Evaluate the following mathematical expression using the standard BODMAS rule: 40\% \text{… — State PSC Exam

Evaluate the following mathematical expression using the standard BODMAS rule:

40\% \text{ of } 150 + \left[ 72 \div \left\{ 18 - \left( 2\frac{1}{2} \times 4 + \overline{11 - 5} \right) \right\} \right]

What is the final simplified numerical value?

Answer: 96

The simplified numerical value of the given expression is 96.

Applying the standard BODMAS rule: first evaluate the vinculum

\overline{11 - 5} = 6

. Next, evaluate inside the round brackets:

2.5 \times 4 + 6 = 16

. Then simplify inside the curly braces:

18 - 16 = 2

. Following that, perform division inside the square brackets:

72 \div 2 = 36

. Separately, evaluate the percentage term:

40\% \text{ of } 150 = 60

. Summing these two terms gives

60 + 36 = 96

Evaluate the bar (vinculum) expression.

\overline{11 - 5} = 6

The vinculum (bar) has highest priority within bracket operations.

Simplify the terms within the round parentheses.

2\frac{1}{2} \times 4 + 6 = 10 + 6 = 16

Perform multiplication before addition inside parentheses.

Evaluate the expression inside the curly braces.

18 - 16 = 2

Subtract the result of the round brackets from 18.

Perform the division inside the square brackets.

72 \div 2 = 36

Divide 72 by the value obtained from curly braces.

Calculate the percentage component of the expression.

40\% \text{ of } 150 = \frac{40}{100} \times 150 = 60

The word 'of' indicates multiplication applied to the percentage value.

Perform the final addition.

60 + 36 = 96

Add the result of the percentage calculation to the result of the bracket evaluation.

Order of Operations (BODMAS Rule) with Vinculum, Nested Brackets, and Percentages

Estimated Time:1m 30s

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