Simplify the following :$(\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times- \frac{10}{9})$

Given :

The given expression is $(\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times- \frac{10}{9})$

To do :

We have to simplify the given expression and find it's value.

Solution : 

$(\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times- \frac{10}{9})$

$\frac{25}{8}\times \frac{2}{5} = \frac{5}{4}$

$\frac{3}{5}\times- \frac{10}{9} = \frac{-2}{3}$

Therefore,

$(\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times- \frac{10}{9}) = \frac{5}{4}-\frac{-2}{3}$

                                           $=  \frac{5}{4}+\frac{2}{3}$

                                            $= \frac{(5\times3+4\times2)}{12}$           $(LCM of 4 and 3 is 12)$

                                            $= \frac{15+8}{12}$

                                            $= \frac{23}{12}$.

The simplified value of the given expression $(\frac{25}{8}\times \frac{2}{5})-(\frac{3}{5}\times- \frac{10}{9})$ is   $\frac{23}{12}$.

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Updated on: 10-Oct-2022

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