(1/2 ÷1/3 −2/3 )×(1/2 ÷1/3 +2/3 )

asked by guest
on Nov 14, 2024 at 10:25 pm



You asked:

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

MathBot Answer:

\[\left(\frac{\frac{\frac{1}{2}}{1}}{3} - \frac{2}{3}\right) \cdot \left(\frac{\frac{\frac{1}{2}}{1}}{3} + \frac{2}{3}\right) = - \frac{5}{12} = -0.41\overline{6}\]

\[\begin{aligned}\left(\frac{\frac{\frac{1}{2}}{1}}{3} - \frac{2}{3}\right) \cdot \left(\frac{\frac{\frac{1}{2}}{1}}{3} + \frac{2}{3}\right)& = \left(\frac{1}{2} \cdot 1^{-1} \cdot \frac{1}{3} - \frac{2}{3}\right) \cdot \left(\frac{1}{2} \cdot 1^{-1} \cdot \frac{1}{3} + \frac{2}{3}\right)\\& = \left(\frac{1}{2} \cdot \frac{1}{3} - \frac{2}{3}\right) \cdot \left(\frac{1}{2} \cdot 1^{-1} \cdot \frac{1}{3} + \frac{2}{3}\right)\\& = \left(\frac{1}{6} - \frac{2}{3}\right) \cdot \left(\frac{1}{2} \cdot 1^{-1} \cdot \frac{1}{3} + \frac{2}{3}\right)\\& = - \frac{1}{2} \cdot \left(\frac{1}{2} \cdot 1^{-1} \cdot \frac{1}{3} + \frac{2}{3}\right)\\& = - \frac{1}{2} \cdot \left(\frac{1}{2} \cdot \frac{1}{3} + \frac{2}{3}\right)\\& = - \frac{1}{2} \cdot \left(\frac{1}{6} + \frac{2}{3}\right)\\& = - \frac{1}{2} \cdot \frac{5}{6}\\& = - \frac{5}{12}\end{aligned}\]

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