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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated strictly using the BODMAS rule?
50−[8+{16÷(8−7−3‾)}]50 - \left[ 8 + \left\{ 16 \div \left( 8 - \overline{7 - 3} \right) \right\} \right]
  1. 38Answer
  2. B
    44
  3. C
    50
  4. D
    46

Answer

The simplified numerical value of the expression is 38.
Evaluating step-by-step according to VBODMAS order gives: first vinculum 7 - 3 = 4, then round brackets 8 - 4 = 4, followed by curly bracket division 16 ÷ 4 = 4, then square bracket addition 8 + 4 = 12, and finally 50 - 12 = 38. The value 38 correctly demonstrates strict adherence to order of operations.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
\overline{7 - 3} = 4
According to VBODMAS rules, operations under a vinculum bar have the highest priority.
2
Evaluate the expression inside the round brackets
8 - 4 = 4
Substitute the vinculum result into the round bracket.
3
Perform division inside the curly brackets
16÷4=416 \div 4 = 4
Curly brackets are evaluated next after simplifying the inner round brackets.
4
Perform addition inside the square brackets
8 + 4 = 12
Resolve the remaining operations inside the outermost square brackets.
5
Perform final subtraction outside the brackets
50 - 12 = 38
Complete the evaluation by subtracting the bracket value from 50.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
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Topics

Simplification and BODMAS Rule

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