What is the simplified numerical value of the mathematical expression given below when eva… — State PSC Exam

What is the simplified numerical value of the mathematical expression given below when evaluated strictly according to the VBODMAS rule?

16.5 + \left\{ 4.5 \times \left[ 12 - \left( 3.2 + \overline{4.8 - 1.6} \div 0.8 \right) \right] \right\}

The simplified numerical value of the expression is

38.1

Following the VBODMAS priority sequence: resolving the vinculum gives

3.2

; evaluating division inside the round bracket yields

3.2 \div 0.8 = 4

; finishing the round bracket yields

3.2 + 4 = 7.2

; evaluating the square bracket gives

12 - 7.2 = 4.8

; evaluating the curly bracket gives

4.5 \times 4.8 = 21.6

; finally, adding

16.5 + 21.6

yields

38.1

Evaluate the expression under the vinculum (bar)

\overline{4.8 - 1.6} = 3.2

According to the VBODMAS rule, operations under a vinculum take highest priority.

Evaluate the division inside the innermost round bracket

3.2 \div 0.8 = 4

Division takes precedence over addition within parentheses.

Complete the evaluation inside the round bracket

3.2 + 4 = 7.2

Add the remaining terms within the round bracket.

Evaluate the expression inside the square bracket

12 - 7.2 = 4.8

Subtract the result of the round bracket from

12

Evaluate the multiplication inside the curly bracket

4.5 \times 4.8 = 21.6

Multiply the term outside the square bracket by the simplified square bracket value.

Perform the final addition

16.5 + 21.6 = 38.1

Add the initial constant to the simplified curly bracket term.

Order of Operations (VBODMAS Rule)

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