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Zorluk: Çok zorSimplification and BODMAS Rule
What is the simplified numerical value of the following mathematical expression when evaluated using the standard BODMAS rule?
240÷[212×{14−(312+25% of (14−1.8+2.2‾))}]240 \div \left[ 2 \frac{1}{2} \times \left\{ 14 - \left( 3 \frac{1}{2} + 25\% \text{ of } \left( 14 - \overline{1.8 + 2.2} \right) \right) \right\} \right]
  1. 12Cevap
  2. B
    16
  3. C
    768
  4. D
    8

Cevap

12
Following the strict hierarchical order of operations (BODMAS: Vinculum →\rightarrow Brackets →\rightarrow Orders →\rightarrow Division/Multiplication →\rightarrow Addition/Subtraction), the innermost vinculum 1.8+2.2‾\overline{1.8 + 2.2} evaluates to 44. Then 14−4=1014 - 4 = 10, and 25%25\% of 1010 equals 2.52.5. Adding this to 312(3.5)3 \frac{1}{2} (3.5) yields 66. Inside the curly brackets, 14−6=814 - 6 = 8. Inside the square brackets, 212(2.5)×8=202 \frac{1}{2} (2.5) \times 8 = 20. Finally, 240÷20=12240 \div 20 = 12.

Adım Adım Çözüm

1
Evaluate the expression under the vinculum (bar)
\overline{1.8 + 2.2} = 4
The vinculum acts as the innermost grouping symbol and must be simplified first.
2
Simplify the innermost parenthetical difference
14 - 4 = 10
Subtract the vinculum result from 14 within the round brackets.
3
Calculate the percentage of the result from Step 2
25\% \text{ of } 10 = \frac{25}{100} \times 10 = 2.5
'Of' represents multiplication in percentage evaluation.
4
Complete the evaluation inside the round brackets
3 \frac{1}{2} + 2.5 = 3.5 + 2.5 = 6
Convert the mixed fraction 3123 \frac{1}{2} to decimal 3.53.5 and sum with 2.52.5.
5
Evaluate the expression inside the curly brackets
14 - 6 = 8
Subtract the round bracket total from 14.
6
Simplify the expression inside the square brackets
2 \frac{1}{2} \times 8 = 2.5 \times 8 = 20
Multiply the mixed fraction 2122 \frac{1}{2} by the curly bracket result.
7
Perform the final division outside the brackets
240÷20=12240 \div 20 = 12
Divide 240 by the completely simplified value of the square brackets.

Anahtar Kavram

BODMAS Rule with Vinculum and Multi-level Brackets
Bu soruyu puanla

Konular

Simplification and BODMAS Rule

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