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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified value of the following mathematical expression when evaluated strictly using the BODMAS rule?
25% of 160+[45÷{15−(3.5×2+8−5‾)}]×2.525\% \text{ of } 160 + \left[ 45 \div \left\{ 15 - \left( 3.5 \times 2 + \overline{8 - 5} \right) \right\} \right] \times 2.5
  1. 62.5Answer
  2. B
    122.5
  3. C
    -5
  4. D
    43.6

Answer

62.5
Evaluating step-by-step according to BODMAS: first the vinculum gives 3; the round bracket gives 3.5 × 2 + 3 = 10; the curly bracket gives 15 - 10 = 5; the square bracket gives 45 ÷ 5 = 9. Next, 25% of 160 yields 40. Then multiplication gives 9 × 2.5 = 22.5. Finally, adding 40 + 22.5 gives 62.5.

Step-by-Step Solution

1
Evaluate the expression under the bar (vinculum)
\overline{8 - 5} = 3
The bar (vinculum) acts as the innermost bracket and takes highest priority.
2
Evaluate the innermost round brackets, applying multiplication before addition
(3.5 \times 2 + 3) = (7 + 3) = 10
Within round brackets, multiplication precedes addition.
3
Evaluate the curly brackets
\{15 - 10\} = 5
Perform subtraction inside the curly brackets.
4
Evaluate the square brackets
[45÷5]=9[45 \div 5] = 9
Perform division inside the square brackets.
5
Calculate the percentage term ('of' operation)
25\% \text{ of } 160 = \frac{25}{100} \times 160 = 40
'Of' represents multiplication linked to percentage.
6
Perform multiplication before addition in the outer expression
9×2.5=22.59 \times 2.5 = 22.5
Multiplication takes precedence over addition.
7
Perform final addition
40 + 22.5 = 62.5
Add the result of the percentage term to the bracket evaluation term.

Key Concept

BODMAS Rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) with Vinculum and Percentages
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Topics

Simplification and BODMAS Rule

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