From the sum of $\frac{-18}{51}$ and $\frac{2}{17}$ subtract the sum of $\frac{1}{85}$ and $\frac{-2}{5}$

Given :

The given terms are, 

 $\frac{-18}{51}$ and $\frac{2}{17}$ , $\frac{1}{85}$ and $\frac{-2}{5}$ 

To do :

We have to find the sum of $\frac{-18}{51}$ and $\frac{2}{17}$ subtract the sum of $\frac{1}{85}$ and $\frac{-2}{5}$ 

Solution :

$\frac{-18}{51} +\frac{2}{17} = \frac{(-18+2\times3)}{51}$          (LCM of 51 and 17 is 51)

                             $= \frac{(-18+6)}{51}$

                             $=\frac{-12}{51}$

                             $= \frac{-4}{17}$

$\frac{1}{85} + \frac{-2}{5} = \frac{(1+2\times 17)}{85}$               (LCM of 85 and 5 is 85)

                        $= \frac{(1+34)}{85}$

                        $=\frac{35}{85}$

                       $= \frac{7}{17}$

Therefore,

$(\frac{-18}{51} +\frac{2}{17}) -(\frac{1}{85} + \frac{-2}{5})= \frac{-4}{17} - \frac{7}{17}$

                                                         $ =\frac {(-4-7)}{17}$

                                                          $= \frac{-11}{17}$.

The difference between the sum of $\frac{-18}{51}$ and $\frac{2}{17}$ and the sum of $\frac{1}{85}$ and $\frac{-2}{5}$ is $\frac{-11}{17}$

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Updated on: 10-Oct-2022

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