Question

Simplify:
$\left(\frac{-4}{5}\times \frac{15}{8}\right)+\left(\frac{-1}{3}\times \frac{-9}{7}\right)-\left(\frac{2}{1}\times \frac{25}{14}\right)$

Answer 1

$\left(\frac{-4}{5}\times \frac{15}{8}\right)+\left(\frac{-1}{3}\times \frac{-9}{7}\right)-\left(\frac{2}{1}\times \frac{25}{14}\right)$

$=\left(\frac{-1}{1}\times \frac{3}{2}\right)+\left(\frac{-1}{1}\times \frac{-3}{7}\right)-\left(\frac{1}{1}\times \frac{25}{7}\right)$

$=-\frac{3}{2}+\frac{3}{7}-\frac{25}{7}$

LCM of $2,2,7$ is $14$ [ Since, $2,7$ are co-primes]

$=(-\frac{3}{2}\times \frac{14}{14})+(\frac{3}{7}\times \frac{14}{14})-(\frac{25}{7}\times \frac{14}{14})$

$=(-\frac{3}{1}\times \frac{7}{14})+(\frac{3}{1}\times \frac{2}{14})-(\frac{25}{1}\times \frac{2}{14})$

$=-\frac{21}{14}+\frac{6}{14}-\frac{50}{14}$

$=\frac{-21+6-50}{14}$

$=\frac{-71+6}{14}$

$=\frac{-65}{14}$

$\therefore \left(\frac{-4}{5}\times \frac{15}{8}\right)+\left(\frac{-1}{3}\times \frac{-9}{7}\right)-\left(\frac{2}{1}\times \frac{25}{14}\right)=\frac{-65}{14}$