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Difficulty: HardSimplification and BODMAS Rule
Calculate the exact numerical value of the following expression by applying the standard BODMAS/VBODMAS order of operations:
45% of 160−[12.5+{34×(36÷3−4.2+1.8‾)+5.5}÷0.5]45\% \text{ of } 160 - \left[ 12.5 + \left\{ \frac{3}{4} \times \left( 36 \div 3 - \overline{4.2 + 1.8} \right) + 5.5 \right\} \div 0.5 \right]

Answer: 39.5

Answer

The simplified numerical value of the given expression is 39.5.
Evaluating step by step according to VBODMAS rules yields 39.5. First, the vinculum gives 6. The round bracket gives 36 ÷ 3 - 6 = 6. The curly bracket gives (3/4) × 6 + 5.5 = 10. The square bracket gives 12.5 + 10 ÷ 0.5 = 32.5. Finally, 45% of 160 = 72, and 72 - 32.5 = 39.5.

Step-by-Step Solution

1
Evaluate the expression under the vinculum (bar)
\overline{4.2 + 1.8} = 6
The vinculum acts as a top-priority bracket, so the addition under the bar must be executed before other operations.
2
Simplify the innermost round brackets ( )
36 \div 3 - 6 = 12 - 6 = 6
Inside the round bracket, division precedes subtraction according to BODMAS.
3
Simplify the curly brackets { }
\frac{3}{4} \times 6 + 5.5 = 4.5 + 5.5 = 10
Inside the curly bracket, multiplication of fractions precedes addition.
4
Simplify the square brackets [ ]
12.5 + 10 \div 0.5 = 12.5 + 20 = 32.5
Inside the square bracket, division by decimal (10 / 0.5 = 20) takes precedence over addition.
5
Calculate the percentage term ('of' operation)
45\% \text{ of } 160 = 0.45 \times 160 = 72
The 'of' operation represents multiplication for percentage evaluation.
6
Perform the final subtraction
72 - 32.5 = 39.5
Subtract the fully simplified bracket result from the percentage term.

Key Concept

BODMAS / VBODMAS Rule with Nested Brackets, Percentages, and Vinculum
Estimated Time:2m 0s
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Topics

Simplification and BODMAS Rule

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