Problem 47 - Prealgebra

Question

Find each of the following absolute values. $$|8|$$

Step-by-Step Solution

Answer

The absolute value of 8 is 8.

Step 1: Understanding Absolute Value

The absolute value of a number is the distance of that number from zero on the number line, without considering direction. It is always a non-negative number.

Step 2: Identify the Absolute Value of 8

Given the number 8, we need to find its absolute value. Since 8 is a positive number, its absolute value is the number itself.

Step 3: Final Answer

The absolute value of 8 is 8 because the distance of 8 from zero is 8 units.

Key Concepts

Exploring the Number Line

The number line is a visual representation where every point corresponds to a real number. Imagine it as an infinite straight line stretching in both directions.
On this line, numbers to the right of zero are positive, while those to the left are negative. Zero sits right in the center.
A helpful way to visualize numbers and their absolute values:

• Each point on the line marks a specific number.
• The space between points is equal, representing consistent increments of 1 unit.
• Positive numbers extend to the right of zero.
• Negative numbers extend to the left of zero.
• The number line helps in quickly determining the absolute value by observing how far a number is from zero, regardless of direction.

Understanding the number line is fundamental in grasping the concept of absolute value and aids in visualizing distances effectively.

Understanding Positive Numbers

Positive numbers are values greater than zero, appearing on the right side of the number line. They give us a sense of quantifiable addition or increase in value.
Here’s what to remember about positive numbers:

• They are represented without a plus sign (+) as the sign is implied.
• Commonly used in everyday contexts like temperature, height, distance, and counting objects.
• When determining absolute value, if a number is positive, its absolute value is simply the same number.

In our exercise, the number 8 is positive, and therefore, its absolute value remains 8. Understanding and identifying positive numbers is crucial when working with numerical properties like absolute value.

Calculating the Distance from Zero

The absolute value is essential for identifying how far a number is from zero on the number line, regardless of whether it's positive or negative.
This concept highlights:**Distance from Zero**:

• The absolute value of any number is its distance from zero.
• It is always non-negative, as it measures a magnitude.
• No matter the direction on the number line, the focus is solely on how many units away a number is from zero.
• The notation with vertical bars, such as \( |8| \), signifies this distance.

In our specific example, the distance of 8 from zero is 8 units. Thus, the absolute value \( |8| \) equals 8. Recognizing this distance helps solidly grasp absolute value by showing its reliance on numerical placement, not direction.