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Zorluk: Çok zorSimplification and BODMAS Rule
Evaluate the following mathematical expression by strictly applying the BODMAS rule:
150% of 48−[14.5−{412×(12.8÷2.5+1.5‾−135)+2.8}]÷0.15150\% \text{ of } 48 - \left[ 14.5 - \left\{ 4 \frac{1}{2} \times \left( 12.8 \div \overline{2.5 + 1.5} - 1 \frac{3}{5} \right) + 2.8 \right\} \right] \div 0.15
What is the simplified numerical value?

Cevap: 42

Cevap

The simplified numerical value of the given mathematical expression is 42.
Following the strict BODMAS order of operations: Vinculum -> Round brackets -> Curly brackets -> Square brackets -> Division -> 'Of' -> Subtraction gives the exact result 42.

Adım Adım Çözüm

1
Evaluate the term under the vinculum (bar)
2.5 + 1.5 = 4
The vinculum has highest priority among grouping symbols.
2
Evaluate operations inside the round brackets (parentheses)
12.8 / 4 - 1.6 = 3.2 - 1.6 = 1.6
Division inside parentheses precedes subtraction, and 1 3/5 converts to decimal 1.6.
3
Evaluate operations inside the curly brackets
4.5 * 1.6 + 2.8 = 7.2 + 2.8 = 10
Multiplication precedes addition inside curly brackets, with 4 1/2 converting to 4.5.
4
Evaluate operations inside the square brackets
14.5 - 10 = 4.5
Subtract the evaluated inner expression from 14.5.
5
Perform the division following the bracket result
4.5 / 0.15 = 30
Division operation takes precedence over final subtraction.
6
Calculate the percentage 'of' expression
150% of 48 = (150 / 100) * 48 = 72
'Of' operation is evaluated before basic addition and subtraction.
7
Compute the final subtraction
72 - 30 = 42
Subtract the result of the bracketed division term from the percentage evaluation.

Anahtar Kavram

Order of Operations (BODMAS / PEMDAS) with Vinculum and Nested Brackets
Bu soruyu puanla

Konular

Simplification and BODMAS Rule

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