find the value of 2/3-5/7+3/4/7 of 5/14
You asked:
Evaluate the expression: \(\frac{2}{3} - \frac{5}{7} + \frac{3}{\frac{4}{7} \cdot \frac{5}{14}}\)
MathBot Answer:
\[\frac{2}{3} - \frac{5}{7} + \frac{3}{\frac{4}{7} \cdot \frac{5}{14}} = \frac{3077}{210} = 14.6\overline{523809}\]
\[\begin{aligned}\frac{2}{3} - \frac{5}{7} + \frac{3}{\frac{4}{7} \cdot \frac{5}{14}}& = \frac{2}{3} - \frac{5}{7} + 3 \cdot \frac{1}{\frac{4}{7} \cdot \frac{5}{14}}\\& = \frac{2}{3} - \frac{5}{7} + 3 \cdot \frac{1}{\frac{10}{49}}\\& = \frac{2}{3} - \frac{5}{7} + \frac{147}{10}\\& = - \frac{1}{21} + \frac{147}{10}\\& = \frac{3077}{210}\end{aligned}\]