What is the simplified value of the following mathematical expression when evaluated using… — State PSC Exam

What is the simplified value of the following mathematical expression when evaluated using the standard BODMAS rule?

60 - [15 + \{20 \div 5 + 3 \times (8 - \overline{4 + 2})\}]

The simplified value of the expression is

35

Following the BODMAS rule strictly: first resolve the vinculum

\overline{4 + 2} = 6

, then the round brackets

(8 - 6) = 2

. Inside the curly brackets, division and multiplication are evaluated before addition (

20 \div 5 + 3 \times 2 = 4 + 6 = 10

). Adding this to

15

inside the square brackets gives

25

. Subtracting

25

from

60

gives the correct simplified result of

35

Evaluate the expression under the vinculum bar.

\overline{4 + 2} = 6

Operations under a vinculum (line bracket) take highest priority.

Simplify the innermost round brackets

(8 - 6)

8 - 6 = 2

Parentheses must be evaluated next.

Evaluate the terms inside the curly brackets

\{20 \div 5 + 3 \times 2\}

. Perform division and multiplication before addition.

20 \div 5 = 4

and

3 \times 2 = 6

, so

4 + 6 = 10

According to BODMAS, division and multiplication precede addition.

Simplify the square brackets

[15 + 10]

15 + 10 = 25

Resolve the remaining bracket structure.

Perform the final subtraction

60 - 25

35

Complete the outermost operation.

Simplification using hierarchical order of operations (BODMAS / Vinculum rule)

Question