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Difficulty: MediumSimplification and BODMAS Rule
What is the final numerical value of the following expression when evaluated strictly according to the VBODMAS rule?
12.5×4−[16+{25÷(3.5+2.8−1.3‾)}]12.5 \times 4 - \left[ 16 + \left\{ 25 \div \left( 3.5 + \overline{2.8 - 1.3} \right) \right\} \right]

Answer: 29

Answer

The simplified numerical value of the expression is 29.
Applying VBODMAS step-by-step resolves the vinculum first (2.8 - 1.3 = 1.5), then the round brackets (3.5 + 1.5 = 5), curly brackets (25 / 5 = 5), square brackets (16 + 5 = 21), and finally the multiplication and subtraction (50 - 21 = 29).

Step-by-Step Solution

1
Evaluate the vinculum (bar) operation first
\overline{2.8 - 1.3} = 1.5
According to VBODMAS, the vinculum takes top priority over all other operations.
2
Simplify the expression inside the innermost round brackets
3.5 + 1.5 = 5
Next in hierarchy are the round brackets (parentheses).
3
Simplify the expression inside the curly brackets
25÷5=525 \div 5 = 5
Evaluate operations inside curly braces next.
4
Simplify the expression inside the square brackets
16 + 5 = 21
Complete the evaluation of the outer square brackets.
5
Perform the multiplication and final subtraction outside the brackets
12.5 \times 4 = 50 \text{ and then } 50 - 21 = 29
Perform multiplication before final subtraction following standard operator precedence.

Key Concept

VBODMAS Rule (Vinculum, Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Estimated Time:1m 30s
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Topics

Simplification and BODMAS Rule

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