2/5÷[(1/5-1/9+4/9)×1/2]
You asked:
Evaluate the expression: \(\frac{\frac{2}{5}}{\frac{\left(\frac{1}{5} - \frac{1}{9} + \frac{4}{9}\right) \cdot 1}{2}}\)
MathBot Answer:
\[\frac{\frac{2}{5}}{\frac{\left(\frac{1}{5} - \frac{1}{9} + \frac{4}{9}\right) \cdot 1}{2}} = \frac{3}{2} = 1.5\]
\[\begin{aligned}\frac{\frac{2}{5}}{\frac{\left(\frac{1}{5} - \frac{1}{9} + \frac{4}{9}\right) \cdot 1}{2}}& = \frac{2}{5} \cdot \frac{1}{\left(\frac{1}{5} - \frac{1}{9} + \frac{4}{9}\right) \cdot \frac{1}{2}}\\& = \frac{2}{5} \cdot \frac{1}{\left(\frac{4}{45} + \frac{4}{9}\right) \cdot \frac{1}{2}}\\& = \frac{2}{5} \cdot \frac{1}{\frac{8}{15} \cdot \frac{1}{2}}\\& = \frac{2}{5} \cdot \frac{1}{\frac{4}{15}}\\& = \frac{3}{2}\end{aligned}\]