What is the simplified value of the following mathematical expression? \frac{7}{2} \div \l… — State PSC Exam

What is the simplified value of the following mathematical expression?

\frac{7}{2} \div \left[ 1 \frac{1}{4} + \left\{ 2 \frac{1}{2} - \frac{1}{2} \times \left( 2.5 - \overline{\frac{1}{4} + \frac{1}{6}} \right) \right\} \right] \times \frac{5}{12}

The simplified value of the expression is

\frac{7}{13}

Following strict BODMAS precedence: First, simplify the bar term

\overline{\frac{1}{4} + \frac{1}{6}} = \frac{5}{12}

. Next, resolve the round bracket

\frac{5}{2} - \frac{5}{12} = \frac{25}{12}

. Multiplying by

\frac{1}{2}

gives

\frac{25}{24}

. The curly bracket simplifies to

\frac{5}{2} - \frac{25}{24} = \frac{35}{24}

. The square bracket yields

\frac{5}{4} + \frac{35}{24} = \frac{65}{24}

. Finally, evaluating left to right gives

\frac{7}{2} \times \frac{24}{65} \times \frac{5}{12} = \frac{7}{13}

Evaluate the expression under the vinculum (bar bracket)

\overline{\frac{1}{4} + \frac{1}{6}} = \frac{3 + 2}{12} = \frac{5}{12}

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

Evaluate the terms inside the round brackets

2.5 - \frac{5}{12} = \frac{5}{2} - \frac{5}{12} = \frac{30 - 5}{12} = \frac{25}{12}

Convert decimal

2.5

to fraction

\frac{5}{2}

and perform subtraction.

Perform multiplication inside the curly brackets

\frac{1}{2} \times \frac{25}{12} = \frac{25}{24}

Multiplication inside brackets precedes subtraction.

Evaluate the terms inside the curly brackets

2 \frac{1}{2} - \frac{25}{24} = \frac{5}{2} - \frac{25}{24} = \frac{60 - 25}{24} = \frac{35}{24}

Complete the subtraction inside the curly brackets.

Evaluate the terms inside the square brackets

1 \frac{1}{4} + \frac{35}{24} = \frac{5}{4} + \frac{35}{24} = \frac{30 + 35}{24} = \frac{65}{24}

Perform addition within the square brackets.

Perform division and multiplication from left to right

\frac{7}{2} \div \frac{65}{24} \times \frac{5}{12} = \frac{7}{2} \times \frac{24}{65} \times \frac{5}{12} = \frac{84}{65} \times \frac{5}{12} = \frac{7}{13}

Division and multiplication have equal precedence and are executed strictly from left to right.

BODMAS Rule with Vinculum and Nested Brackets

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