1/2 + (2/3 divided by 3/4) - (4/5 - 5/6)
You asked:
Evaluate the expression: \(\frac{1}{2} + \frac{\frac{2}{3}}{\frac{3}{4}} - \left(\frac{4}{5} - \frac{5}{6}\right)\)
MathBot Answer:
\[\frac{1}{2} + \frac{\frac{2}{3}}{\frac{3}{4}} - \left(\frac{4}{5} - \frac{5}{6}\right) = \frac{64}{45} = 1.4\overline{2}\]
\[\begin{aligned}\frac{1}{2} + \frac{\frac{2}{3}}{\frac{3}{4}} - \left(\frac{4}{5} - \frac{5}{6}\right)& = \frac{1}{2} + \frac{2}{3} \cdot \frac{1}{\frac{3}{4}} - \left(\frac{4}{5} - \frac{5}{6}\right)\\& = \frac{1}{2} + \frac{8}{9} - \left(\frac{4}{5} - \frac{5}{6}\right)\\& = \frac{1}{2} + \frac{8}{9} - - \frac{1}{30}\\& = \frac{1}{2} + \frac{8}{9} + \frac{1}{30}\\& = \frac{25}{18} + \frac{1}{30}\\& = \frac{64}{45}\end{aligned}\]