10/3 of 1/2+2/[2*{2-(2-1/5)}] solve it:

asked by guest
on Sep 19, 2024 at 10:11 am



You asked:

Evaluate the expression: \(\frac{10}{3} \cdot \left(\frac{1}{2} + \frac{2}{2 \cdot \left(2 - \left(2 - \frac{1}{5}\right)\right)}\right)\)

MathBot Answer:

\[\frac{10}{3} \cdot \left(\frac{1}{2} + \frac{2}{2 \cdot \left(2 - \left(2 - \frac{1}{5}\right)\right)}\right) = \frac{55}{3} = 18.\overline{3}\]

\[\begin{aligned}\frac{10}{3} \cdot \left(\frac{1}{2} + \frac{2}{2 \cdot \left(2 - \left(2 - \frac{1}{5}\right)\right)}\right)& = \frac{10}{3} \cdot \left(\frac{1}{2} + 2 \cdot \frac{1}{2 \cdot \left(2 - \left(2 - \frac{1}{5}\right)\right)}\right)\\& = \frac{10}{3} \cdot \left(\frac{1}{2} + 2 \cdot \frac{1}{2 \cdot \left(2 - \frac{9}{5}\right)}\right)\\& = \frac{10}{3} \cdot \left(\frac{1}{2} + 2 \cdot \frac{1}{\frac{2}{5}}\right)\\& = \frac{10}{3} \cdot \left(\frac{1}{2} + 5\right)\\& = \frac{10}{3} \cdot \frac{11}{2}\\& = \frac{55}{3}\end{aligned}\]

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