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Difficulty: MediumSimplification and BODMAS Rule
Evaluate the following numerical expression strictly according to the VBODMAS rule:
2.5×12−[8+{15÷(4.5−2.1+0.9‾)}]2.5 \times 12 - \left[ 8 + \left\{ 15 \div \left( 4.5 - \overline{2.1 + 0.9} \right) \right\} \right]
What is the final calculated value?

Answer: 12

Answer

12
Evaluating the expression following strict VBODMAS priority yields: Vinculum (2.1 + 0.9 = 3) -> Round brackets (4.5 - 3 = 1.5) -> Curly brackets (15 / 1.5 = 10) -> Square brackets (8 + 10 = 18) -> Multiplication (2.5 * 12 = 30) -> Subtraction (30 - 18 = 12).

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
2.1 + 0.9 = 3
According to the VBODMAS rule, operations under a vinculum take highest priority.
2
Evaluate the innermost round brackets
4.5 - 3 = 1.5
Perform subtraction inside the round brackets after resolving the vinculum.
3
Perform division within the curly brackets
15 / 1.5 = 10
Division inside curly brackets must be calculated before simplifying the outer bracket.
4
Perform addition within the square brackets
8 + 10 = 18
Complete the evaluation of the square bracket section.
5
Perform multiplication outside the brackets
2.5 * 12 = 30
Multiplication takes precedence over final subtraction.
6
Perform final subtraction
30 - 18 = 12
Complete the expression by subtracting the bracket result from the product.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
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Topics

Simplification and BODMAS Rule

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