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?

25\% \text{ of } 180 - \left[ 4.8 + \left\{ 12 \div \left( 3\frac{1}{3} \times \overline{0.8 + 0.4} \right) \right\} \right]

The simplified value of the expression is

37.2

Evaluating strictly according to the BODMAS hierarchical priority: first resolve the vinculum

\overline{0.8 + 0.4} = 1.2

, then the round brackets

\frac{10}{3} \times 1.2 = 4

, then the division in curly brackets

12 \div 4 = 3

, followed by square bracket addition

4.8 + 3 = 7.8

, and finally subtracting this from

25\% \text{ of } 180 = 45

gives

45 - 7.8 = 37.2

Evaluate the expression under the vinculum bar first

\overline{0.8 + 0.4} = 1.2

According to the BODMAS rule, operations under a vinculum bar have the highest priority over all other brackets.

Convert the mixed fraction and evaluate the round brackets

3\frac{1}{3} \times 1.2 = \frac{10}{3} \times \frac{12}{10} = 4

Convert

3\frac{1}{3}

to the improper fraction

\frac{10}{3}

and multiply by

1.2

(or

\frac{6}{5}

Evaluate the expression inside the curly brackets

12 \div 4 = 3

Perform division of

12

by the result of the round brackets (

4

Evaluate the expression inside the square brackets

4.8 + 3 = 7.8

Add

4.8

to the result obtained from the curly brackets (

3

Calculate the percentage term and perform the final subtraction

25\% \text{ of } 180 = \frac{25}{100} \times 180 = 45

; then

45 - 7.8 = 37.2

'Of' represents multiplication for the percentage term, which is evaluated and then reduced by the square bracket result.

BODMAS Rule with Vinculum and Mixed Operations

Question