Simplify: $$5 \frac{1}{2} + 6 \frac{1}{2} - 8 \frac{1}{4} + 24 - [9 - (6 - (10 - \overline{4 - 3}))]$$​ 

Correct option is D

Given:

​$$5 \frac{1}{2} + 6 \frac{1}{2} - 8 \frac{1}{4} + 24 - [9 - (6 - (10 - \overline{4 - 3}))]$$​​

Concept Used:​

Solution:​

​$$5 \frac{1}{2} + 6 \frac{1}{2} - 8 \frac{1}{4} + 24 - [9 - (6 - (10 - \overline{4 - 3}))] \\ \ \\ =5 \frac{1}{2} + 6 \frac{1}{2} - 8 \frac{1}{4} + 24 - [9 - (6 - (9))] \\ \ \\ =5 \frac{1}{2} + 6 \frac{1}{2} - 8 \frac{1}{4} + 24 - [9 -(-3)] \\ \ \\ = \frac{11}{2} + \frac{13}{2} - \frac{33}{4} + 24 - [12] \\ \ \\ = \frac{22+26-33+48}{2}\\ \ \\ = \frac{63}{4} = 15\frac34$$​​