Which expression has the greatest absolute value?
$|-9|$
$|17|$
$|-15|$
$|5|$

Calculate the absolute value of each expression: ∣ − 9∣ = 9 , ∣17∣ = 17 , ∣ − 15∣ = 15 , ∣5∣ = 5 .
Compare the absolute values: 9, 17, 15, 5.
Identify the greatest absolute value: 17.
The expression with the greatest absolute value is: ∣17∣ ​ .

Explanation

Understanding the Problem We are given four expressions involving absolute values: ∣ − 9∣ , ∣17∣ , ∣ − 15∣ , and ∣5∣ . The absolute value of a number is its distance from zero on the number line. Our goal is to determine which expression has the greatest absolute value.

Calculating Absolute Values Let's calculate the absolute value of each expression:


∣ − 9∣ = 9 ∣17∣ = 17 ∣ − 15∣ = 15 $|5| = 5

Comparing Absolute Values and Finding the Greatest Now, we compare the absolute values we calculated: 9, 17, 15, and 5. The largest of these values is 17. Therefore, the expression with the greatest absolute value is ∣17∣ .

Examples
Understanding absolute values is crucial in many real-world scenarios. For example, when measuring errors in experiments, we often care about the magnitude of the error, not its direction (positive or negative). Similarly, in finance, the absolute value can represent the volatility of an investment, indicating how much the price fluctuates regardless of whether it goes up or down. This concept helps in risk assessment and decision-making.

Answered by GinnyAnswer | 2025-07-08

The expression with the greatest absolute value is ∣17∣ since its absolute value is 17, which is greater than the others: 9, 15, and 5.
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Answered by Anonymous | 2025-07-29