Evaluate the following.

$\begin{array}{r}
|-6|=\square \\
|9|=\square
\end{array}$

The absolute value of a number is its distance from zero.
The distance of -6 from 0 is 6, so ∣ − 6∣ = 6 .
The distance of 9 from 0 is 9, so ∣9∣ = 9 .
Therefore, the answers are 6 ​ and 9 ​ .

Explanation

Understanding Absolute Value We need to find the absolute values of -6 and 9. The absolute value of a number is its distance from zero on the number line.

Calculating |-6| The absolute value of -6, written as ∣ − 6∣ , is the distance between -6 and 0. Since distance is always non-negative, ∣ − 6∣ = 6 .

Calculating |9| The absolute value of 9, written as ∣9∣ , is the distance between 9 and 0. Therefore, ∣9∣ = 9 .


Examples
Absolute values are used 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 navigation, the distance to a destination is an absolute value, as direction is handled separately. Understanding absolute values helps in quantifying magnitudes and distances without considering direction.

Answered by GinnyAnswer | 2025-07-05