4/3 / (2/3 + 0.2/10)

asked by guest
on Sep 22, 2024 at 6:27 am



You asked:

Evaluate the expression: \(\frac{\frac{4}{3}}{\frac{2}{3} + \frac{0.2}{10}}\)

MathBot Answer:

\[\frac{\frac{4}{3}}{\frac{2}{3} + \frac{0.2}{10}} = \frac{200}{103} = 1.\overline{9417475728155339805825242718446601}\]

\[\begin{aligned}\frac{\frac{4}{3}}{\frac{2}{3} + \frac{0.2}{10}}& = \frac{4}{3} \cdot \frac{1}{\frac{2}{3} + \frac{2}{10} \cdot \frac{1}{10}}\\& = \frac{4}{3} \cdot \frac{1}{\frac{2}{3} + \frac{2}{100}}\\& = \frac{4}{3} \cdot \frac{1}{\frac{2}{3} + \frac{1}{50}}\\& = \frac{4}{3} \cdot \frac{1}{\frac{103}{150}}\\& = \frac{200}{103}\end{aligned}\]

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