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

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

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

Solution:

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

Using BODMAS rule to solve this problem:

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

$=\ \left(\frac{3}{8}\right) \ \div \ \left(\frac{12}{2}\right)$

$=\ \left(\frac{3}{8}\right) \ \div \ \left(\frac{6}{1}\right)$

$=\ \frac{3}{8} \ \times \ \frac{1}{6}$

$=\ \frac{1}{8} \ \times \ \frac{1}{2}$

$=\ \mathbf{\frac{1}{16}}$

So, the value of the given expression is $\frac{1}{16}$.