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Difficulty: MediumSimplification and BODMAS Rule

What is the simplified value of the following mathematical expression when evaluated using the standard BODMAS rule?

20+4×[36÷{12−(3+7−4‾)}]20 + 4 \times \left[ 36 \div \left\{ 12 - \left( 3 + \overline{7 - 4} \right) \right\} \right]
  1. 44Answer
  2. B
    144
  3. C
    32
  4. D
    72

Answer

44
Following the BODMAS order of operations, we first evaluate the vinculum line to get 3, then solve the round bracket (3 + 3 = 6), followed by the curly bracket (12 - 6 = 6), and then the square bracket (36 ÷ 6 = 6). Finally, performing multiplication before addition gives 20 + (4 × 6) = 20 + 24 = 44.

Step-by-Step Solution

1
Simplify the expression under the vinculum (bar)
7 - 4 = 3
The vinculum has the highest priority and must be evaluated first.
2
Simplify the innermost round brackets
3 + 3 = 6
Perform addition inside the parentheses.
3
Simplify the curly brackets
12 - 6 = 6
Subtract the result of the round brackets from 12.
4
Simplify the square brackets
36 ÷ 6 = 6
Perform division inside the square brackets.
5
Apply multiplication before addition in the outer expression
4 × 6 = 24
Multiplication has higher priority than addition according to BODMAS.
6
Perform final addition
20 + 24 = 44
Add 20 to 24 to get the final simplified answer.

Key Concept

Simplification and BODMAS Rule
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Topics

Simplification and BODMAS Rule

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