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Difficulty: EasySimplification and BODMAS Rule
What is the simplified numerical value of the mathematical expression 25−[10+{8÷(6−4−2‾)}]25 - \left[ 10 + \left\{ 8 \div \left( 6 - \overline{4 - 2} \right) \right\} \right] when evaluated using the standard BODMAS rule?
  1. 1313Answer
  2. B
    1717
  3. C
    1111
  4. D
    77

Answer

The correct simplified value of the given expression is 13.
Evaluating the expression step-by-step using VBODMAS rules:
1. Vinculum: 4−2‾=2\overline{4 - 2} = 2
2. Round brackets: 6−2=46 - 2 = 4
3. Curly brackets: 8÷4=28 \div 4 = 2
4. Square brackets: 10+2=1210 + 2 = 12
5. Final subtraction: 25−12=1325 - 12 = 13.
Thus, the correct value is 13.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
4−2‾=2\overline{4 - 2} = 2
According to VBODMAS, operations under a vinculum (bar) have the highest precedence.
2
Simplify the innermost round brackets
6−2=46 - 2 = 4
Substitute the vinculum result into the round brackets (6−2)(6 - 2).
3
Evaluate the division inside the curly brackets
8÷4=28 \div 4 = 2
Division within the curly braces {8÷4}\{8 \div 4\} takes precedence.
4
Evaluate the addition inside the square brackets
10+2=1210 + 2 = 12
Add the terms inside the square brackets [10+2][10 + 2].
5
Perform the final subtraction
25−12=1325 - 12 = 13
Subtract the bracket result from 25.

Key Concept

Order of operations following the VBODMAS rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
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Topics

Simplification and BODMAS Rule

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