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Question

Difficulty: EasySimplification and BODMAS Rule

What is the value of the following mathematical expression?

25−[18−{12−(6−4−1‾)}]25 - [18 - \{12 - (6 - \overline{4 - 1})\}]
  1. 16Answer
  2. B
    18
  3. C
    22
  4. D
    12

Answer

16
Following the BODMAS priority (Vinculum →\rightarrow Round Brackets →\rightarrow Curly Braces →\rightarrow Square Brackets →\rightarrow Outermost Subtraction):
1. Vinculum: 4−1‾=3\overline{4 - 1} = 3
2. Round brackets: 6−3=36 - 3 = 3
3. Curly braces: 12−3=912 - 3 = 9
4. Square brackets: 18−9=918 - 9 = 9
5. Outer subtraction: 25−9=1625 - 9 = 16.
Thus, 16 is the mathematically correct answer.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
4−1‾=3\overline{4 - 1} = 3
According to BODMAS, vinculum (bar bracket) has the highest priority.
2
Simplify the innermost round brackets (6−3)(6 - 3)
6−3=36 - 3 = 3
Evaluate terms inside round brackets next.
3
Simplify the curly braces {12−3}\{12 - 3\}
12−3=912 - 3 = 9
Evaluate terms inside curly braces next.
4
Simplify the square brackets [18−9][18 - 9]
18−9=918 - 9 = 9
Evaluate terms inside square brackets next.
5
Perform final subtraction from 25
25−9=1625 - 9 = 16
Complete the outermost operation.

Key Concept

BODMAS Rule with Vinculum (Bar Bracket)
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Topics

Simplification and BODMAS Rule

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