Examkin

Question

Difficulty: HardSimplification and BODMAS Rule
Calculate the numerical value of the following mathematical expression:
75% of 240−[42÷{214+(3.5−1.8−0.8‾)×1.5}]75\% \text{ of } 240 - \left[ 42 \div \left\{ 2\frac{1}{4} + \left( 3.5 - \overline{1.8 - 0.8} \right) \times 1.5 \right\} \right]

Answer: 173

Answer

The simplified numerical value of the expression is 173.
Applying the VBODMAS rule sequentially (vinculum, round brackets, multiplication, addition within curly brackets, square bracket division, percentage evaluation, and final subtraction) yields 173.

Step-by-Step Solution

1
Evaluate the vinculum bar expression
1.8−0.8‾=1.0\overline{1.8 - 0.8} = 1.0
Under VBODMAS rules, the vinculum (bar) grouping has the highest priority and must be evaluated first.
2
Evaluate the subtraction inside the round brackets
3.5−1.0=2.53.5 - 1.0 = 2.5
Evaluate the parentheses next using the result from the vinculum evaluation.
3
Perform multiplication inside the curly brackets
2.5×1.5=3.752.5 \times 1.5 = 3.75
Within the curly brackets, multiplication precedes addition according to BODMAS.
4
Perform addition inside the curly brackets
214+3.75=2.25+3.75=6.02\frac{1}{4} + 3.75 = 2.25 + 3.75 = 6.0
Convert the mixed fraction 2142\frac{1}{4} to decimal 2.252.25 and add to 3.753.75.
5
Perform division inside the square brackets
42÷6.0=742 \div 6.0 = 7
Resolve the square brackets by dividing 42 by the value of the curly bracket expression.
6
Evaluate the percentage 'of' expression
75% of 240=0.75×240=18075\% \text{ of } 240 = 0.75 \times 240 = 180
The 'of' operator indicates multiplication applied to percentage.
7
Subtract the square bracket result from the percentage value
180−7=173180 - 7 = 173
Perform final subtraction to complete the calculation.

Key Concept

Hierarchical priority of operations in VBODMAS (Vinculum -> Brackets -> Of -> Division -> Multiplication -> Addition -> Subtraction)
Rate this question

Topics

Simplification and BODMAS Rule

More questions from this topic