Simplify the following.
​$$7\frac{1}{2} \div \left\{ 4\frac{1}{4} - \frac{1}{2} \times \left( 2\frac{1}{2} - 1\frac{1}{4} - \frac{3}{4} \right) \right\}$$​​

Correct option is C

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

​$$7\frac{1}{2} \div \left\{ 4\frac{1}{4} - \frac{1}{2} \times \left( 2\frac{1}{2} - 1\frac{1}{4} - \frac{3}{4} \right) \right\}\\ \ \\= \frac{15}{2} \div \left\{ \frac{17}{4} - \frac{1}{2} \times \left( \frac{5}{2} - \frac{5}{4} - \frac{3}{4} \right) \right\}\\ \ \\= \frac{15}{2} \div \left\{ \frac{17}{4} - \frac{1}{2} \times \left( \frac{10 - 5 - 3}{4} \right) \right\}\\ \ \\= \frac{15}{2} \div \left\{ \frac{17}{4} - \frac{1}{2} \times \frac{2}{4} \right\}\\ \ \\= \frac{15}{2} \div \left\{ \frac{17}{4} - \frac{1}{4} \right\}\\ \ \\= \frac{15}{2} \div \frac{16}{4} \\ \ \\= \frac{15}{2} \times \frac{4}{16}\\ \ \\ = \frac{30}{16} = 1.875$$​​