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Zorluk: ZorSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated using the standard BODMAS rule?
60% of 350−[514+{36÷(4.5−2.1+0.9‾)}]×460\% \text{ of } 350 - \left[ 5 \frac{1}{4} + \left\{ 36 \div \left( 4.5 - \overline{2.1 + 0.9} \right) \right\} \right] \times 4
  1. 93Cevap
  2. B
    100
  3. C
    169
  4. D
    723

Cevap

The simplified numerical value of the given expression is 93.
Following the BODMAS rule: first evaluate the vinculum \(\overline{2.1 + 0.9} = 3\), then the round bracket \(4.5 - 3 = 1.5\), then the curly bracket \(36 \div 1.5 = 24\), then the square bracket \(5.25 + 24 = 29.25\). Next, evaluate the percentage term \(60\% \text{ of } 350 = 210\) and the product \(29.25 \times 4 = 117\). Finally, subtracting 117 from 210 gives 93.

Adım Adım Çözüm

1
Evaluate the expression under the vinculum bar
\overline{2.1 + 0.9} = 3.0
The vinculum (bar) has the highest priority inside nested grouping symbols.
2
Evaluate the terms inside the round brackets
4.5 - 3.0 = 1.5
Subtract the result of the vinculum from 4.5 inside the round brackets.
3
Evaluate the division inside the curly brackets
36÷1.5=2436 \div 1.5 = 24
Perform division within the curly braces.
4
Evaluate the addition inside the square brackets
5 \frac{1}{4} + 24 = 5.25 + 24 = 29.25
Convert the mixed fraction to decimal (5.25) and add to 24.
5
Calculate the percentage term and multiplication term
60\% \text{ of } 350 = \frac{60}{100} \times 350 = 210 \quad \text{and} \quad 29.25 \times 4 = 117
According to BODMAS, percentage/off and multiplication must be computed before final subtraction.
6
Perform the final subtraction
210 - 117 = 93
Subtract the multiplied bracket result from the percentage value.

Anahtar Kavram

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

Konular

Simplification and BODMAS Rule

Bu konudan daha fazla soru