Simplify the following:

$ 8 \frac{3}{5}-\left(6 \frac{1}{2}-4 \frac{1}{4}-3 \frac{3}{4}\right) $

Given: $8\frac{3}{5} \ -\ \left( 6\frac{1}{2} \ -\ 4\frac{1}{4} \ -\ 3\frac{3}{4}\right)$

To find: Here we have to find the value of  $8\frac{3}{5} \ -\ \left( 6\frac{1}{2} \ -\ 4\frac{1}{4} \ -\ 3\frac{3}{4}\right)$.

Solution:

$8\frac{3}{5} \ -\ \left( 6\frac{1}{2} \ -\ 4\frac{1}{4} \ -\ 3\frac{3}{4}\right)$

$=\ \frac{43}{5} \ -\ \left(\frac{13}{2} \ -\ \frac{17}{4} \ -\ \frac{15}{4}\right)$

$=\ \frac{43}{5} \ -\ \left(\frac{13}{2} \ -\ \frac{32}{4}\right)$

$=\ \frac{43}{5} \ -\ \left(\frac{26\ -\ 32}{4}\right)$

$=\ \frac{43}{5} \ -\ \left( -\ \frac{6}{4}\right)$

$=\ \frac{43}{5} \ -\ \left( -\ \frac{3}{2}\right)$

$=\ \frac{43}{5} \ +\ \frac{3}{2}$

$=\ \frac{86\ +\ 15}{10}$

$=\ \mathbf{\frac{101}{10}}$

So, the answer is  $\frac{101}{10}$.