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Difficulty: HardSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated strictly according to the BODMAS rule?
45−[3×{12÷(1.5+2.7−1.2‾)}+2.5]×245 - \left[ 3 \times \left\{ 12 \div \left( 1.5 + \overline{2.7 - 1.2} \right) \right\} + 2.5 \right] \times 2
  1. 16Answer
  2. B
    6
  3. C
    61
  4. D
    -17

Answer

16
Evaluating the expression according to VBODMAS rules step-by-step: first the vinculum gives 1.5; adding inside round brackets gives 3; dividing inside curly braces gives 4; multiplying and adding inside square brackets gives 14.5; finally multiplying by 2 gives 29, and subtracting from 45 yields 16.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{2.7 - 1.2} = 1.5
According to VBODMAS, operations under a vinculum must be simplified first.
2
Simplify the expression inside the round brackets (parentheses)
1.5 + 1.5 = 3
Parentheses have priority after the vinculum is resolved.
3
Evaluate the division inside the curly braces
12÷3=412 \div 3 = 4
Operations within braces are evaluated next.
4
Simplify the expression inside the square brackets
3 \times 4 + 2.5 = 12 + 2.5 = 14.5
Inside brackets, multiplication takes precedence over addition.
5
Perform final operations outside brackets using standard operator precedence
45 - 14.5 \times 2 = 45 - 29 = 16
Multiplication must be executed before subtraction.

Key Concept

Hierarchy of operations in VBODMAS (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
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Topics

Simplification and BODMAS Rule

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