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 strictly according to the BODMAS rule?

25\% \text{ of } 120 - \left[ 4 \times \left\{ 15 - \left( 18 \div \overline{7 - 4} \right) \right\} \right] \div 1.5

Evaluating the vinculum

\overline{7 - 4}

yields

3

. The round bracket becomes

18 \div 3 = 6

. The curly bracket yields

15 - 6 = 9

. The square bracket evaluates to

4 \times 9 = 36

. Concurrently,

25\%

120

equals

30

. Following operator hierarchy, division is executed next:

36 \div 1.5 = 24

. Finally, performing subtraction gives

30 - 24 = 6

Evaluate the expression under the bar (vinculum)

\overline{7 - 4} = 3

According to BODMAS, vinculum (bar bracket) has the highest priority among all grouping symbols.

Evaluate the innermost round bracket

18 \div 3 = 6

Perform division inside the round bracket after resolving the vinculum.

Evaluate the curly bracket

15 - 6 = 9

Subtract the result of the round bracket from 15 inside the curly bracket.

Evaluate the square bracket and the percentage term

4 \times 9 = 36

and

25\% \text{ of } 120 = \frac{25}{100} \times 120 = 30

Multiply 4 by the curly bracket result, and independently calculate the percentage term.

Perform division before final subtraction

36 \div 1.5 = 24

BODMAS mandates performing division before subtraction.

Perform the final subtraction

30 - 24 = 6

Subtract the quotient from the percentage value.

BODMAS Order of Operations with Vinculum and Mixed Numbers

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