2/3[3/{(5/6)/(5/4)*(2/3)}]=

asked by guest
on Nov 15, 2024 at 9:31 pm



You asked:

Evaluate the expression: \(\frac{2}{3 \cdot \frac{3}{\frac{\frac{5}{6}}{\frac{5}{4}} \cdot \frac{2}{3}}}\)

MathBot Answer:

\[\frac{2}{3 \cdot \frac{3}{\frac{\frac{5}{6}}{\frac{5}{4}} \cdot \frac{2}{3}}} = \frac{8}{81} = 0.\overline{098765432}\]

\[\begin{aligned}\frac{2}{3 \cdot \frac{3}{\frac{\frac{5}{6}}{\frac{5}{4}} \cdot \frac{2}{3}}}& = 2 \cdot \frac{1}{3 \cdot 3 \cdot \frac{1}{\frac{5}{6} \cdot \frac{1}{\frac{5}{4}} \cdot \frac{2}{3}}}\\& = 2 \cdot \frac{1}{3 \cdot 3 \cdot \frac{1}{\frac{5}{6} \cdot \frac{4}{5} \cdot \frac{2}{3}}}\\& = 2 \cdot \frac{1}{3 \cdot 3 \cdot \frac{1}{\frac{2}{3} \cdot \frac{2}{3}}}\\& = 2 \cdot \frac{1}{3 \cdot 3 \cdot \frac{1}{\frac{4}{9}}}\\& = 2 \cdot \frac{1}{3 \cdot \frac{27}{4}}\\& = 2 \cdot \frac{1}{\frac{81}{4}}\\& = \frac{8}{81}\end{aligned}\]

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