(0.9/.84)-(.84/.9)

asked by guest
on Oct 06, 2024 at 11:32 pm



You asked:

Evaluate the expression: \(\frac{0.9}{.84} - \frac{.84}{.9}\)

MathBot Answer:

\[\frac{0.9}{.84} - \frac{.84}{.9} = \frac{29}{210} = 0.1\overline{380952}\]

\[\begin{aligned}\frac{0.9}{.84} - \frac{.84}{.9}& = \frac{9}{10} \cdot \frac{1}{\frac{84}{100}} - \frac{84}{100} \cdot \frac{1}{\frac{9}{10}}\\& = \frac{9}{10} \cdot \frac{1}{\frac{21}{25}} - \frac{84}{100} \cdot \frac{1}{\frac{9}{10}}\\& = 9 \cdot \frac{5}{42} - \frac{84}{100} \cdot \frac{1}{\frac{9}{10}}\\& = \frac{15}{14} - \frac{84}{100} \cdot \frac{1}{\frac{9}{10}}\\& = \frac{15}{14} - \frac{84}{90}\\& = \frac{15}{14} - \frac{14}{15}\\& = \frac{29}{210}\end{aligned}\]

+ Submit Question