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Zorluk: OrtaOrder of Operations

What is the exact numerical value of the following mathematical expression?

∣−18∣−72+45−9 |-18| - 7^2 + \frac{45}{-9}

Cevap: -36

Cevap

The correct numerical value is -36.
To evaluate the expression, follow the order of operations strictly. First, resolve the absolute value: |-18| becomes 18. Next, evaluate the exponent: 7^2 becomes 49 (note that the negative sign is separate from the squared base). Then, perform the division: 45 divided by -9 equals -5. Finally, perform the remaining subtraction and addition from left to right: 18 - 49 equals -31, and -31 + (-5) yields the final answer of -36.

Adım Adım Çözüm

1
Evaluate the absolute value.
|-18| = 18
Absolute value acts as a grouping symbol and must be processed first, returning the non-negative distance from zero.
2
Evaluate the exponential term.
7^2 = 49
Exponents are evaluated before multiplication, division, addition, and subtraction. The negative sign is outside the base, so only the 7 is squared.
3
Evaluate the division.
45−9=−5\frac{45}{-9} = -5
Division and multiplication are evaluated before addition and subtraction.
4
Evaluate addition and subtraction from left to right.
18 - 49 + (-5) = -36
Addition and subtraction hold the same precedence and are solved strictly from left to right as they appear.

Anahtar Kavram

Order of Operations with signed numbers, absolute value, and exponents
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Konular

Order of Operations

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