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Difficulty: HardSimplification and BODMAS Rule

Determine the exact result of the given mathematical expression after applying the standard order of operations (BODMAS):

32.4−45×[45÷{2.5×4−(7.6−4.1−1.5‾)}]32.4 - \frac{4}{5} \times \left[ 45 \div \left\{ 2.5 \times 4 - \left( 7.6 - \overline{4.1 - 1.5} \right) \right\} \right]

Answer: 25.2

Answer

The simplified numerical value of the expression is 25.2.
Following the standard BODMAS priority order: evaluate the vinculum (4.1 - 1.5 = 2.6), round brackets (7.6 - 2.6 = 5), curly brackets (2.5 * 4 - 5 = 5), square brackets (45 / 5 = 9), multiplication ((4/5) * 9 = 7.2), and finally subtraction (32.4 - 7.2 = 25.2).

Step-by-Step Solution

1
Evaluate the sub-expression under the vinculum bar
\overline{4.1 - 1.5} = 2.6
The vinculum acts as the innermost grouping symbol and takes highest priority.
2
Simplify the expression inside the round brackets
(7.6 - 2.6) = 5.0
Parentheses (round brackets) are evaluated next.
3
Evaluate operations inside the curly brackets using operator precedence
\{2.5 \times 4 - 5.0\} = \{10 - 5.0\} = 5
Multiplication precedes subtraction inside the curly brackets.
4
Evaluate the division inside the square brackets
[45÷5]=9[45 \div 5] = 9
Square brackets are solved after resolving inner curly brackets.
5
Perform multiplication outside the bracket
\frac{4}{5} \times 9 = 0.8 \times 9 = 7.2
Multiplication takes precedence over final addition/subtraction.
6
Perform the final subtraction
32.4 - 7.2 = 25.2
Subtraction is the final step in the BODMAS order of operations.

Key Concept

BODMAS Rule with Vinculum and Nested Brackets
Estimated Time:1m 30s
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Topics

Simplification and BODMAS Rule

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