1/3+1/3×1/3×1/3×3/1-1/3×1/3

asked by guest
on Nov 19, 2024 at 3:15 am



You asked:

Evaluate the expression: \(\frac{1}{3} + \frac{\frac{\frac{\frac{1}{3} \cdot 1}{3} \cdot 1}{3} \cdot 3}{1} - \frac{\frac{1}{3} \cdot 1}{3}\)

MathBot Answer:

\[\frac{1}{3} + \frac{\frac{\frac{\frac{1}{3} \cdot 1}{3} \cdot 1}{3} \cdot 3}{1} - \frac{\frac{1}{3} \cdot 1}{3} = \frac{1}{3} = 0.\overline{3}\]

\[\begin{aligned}\frac{1}{3} + \frac{\frac{\frac{\frac{1}{3} \cdot 1}{3} \cdot 1}{3} \cdot 3}{1} - \frac{\frac{1}{3} \cdot 1}{3}& = \frac{1}{3} + \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{3}{3} \cdot 1^{-1} - \frac{1}{3} \cdot \frac{1}{3}\\& = \frac{1}{3} + \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{1}{3}\\& = \frac{1}{3} + \frac{1}{9} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{1}{3}\\& = \frac{1}{3} + \frac{3}{27} - \frac{1}{3} \cdot \frac{1}{3}\\& = \frac{1}{3} + \frac{1}{9} - \frac{1}{3} \cdot \frac{1}{3}\\& = \frac{1}{3} + \frac{1}{9} - \frac{1}{9}\\& = \frac{4}{9} - \frac{1}{9}\\& = \frac{1}{3}\end{aligned}\]

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