A rational number $\frac{6}{7}$ is subtracted from $\frac{9}{11}$. The result is then added to the additive inverse of $\frac{-5}{8}$. What is the reciprocal of the final sum?
Given :
$\frac{6}{7}$ subtracted from $\frac{9}{11}$.
The result is then added to the additive inverse of $\frac{-5}{8}$.
To do :
We have to find the reciprocal of the final sum.
Solution :
$\frac{9}{11} - \frac{6}{7}$
$= \frac{(9\times7-11\times6)}{(11\times7)}$
$= \frac{(63-66)}{77}$
$= \frac{-3}{77}$
$\frac{-3}{77}$ is added to the additive inverse of $\frac{-5}{8}$.
Additive inverse of $\frac{-5}{8} = - \frac{-5}{8} = \frac{5}{8}$
$\frac{-3}{77} +\frac{5}{8} $
$=\frac{(-3\times8+77\times5)}{(77\times8)}$
$= \frac{(-24+385)}{616}$
$= \frac{361}{616}$
The reciprocal of $\frac{361}{616}$ is $\frac{1}{\frac{361}{616}} = \frac{616}{361}$.
Therefore, the answer is $ \frac{616}{361}$.
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