Examkin

Question

Difficulty: HardSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated using the correct BODMAS order of operations?
20% of 150−[3.5+2×{7.2−(1.4+3.8−1.6‾)÷0.6}]20\% \text{ of } 150 - \left[ 3.5 + 2 \times \left\{ 7.2 - \left( 1.4 + \overline{3.8 - 1.6} \right) \div 0.6 \right\} \right]
  1. 24.1Answer
  2. B
    14.5
  3. C
    23.4
  4. D
    28.82

Answer

24.1
Evaluating the expression by strictly following the VBODMAS hierarchy (Vinculum -> Brackets -> Of/Orders -> Division -> Multiplication -> Addition -> Subtraction) yields the step-by-step values: vinculum gives 2.2, round brackets give 3.6, division inside curly braces gives 6, curly braces give 1.2, multiplication inside square brackets gives 2.4, square brackets give 5.9, percentage gives 30, and final subtraction gives 24.1.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{3.8 - 1.6} = 2.2
The vinculum has the highest priority in the hierarchy of brackets.
2
Simplify the terms within the parentheses (round brackets)
1.4 + 2.2 = 3.6
Complete the inner addition inside the round brackets.
3
Perform division inside the braces (curly brackets)
3.6÷0.6=63.6 \div 0.6 = 6
Division takes precedence over subtraction inside the curly brackets.
4
Perform subtraction inside the braces (curly brackets)
7.2 - 6 = 1.2
Complete the remaining operation inside the curly brackets.
5
Perform multiplication inside the square brackets
2×1.2=2.42 \times 1.2 = 2.4
Multiplication takes precedence over addition inside the square brackets.
6
Perform addition inside the square brackets
3.5 + 2.4 = 5.9
Complete the final operation inside the square brackets.
7
Calculate the percentage value
20\% \text{ of } 150 = \frac{20}{100} \times 150 = 30
Evaluate the 'Of' operation / percentage computation.
8
Subtract the bracket result from the percentage value
30 - 5.9 = 24.1
Execute the final subtraction outside all brackets.

Key Concept

Hierarchy of Order of Operations (BODMAS / VBODMAS)
Rate this question

Topics

Simplification and BODMAS Rule

More questions from this topic