Find the exact numerical value of the following mathematical expression evaluated strictly… — State PSC Exam

Find the exact numerical value of the following mathematical expression evaluated strictly according to the VBODMAS rule:

75\% \text{ of } 160 - \left[ 3.5 \times 8 + \left\{ 48 \div \left( 14 - \overline{5 \times 2} \right) \right\} \right]

Answer: 80

The simplified numerical value of the expression is

80

Evaluating the expression following strict VBODMAS hierarchy: bar expression

\overline{5 \times 2} = 10

, round brackets

14 - 10 = 4

, curly brackets

48 \div 4 = 12

, square brackets

3.5 \times 8 + 12 = 40

, and percentage 'of' term

75\% \text{ of } 160 = 120

. Finally,

120 - 40 = 80

Evaluate the expression under the vinculum (bar)

\overline{5 \times 2} = 10

According to VBODMAS, operations grouped under a bar take highest priority.

Evaluate inside the innermost round brackets

(14 - 10)

14 - 10 = 4

Perform subtraction inside the parentheses.

Evaluate inside the curly brackets

\{48 \div 4\}

48 \div 4 = 12

Divide the number outside the round bracket by the result of the round bracket.

Evaluate inside the square brackets

[3.5 \times 8 + 12]

28 + 12 = 40

Perform multiplication (

3.5 \times 8 = 28

) before adding

12

Calculate the percentage term

75\% \text{ of } 160

\frac{75}{100} \times 160 = 120

Evaluate the 'of' operation before final subtraction.

Perform final subtraction

120 - 40

Subtract the total result of the bracketed expression from the percentage term.

Order of Operations (VBODMAS Rule)

Question