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Difficulty: MediumSimplification and BODMAS Rule
Evaluate the expression given below by applying the standard order of operations (VBODMAS):
2.5×[18÷{4.5+12 of (7.8−3.4+1.4‾)}]+3.52.5 \times \left[ 18 \div \left\{ 4.5 + \frac{1}{2} \text{ of } \left( 7.8 - \overline{3.4 + 1.4} \right) \right\} \right] + 3.5
Which of the following represents the correct simplified result?
  1. 11Answer
  2. B
    16.25
  3. C
    6.5
  4. D
    17.25

Answer

The correct simplified result is 11.
Evaluating step-by-step using VBODMAS order yields: Vinculum gives 4.8; Round bracket yields 7.8 - 4.8 = 3.0; 'of' operation gives 0.5 * 3.0 = 1.5; Curly brackets give 4.5 + 1.5 = 6.0; Square bracket gives 18 / 6.0 = 3; Final calculation gives 2.5 * 3 + 3.5 = 7.5 + 3.5 = 11.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar line).
\overline{3.4 + 1.4} = 4.8
According to VBODMAS, the vinculum takes precedence over all standard brackets.
2
Simplify the innermost round brackets.
7.8 - 4.8 = 3.0
Resolve terms within parenthetical brackets next.
3
Execute the 'of' operation inside the curly brackets.
\frac{1}{2} \text{ of } 3.0 = 1.5
The 'of' operator represents multiplication with higher priority than division and standard addition.
4
Complete the addition within the curly brackets.
4.5 + 1.5 = 6.0
Finish evaluating all operations contained within the curly brackets.
5
Perform division inside the square brackets.
18÷6.0=318 \div 6.0 = 3
Evaluate the remaining square bracket operation.
6
Perform final multiplication and addition operations from left to right according to operator precedence.
2.5 \times 3 + 3.5 = 7.5 + 3.5 = 11
Multiplication takes precedence over final addition.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction)
Estimated Time:1m 15s
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Topics

Simplification and BODMAS Rule

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