What is the simplified numerical value of the following mathematical expression when evalu… — State PSC Exam

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

240 \div \left[ 2 \frac{1}{2} \times \left\{ 14 - \left( 3 \frac{1}{2} + 25\% \text{ of } \left( 14 - \overline{1.8 + 2.2} \right) \right) \right\} \right]

12Answer
B
16
C
768
D
8

Answer

Following the strict hierarchical order of operations (BODMAS: Vinculum

\rightarrow

Brackets

\rightarrow

Orders

\rightarrow

Division/Multiplication

\rightarrow

Addition/Subtraction), the innermost vinculum

\overline{1.8 + 2.2}

evaluates to

4

. Then

14 - 4 = 10

, and

25\%

10

equals

2.5

. Adding this to

3 \frac{1}{2} (3.5)

yields

6

. Inside the curly brackets,

14 - 6 = 8

. Inside the square brackets,

2 \frac{1}{2} (2.5) \times 8 = 20

. Finally,

240 \div 20 = 12

Step-by-Step Solution

Evaluate the expression under the vinculum (bar)

\overline{1.8 + 2.2} = 4

The vinculum acts as the innermost grouping symbol and must be simplified first.

Simplify the innermost parenthetical difference

14 - 4 = 10

Subtract the vinculum result from 14 within the round brackets.

Calculate the percentage of the result from Step 2

25\% \text{ of } 10 = \frac{25}{100} \times 10 = 2.5

'Of' represents multiplication in percentage evaluation.

Complete the evaluation inside the round brackets

3 \frac{1}{2} + 2.5 = 3.5 + 2.5 = 6

Convert the mixed fraction

3 \frac{1}{2}

to decimal

3.5

and sum with

2.5

Evaluate the expression inside the curly brackets

14 - 6 = 8

Subtract the round bracket total from 14.

Simplify the expression inside the square brackets

2 \frac{1}{2} \times 8 = 2.5 \times 8 = 20

Multiply the mixed fraction

2 \frac{1}{2}

by the curly bracket result.

Perform the final division outside the brackets

240 \div 20 = 12

Divide 240 by the completely simplified value of the square brackets.

Key Concept

BODMAS Rule with Vinculum and Multi-level Brackets

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