Find the value of:
$\left(\frac{3}{4}\ +\ \frac{1}{4}\right)\ \div\ 2\frac{1}{2}\ -\ \left(\frac{2}{3}\ \times\ \frac{7}{8}\right)\ \div\ 1\frac{1}{4}$

Given: $\left(\frac{3}{4}\ +\ \frac{1}{4}\right)\ \div\ 2\frac{1}{2}\ -\ \left(\frac{2}{3}\ \times\ \frac{7}{8}\right)\ \div\ 1\frac{1}{4}$

To find: Here we have to find the value of the given expression $\left(\frac{3}{4}\ +\ \frac{1}{4}\right)\ \div\ 2\frac{1}{2}\ -\ \left(\frac{2}{3}\ \times\ \frac{7}{8}\right)\ \div\ 1\frac{1}{4}$

Solution:

$\left(\frac{3}{4}\ +\ \frac{1}{4}\right)\ \div\ 2\frac{1}{2}\ -\ \left(\frac{2}{3}\ \times\ \frac{7}{8}\right)\ \div\ 1\frac{1}{4}$

$=\ \left(\frac{3}{4} \ +\ \frac{1}{4}\right) \ \div \ \frac{5}{2} \ -\ \left(\frac{2}{3} \ \times \ \frac{7}{8}\right) \ \div \ \frac{5}{4}$

$=\ \left(\frac{4}{4}\right) \ \div \ \frac{5}{2} \ -\ \left(\frac{1}{3} \ \times \ \frac{7}{4}\right) \ \div \ \frac{5}{4}$

$=\ 1\ \div \ \frac{5}{2} \ -\ \frac{7}{12} \ \div \ \frac{5}{4}$

$=\ 1\ \times \ \frac{2}{5} \ -\ \frac{7}{12} \ \times \ \frac{4}{5}$

$=\ \frac{2}{5} \ -\ \frac{7}{3} \ \times \ \frac{1}{5}$

$=\ \frac{2}{5} \ -\ \frac{7}{15}$

$=\ \frac{3( 2) \ -\ 1( 7)}{15}$

$=\ \frac{6\ -\ 7}{15}$

$=\ \mathbf{-\ \frac{1}{15}}$

So, value of the given expression is $- \frac{1}{15}$.