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Difficulty: MediumSimplification and BODMAS Rule
What is the simplified value of the following mathematical expression when evaluated strictly using the VBODMAS rule?
15+2.5×[16−{10÷(3.5−2.1−0.6‾)}]15 + 2.5 \times \left[ 16 - \left\{ 10 \div \left( 3.5 - \overline{2.1 - 0.6} \right) \right\} \right]
  1. 42.5Answer
  2. B
    192.5
  3. C
    23.75
  4. D
    50

Answer

The simplified value of the expression is 42.5.
Evaluating strictly according to VBODMAS rules, we first simplify the expression under the vinculum bar (2.1 - 0.6 = 1.5), then the round brackets (3.5 - 1.5 = 2), followed by the curly brackets (10 ÷ 2 = 5), and then the square brackets (16 - 5 = 11). Finally, executing multiplication before addition yields 15 + (2.5 × 11) = 15 + 27.5 = 42.5.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{2.1 - 0.6} = 1.5
According to VBODMAS, the vinculum takes highest priority over standard brackets.
2
Evaluate the terms inside the innermost parentheses (round brackets)
3.5 - 1.5 = 2.0
Parentheses are evaluated next after resolving the vinculum.
3
Evaluate the expression inside the curly brackets
10÷2.0=510 \div 2.0 = 5
Division within the curly brackets takes priority before moving outward.
4
Evaluate the expression inside the square brackets
16 - 5 = 11
Resolve the remaining operations within the square brackets.
5
Perform multiplication before addition
15 + (2.5 \times 11) = 15 + 27.5 = 42.5
Multiplication takes precedence over addition according to BODMAS rules.

Key Concept

Order of Operations (VBODMAS Rule)
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Topics

Simplification and BODMAS Rule

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