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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 $\frac{23}{12}$.