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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified value of the following mathematical expression obtained by applying the BODMAS rule?
96÷[4+{25−(12−8−3‾)×3}]96 \div \left[ 4 + \left\{ 25 - \left( 12 - \overline{8 - 3} \right) \times 3 \right\} \right]
  1. 12Answer
  2. B
    28
  3. C
    4
  4. D
    16

Answer

12
Following the standard BODMAS precedence rule: first evaluate the vinculum 8−3‾=5\overline{8-3} = 5, then the round brackets (12−5)=7(12-5) = 7, then multiplication 7×3=217 \times 3 = 21, then curly brackets 25−21=425 - 21 = 4, then square brackets 4+4=84 + 4 = 8, and finally division 96÷8=1296 \div 8 = 12.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{8 - 3} = 5
The vinculum takes precedence over other bracket operations.
2
Evaluate the operation inside the innermost round brackets
12 - 5 = 7
Resolve the expression within the round brackets next.
3
Perform multiplication inside the curly brackets
7×3=217 \times 3 = 21
Multiplication precedes subtraction within the curly brackets according to BODMAS.
4
Complete the subtraction inside the curly brackets
25 - 21 = 4
Evaluate the remaining subtraction inside the curly brackets.
5
Evaluate the addition inside the outer square brackets
4 + 4 = 8
Combine the terms within the square brackets to obtain the final divisor.
6
Perform the final division
96÷8=1296 \div 8 = 12
Divide the initial integer by the evaluated square bracket result.

Key Concept

Simplification and BODMAS Rule with Vinculum
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Topics

Simplification and BODMAS Rule

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