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Difficulty: MediumSimplification and BODMAS Rule
Calculate the exact numerical value of the given mathematical expression using the VBODMAS rule:
35 of 250−[42+{24÷(7.5−4.2+0.3‾)}]\frac{3}{5} \text{ of } 250 - \left[ 42 + \left\{ 24 \div \left( 7.5 - \overline{4.2 + 0.3} \right) \right\} \right]

Answer: 100

Answer

100
Evaluating strictly according to VBODMAS order of operations yields 100: Vinculum gives 4.5, round brackets give 3, division in curly brackets gives 8, addition in square brackets gives 50, 'of' operation gives 150, and 150 - 50 = 100.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar line)
4.2 + 0.3 = 4.5
According to the VBODMAS rule, the vinculum takes precedence over standard brackets and operations.
2
Simplify the innermost round brackets
7.5 - 4.5 = 3
Operations inside round parentheses ( ) are resolved next.
3
Evaluate the expression inside the curly brackets
24 / 3 = 8
Perform the division operation inside curly braces { }.
4
Evaluate the expression inside the square brackets
42 + 8 = 50
Perform addition within the outer square brackets [ ].
5
Calculate the 'of' operation
(3/5) * 250 = 150
The 'of' operation takes priority over standard addition and subtraction outside brackets.
6
Perform final subtraction
150 - 50 = 100
Subtract the total evaluated bracketed quantity from the 'of' calculation result.

Key Concept

Hierarchical priority of operations in VBODMAS involving vinculum, nested brackets, and fractional 'of' operations
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Topics

Simplification and BODMAS Rule

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