Problem 36 - Prealgebra

Question

Find each of the following absolute values. $$|7|$$

Step-by-Step Solution

Answer

The absolute value \(|7|\) is 7.

Step 1: Understanding the Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of the direction. Therefore, it is always non-negative.

Step 2: Applying the Absolute Value

Since the absolute value represents the distance from zero, for any positive number, like 7, the absolute value is the number itself.

Step 3: Writing the Solution

We conclude that since 7 is positive, the absolute value of 7 is simply 7. Thus, \(|7| = 7\).

Key Concepts

Positive Numbers

Positive numbers are those that are greater than zero. They are the numbers that you usually think of when counting, like 1, 2, 3, and so on. Positive numbers have a special importance when it comes to finding absolute values because their absolute values are quite straightforward:

• The absolute value of a positive number is the number itself.
• This is because positive numbers are already at a non-negative distance from zero on the number line.

For example, the number 7 is a positive number. Its absolute value, \( |7| \), is 7 itself. This holds true for any positive number you encounter.

Number Line

A number line is a visual tool that helps us understand the placement and value of numbers relative to each other. Think of it as a horizontal line with zero in the center, and all positive numbers to the right.
It's helpful in visualizing concepts like addition, subtraction, and absolute value:

• Each point on the line represents a real number, with positive numbers on the right side of zero.
• The absolute value of any number is easily seen as the distance from zero along this line.

For example, on a number line, the number 7 is located seven units to the right of zero. This visual representation makes understanding the concept of absolute value simpler and more intuitive.

Distance from Zero

Distance from zero refers to how far a number is from zero on the number line. This concept is the foundation of absolute value:

• No matter whether a number is positive or negative, its absolute value is always the distance from zero.
• This means that absolute values are always non-negative.

When a number is positive, like 7, the distance from zero and thus the absolute value is the number itself: \( |7| = 7 \).
Understanding distance from zero helps solidify why absolute values are always represented as non-negative, emphasizing the idea that they measure magnitude without considering direction.