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Difficulty: MediumSimplification and BODMAS Rule
Evaluate the following mathematical expression by applying the standard order of operations (BODMAS):
18÷[412−{214+34×(4.8−2.4+0.4‾)}]+5.518 \div \left[ 4 \frac{1}{2} - \left\{ 2 \frac{1}{4} + \frac{3}{4} \times \left( 4.8 - \overline{2.4 + 0.4} \right) \right\} \right] + 5.5
What is the final numerical value of the simplified expression?

Answer: 29.5

Answer

The simplified numerical value of the given expression is 29.5.
Following the BODMAS rule systematically, we first resolve the vinculum to get 2.8, then evaluate the round brackets (4.8 - 2.8 = 2.0). Next, inside the curly brackets, multiplication yields 1.5 and addition yields 3.75. Evaluating the square brackets yields 4.5 - 3.75 = 0.75. Dividing 18 by 0.75 gives 24, and adding 5.5 gives the final correct answer of 29.5.

Step-by-Step Solution

1
Evaluate the expression under the vinculum bar
\overline{2.4 + 0.4} = 2.8
The vinculum (bar) takes highest priority over standard parentheses and operations.
2
Simplify the innermost round brackets
4.8 - 2.8 = 2.0
Perform subtraction inside the round brackets next.
3
Perform multiplication inside the curly brackets
34×2.0=1.5\frac{3}{4} \times 2.0 = 1.5
Multiplication precedes addition within the curly brackets according to BODMAS.
4
Complete evaluation inside the curly brackets
2 \frac{1}{4} + 1.5 = 2.25 + 1.5 = 3.75
Convert the mixed fraction 2 1/4 to decimal 2.25 and add 1.5.
5
Evaluate the terms inside the square brackets
4 \frac{1}{2} - 3.75 = 4.5 - 3.75 = 0.75
Convert mixed fraction 4 1/2 to decimal 4.5 and subtract 3.75.
6
Perform division before final addition
18÷0.75=2418 \div 0.75 = 24
Division takes precedence over the final addition operation.
7
Add the final constant
24 + 5.5 = 29.5
Complete the evaluation by adding 5.5 to 24.

Key Concept

Hierarchy of operations in BODMAS including vinculum bar, nested brackets, and precedence of operations.
Estimated Time:1m 30s
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Topics

Simplification and BODMAS Rule

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