$5.5 - [6.5 - \{3.5 \div (6.5 - \overline{5.5 - 2.5})\}]$ is equal to

### Concept & Strategy This problem tests the comprehensive VBODMAS rule. The Vinculum (the overline bar) acts as the innermost parenthesis and must be resolved first. Next, resolve round brackets $()$, followed by curly braces $\{\}$, square brackets $[]$, and finally the operations outside. ### Step-by-Step Solution * **Given:** $$ 5.5 - [6.5 - \{3.5 \div (6.5 - \overline{5.5 - 2.5})\}] $$ * **Calculation:** Resolve the Vinculum (bar bracket) first. $$ \overline{5.5 - 2.5} = 3.0 $$ * Substitute and resolve the round brackets. $$ (6.5 - 3.0) = 3.5 $$ * Substitute and resolve the curly braces. $$ \{3.5 \div 3.5\} = 1 $$ * Substitute and resolve the square brackets. $$ [6.5 - 1] = 5.5 $$ * Final subtraction outside all brackets. $$ 5.5 - 5.5 = 0 $$ ### Exam Strategy & Shortcut Do not rewrite the entire equation for every single step. Instead, simplify the nested brackets mentally or jot down running totals starting from the innermost bar. Track it like this: $5.5 - 2.5 \rightarrow 3$ $6.5 - 3 \rightarrow 3.5$ $3.5 \div 3.5 \rightarrow 1$ $6.5 - 1 \rightarrow 5.5$ Final step: $5.5 - 5.5 \rightarrow 0$. Working inwards-out visually saves critical time. ### Common Pitfall Ignoring the vinculum completely and computing $(6.5 - 5.5 - 2.5)$ straight across as if the bar didn't exist. This incorrectly yields $(1 - 2.5) = -1.5$, which completely derails the subsequent division and leads to a wrong answer. ### Final Answer **Therefore, the correct answer is 0.**