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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified numerical value of the mathematical expression 36−[18÷{6−(4−3−1‾)}×2]36 - \left[ 18 \div \left\{ 6 - \left( 4 - \overline{3 - 1} \right) \right\} \times 2 \right] when evaluated strictly adhering to the VBODMAS rule?
  1. 2727Answer
  2. B
    3030
  3. C
    33.7533.75
  4. D
    2121

Answer

The simplified numerical value of the given expression is 27.
First resolve the vinculum 3−1‾=2\overline{3-1} = 2. Next, simplify the round bracket (4−2)=2(4-2) = 2, then the curly bracket {6−2}=4\{6-2\} = 4. Inside the square bracket, evaluate division before multiplication from left to right: 18÷4=4.518 \div 4 = 4.5, and 4.5×2=94.5 \times 2 = 9. Finally, subtract from 36 to get 36−9=2736 - 9 = 27.

Step-by-Step Solution

1
Evaluate the expression under the bar/vinculum
\overline{3 - 1} = 2
According to VBODMAS rules, vinculum (bar) has highest priority over standard operations.
2
Simplify the innermost round bracket
(4 - 2) = 2
Resolve terms within parenthesis after vinculum.
3
Simplify the curly bracket
\{6 - 2\} = 4
Perform subtraction inside curly braces.
4
Evaluate operations inside the square bracket from left to right
[18 \div 4 \times 2] = 4.5 \times 2 = 9
Division and multiplication have equal priority and must be evaluated left to right.
5
Perform the final outer subtraction
36 - 9 = 27
Complete the remaining operation.

Key Concept

VBODMAS / BODMAS Order of Operations
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Topics

Simplification and BODMAS Rule

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