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Zorluk: OrtaOrder of Operations

Evaluate the following expression:

12−2[32−(5−8)]+412 - 2[3^2 - (5 - 8)] + 4

What is the value of the expression?

  1. -8Cevap
  2. B
    4
  3. C
    -16
  4. D
    124

Cevap

-8
Following the order of operations, the innermost parentheses (5 - 8) evaluate to -3. The exponent 3^2 evaluates to 9. The bracket becomes [9 - (-3)], which simplifies to 12. Multiplying this by 2 yields 24. Finally, evaluating 12 - 24 + 4 from left to right gives -12 + 4, which equals -8.

Adım Adım Çözüm

1
Evaluate the innermost parentheses: (5−8)(5 - 8).
(5−8)=−3(5 - 8) = -3
According to the order of operations, innermost grouping symbols must be resolved first.
2
Evaluate the exponent inside the bracket: 323^2.
32=93^2 = 9
Exponents are evaluated before subtraction inside the grouping symbols.
3
Simplify the expression inside the bracket: [9−(−3)][9 - (-3)].
9−(−3)=9+3=129 - (-3) = 9 + 3 = 12
Subtracting a negative number is equivalent to adding its positive value.
4
Perform the multiplication: 2[12]2[12].
2×12=242 \times 12 = 24
Multiplication takes precedence over addition and subtraction.
5
Perform addition and subtraction from left to right: 12−24+412 - 24 + 4.
12−24=−1212 - 24 = -12, then −12+4=−8-12 + 4 = -8
Addition and subtraction have the same precedence and must be evaluated strictly from left to right.

Anahtar Kavram

Order of Operations (PEMDAS/BODMAS) and integer arithmetic
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Konular

Order of Operations

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