What exact numerical result is obtained when simplifying the following multi-bracket expre… — State PSC Exam

What exact numerical result is obtained when simplifying the following multi-bracket expression according to the BODMAS order of operations?

75\% \text{ of } 240 - \left[ 38.5 + \left\{ 15\frac{1}{2} - \left( 6.8 \times 2.5 - \overline{4.2 + 3.8} \right) \div 0.5 \right\} \right]

Cevap: 144

The final simplified numerical value of the given expression is 144.

Following the BODMAS rule strictly: first evaluate the vinculum

\overline{4.2 + 3.8} = 8

; then resolve round brackets

(6.8 \times 2.5 - 8 = 9)

; next resolve curly brackets

(15.5 - 9 \div 0.5 = -2.5)

; then square brackets

(38.5 - 2.5 = 36)

; and finally compute

75\% \text{ of } 240 = 180

. Subtracting

36

from

180

gives the correct result of 144.

Evaluate the vinculum (bar) operator first

\overline{4.2 + 3.8} = 8

According to BODMAS, the vinculum takes precedence over round brackets.

Simplify the terms inside the round brackets (parentheses)

6.8 \times 2.5 - 8 = 17 - 8 = 9

Multiplication precedes subtraction inside the innermost round brackets.

Simplify the terms inside the curly brackets (braces)

15.5 - (9 \div 0.5) = 15.5 - 18 = -2.5

Division (

9 \div 0.5 = 18

) is performed before subtracting from

15.5

(

15\frac{1}{2}

Simplify the terms inside the square brackets

38.5 + (-2.5) = 36

Adding the negative result from the curly brackets to

38.5

yields

36

Calculate the percentage 'Of' operation and perform final subtraction

75\% \text{ of } 240 - 36 = 180 - 36 = 144

'Of' operation (

75\% \times 240 = 180

) is calculated before subtracting the bracketed total.

BODMAS Rule with Vinculum and Nested Brackets

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