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Difficulty: MediumSimplification and BODMAS Rule

Calculate the exact numerical value of the following mathematical expression by applying the standard order of operations (BODMAS):

36.4−[12.8+{6.5×(4.4−2.6+0.8‾)}÷1.3]36.4 - \left[ 12.8 + \left\{ 6.5 \times \left( 4.4 - \overline{2.6 + 0.8} \right) \right\} \div 1.3 \right]

Answer: 18.6

Answer

The simplified value of the mathematical expression is 18.6.
Strict application of BODMAS requires simplifying grouping symbols from the innermost vinculum outward, followed by resolving division prior to addition within brackets, yielding an exact answer of 18.6.

Step-by-Step Solution

1
Evaluate the expression underneath the vinculum (bar line)
\overline{2.6 + 0.8} = 3.4
The vinculum functions as an innermost bracket with highest evaluation priority.
2
Evaluate the terms inside the round brackets
4.4 - 3.4 = 1.0
Process operations inside round brackets next.
3
Perform multiplication within the curly braces
6.5×1.0=6.56.5 \times 1.0 = 6.5
Complete operations within the curly braces.
4
Execute division inside the square brackets
6.5÷1.3=5.06.5 \div 1.3 = 5.0
Division takes precedence over addition according to BODMAS rules.
5
Perform addition within the square brackets
12.8 + 5.0 = 17.8
Finish evaluating all operations contained within the square brackets.
6
Perform final subtraction from left to right
36.4 - 17.8 = 18.6
Complete the outermost subtraction to arrive at the final simplified value.

Key Concept

BODMAS Rule with Vinculum and Decimals
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Topics

Simplification and BODMAS Rule

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