40.5*52.5 divided by 67.5

asked by guest
on Nov 24, 2024 at 8:06 am



You asked:

Evaluate the expression: \(\frac{40.5 \cdot 52.5}{67.5}\)

MathBot Answer:

\[\frac{40.5 \cdot 52.5}{67.5} = \frac{63}{2} = 31.5\]

\[\begin{aligned}\frac{40.5 \cdot 52.5}{67.5}& = \left(40 + \frac{5}{10}\right) \cdot \left(52 + \frac{5}{10}\right) \cdot \frac{1}{67 + \frac{5}{10}}\\& = \left(40 + \frac{1}{2}\right) \cdot \left(52 + \frac{5}{10}\right) \cdot \frac{1}{67 + \frac{5}{10}}\\& = \frac{81}{2} \cdot \left(52 + \frac{5}{10}\right) \cdot \frac{1}{67 + \frac{5}{10}}\\& = \frac{81}{2} \cdot \left(52 + \frac{1}{2}\right) \cdot \frac{1}{67 + \frac{5}{10}}\\& = \frac{81}{2} \cdot \frac{105}{2} \cdot \frac{1}{67 + \frac{5}{10}}\\& = \frac{81}{2} \cdot \frac{105}{2} \cdot \frac{1}{67 + \frac{1}{2}}\\& = \frac{81}{2} \cdot \frac{105}{2} \cdot \frac{1}{\frac{135}{2}}\\& = \frac{81}{2} \cdot \frac{7}{9}\\& = \frac{63}{2}\end{aligned}\]

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