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Difficulty: MediumSimplification and BODMAS Rule
Evaluate the following mathematical expression using the standard BODMAS (VBODMAS) rule:
40% of 250−[15+{45÷(2+14 of (18−8−2‾))}]40\% \text{ of } 250 - \left[ 15 + \left\{ 45 \div \left( 2 + \frac{1}{4} \text{ of } \left( 18 - \overline{8 - 2} \right) \right) \right\} \right]
What is the final simplified value of the expression?
  1. 76Answer
  2. B
    88
  3. C
    94
  4. D
    24

Answer

The simplified value of the expression is 76.
Following the strict hierarchical order of operations (VBODMAS), resolving the bar vinculum first gives 6, then the inner parenthesis yields 12. Taking 1/4 of 12 gives 3, and adding 2 yields 5. Dividing 45 by 5 yields 9, and adding 15 yields 24 inside the main bracket. Subtracting 24 from 40% of 250 (which equals 100) gives the correct answer of 76.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar: 8−2‾\overline{8 - 2}.
8−2‾=6\overline{8 - 2} = 6
According to VBODMAS, operations under a vinculum take highest priority.
2
Evaluate the innermost round bracket: (18−6)(18 - 6).
18−6=1218 - 6 = 12
Resolve terms within the round parentheses.
3
Evaluate the 'of' operation inside the round bracket context: 14 of 12\frac{1}{4} \text{ of } 12.
14×12=3\frac{1}{4} \times 12 = 3
'Of' precedes basic addition and division.
4
Complete the addition inside the innermost bracket: (2+3)(2 + 3).
2+3=52 + 3 = 5
Finalize inner parentheses.
5
Evaluate the division inside the curly brackets: {45÷5}\{45 \div 5\}.
45÷5=945 \div 5 = 9
Perform division inside curly brackets.
6
Evaluate the addition inside the square brackets: [15+9][15 + 9].
15+9=2415 + 9 = 24
Resolve the square brackets.
7
Evaluate the percentage term: 40% of 25040\% \text{ of } 250.
40100×250=100\frac{40}{100} \times 250 = 100
Calculate the percentage value independently.
8
Perform the final subtraction: 100−24100 - 24.
100−24=76100 - 24 = 76
Subtract the bracket result from the percentage value.

Key Concept

BODMAS / VBODMAS Order of Operations

Alternative Method

Calculate the percentage term 40% of 250 = 100 first, then systematically simplify the bracket from innermost (vinculum) to outermost to subtract from 100.
Estimated Time:1m 15s
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Topics

Simplification and BODMAS Rule

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