9.6รท2.2.4
You asked:
Evaluate the expression: \(\frac{9.6}{2.2 \cdot .4}\)
MathBot Answer:
\[\frac{9.6}{2.2 \cdot .4} = \frac{120}{11} = 10.\overline{90}\]
\[\begin{aligned}\frac{9.6}{2.2 \cdot .4}& = \left(9 + \frac{6}{10}\right) \cdot \frac{1}{\left(2 + \frac{2}{10}\right) \cdot \frac{4}{10}}\\& = \left(9 + \frac{3}{5}\right) \cdot \frac{1}{\left(2 + \frac{2}{10}\right) \cdot \frac{4}{10}}\\& = \frac{48}{5} \cdot \frac{1}{\left(2 + \frac{2}{10}\right) \cdot \frac{4}{10}}\\& = \frac{48}{5} \cdot \frac{1}{\left(2 + \frac{1}{5}\right) \cdot \frac{4}{10}}\\& = \frac{48}{5} \cdot \frac{1}{\frac{11}{5} \cdot \frac{4}{10}}\\& = \frac{48}{5} \cdot \frac{1}{\frac{44}{5} \cdot \frac{1}{10}}\\& = \frac{48}{5} \cdot \frac{1}{\frac{22}{25}}\\& = \frac{120}{11}\end{aligned}\]