What is the value of the mathematical expression 24 + 4 \times \left[ 15 - \left\{ 12 \div… — State PSC Exam

What is the value of the mathematical expression $24 + 4 \times \left[ 15 - \left\{ 12 \div 4 + (8 - \overline{5 - 2}) \right\} \right]$ ?

The simplified value of the expression is 52.

Following the VBODMAS hierarchy: first evaluate the bar line

\overline{5-2} = 3

, then the round brackets

(8-3) = 5

, then division inside the curly braces

12 \div 4 = 3

, followed by addition inside curly braces

3+5 = 8

. Next, subtract within square brackets

15-8 = 7

. Finally, multiply before adding:

4 \times 7 = 28

, and

24 + 28 = 52

Evaluate the vinculum bar

\overline{5 - 2}

5 - 2 = 3

According to VBODMAS rules, operations under a vinculum (bar) have the highest priority among bracket operations.

Evaluate the expression inside the round brackets

(8 - 3)

8 - 3 = 5

Round brackets (parentheses) are simplified next.

Evaluate the expression inside the curly braces

\{12 \div 4 + 5\}

12 \div 4 = 3

, then

3 + 5 = 8

Inside the curly braces, division takes precedence over addition.

Evaluate the expression inside the square brackets

[15 - 8]

15 - 8 = 7

Square brackets are solved after round and curly brackets.

Perform multiplication before final addition

4 \times 7 = 28

Multiplication takes precedence over addition outside the brackets.

Perform the final addition

24 + 28 = 52

Complete the final addition step to obtain the result.

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)

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