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Difficulty: MediumSimplification and BODMAS Rule
What is the final numerical value obtained by evaluating the following mathematical expression strictly according to the BODMAS rule?
50−[52÷{4.5+45×(3.7−1.8−0.6‾)}]50 - \left[ 52 \div \left\{ 4.5 + \frac{4}{5} \times \left( 3.7 - \overline{1.8 - 0.6} \right) \right\} \right]

Answer: 42

Answer

42
Following VBODMAS rule strictly:
1. Vinculum: 1.8 - 0.6 = 1.2
2. Round brackets: 3.7 - 1.2 = 2.5
3. Multiplication in curly brackets: (4/5) * 2.5 = 2
4. Addition in curly brackets: 4.5 + 2 = 6.5
5. Square bracket division: 52 / 6.5 = 8
6. Outer subtraction: 50 - 8 = 42.

Step-by-Step Solution

1
Evaluate the vinculum (bar line above numbers)
\overline{1.8 - 0.6} = 1.2
According to BODMAS (or VBODMAS), the vinculum takes precedence over round brackets.
2
Simplify the terms inside the parentheses (round brackets)
3.7 - 1.2 = 2.5
Parentheses are evaluated next after the vinculum.
3
Evaluate the multiplication inside the curly brackets
\frac{4}{5} \times 2.5 = 0.8 \times 2.5 = 2.0
Within curly brackets, multiplication precedes addition.
4
Complete the addition inside the curly brackets
4.5 + 2.0 = 6.5
Completing all operations within the curly brackets.
5
Evaluate the division inside the square brackets
52÷6.5=852 \div 6.5 = 8
Simplifying the entire square bracket term.
6
Perform the final subtraction outside all brackets
50 - 8 = 42
Final arithmetic step to find the value of the expression.

Key Concept

Order of Operations (BODMAS / VBODMAS)
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Topics

Simplification and BODMAS Rule

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