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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 $\frac{101}{10}$.