5}\right) - \frac{\frac{3}{5}}{\frac{-2}{5} + \frac{2}{3}} = - \frac{3}{2} = -1.5\]

\[\begin{aligned}\left(1 - \frac{7}{2}\right) \cdot \left(\frac{1}{2} - \frac{4}{5}\right) - \frac{\frac{3}{5}}{\frac{-2}{5} + \frac{2}{3}}& = \left(1 - \frac{7}{2}\right) \cdot \left(\frac{1}{2} - \frac{4}{5}\right) - \frac{3}{5} \cdot \frac{1}{- \frac{2}{5} + \frac{2}{3}}\\& = - \frac{5}{2} \cdot \left(\frac{1}{2} - \frac{4}{5}\right) - \frac{3}{5} \cdot \frac{1}{- \frac{2}{5} + \frac{2}{3}}\\& = - \frac{5}{2} \cdot - \frac{3}{10} - \frac{3}{5} \cdot \frac{1}{- \frac{2}{5} + \frac{2}{3}}\\& = \frac{3}{4} - \frac{3}{5} \cdot \frac{1}{- \frac{2}{5} + \frac{2}{3}}\\& = \frac{3}{4} - \frac{3}{5} \cdot \frac{1}{\frac{4}{15}}\\& = \frac{3}{4} - \frac{9}{4}\\& = - \frac{3}{2}\end{aligned}\]

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