Examkin

Question

Difficulty: MediumOrder of Operations

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

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

Answer: -36

Answer

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.

Step-by-Step Solution

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.

Key Concept

Order of Operations with signed numbers, absolute value, and exponents
Rate this question

Topics

Order of Operations

More questions from this topic