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Difficulty: MediumSimplification and BODMAS Rule

Determine the exact numerical value of the following mathematical expression when evaluated strictly according to the VBODMAS rule:

45−[15+{24÷(3+12 of (16−8−2‾))}]45 - \left[ 15 + \left\{ 24 \div \left( 3 + \frac{1}{2} \text{ of } \left( 16 - \overline{8 - 2} \right) \right) \right\} \right]

Answer: 27

Answer

The simplified numerical value of the given expression is 27.
Evaluating step-by-step using VBODMAS order of precedence (Vinculum -> Brackets -> Of -> Division -> Multiplication -> Addition -> Subtraction) yields the simplified result 27.

Step-by-Step Solution

1
Evaluate the vinculum (bar) operation
\overline{8 - 2} = 6
According to VBODMAS, operations under a vinculum take precedence over standard bracket operations.
2
Simplify the innermost subtraction inside the round brackets
16 - 6 = 10
Subtracted the value obtained from the vinculum within the innermost parentheses.
3
Evaluate the 'of' operator
\frac{1}{2} \text{ of } 10 = 5
The 'of' operator represents multiplication with priority immediately following brackets.
4
Complete the addition in the round brackets
3 + 5 = 8
Evaluated the remaining addition within the round brackets.
5
Perform division inside the curly brackets
24÷8=324 \div 8 = 3
Divided 24 by the simplified result of the round brackets.
6
Perform addition inside the square brackets
15 + 3 = 18
Added 15 to the result from the curly brackets.
7
Perform final subtraction
45 - 18 = 27
Subtracted the square bracket result from 45 to obtain the final simplified value.

Key Concept

Order of Operations (VBODMAS Rule)
Estimated Time:1m 30s
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Topics

Simplification and BODMAS Rule

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