Problem 39 - Elementary Algebra

Question

39\. \(|25|\)

Step-by-Step Solution

Answer

25

Step 1: Understand the Problem

The exercise requires finding the absolute value of 25.

Step 2: Define Absolute Value

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

Step 3: Apply the Absolute Value Rule

Since 25 is already a positive number, its absolute value is simply 25. That is \(|25| = 25\).

Key Concepts

Absolute Value Definition

Absolute value is a fundamental concept in mathematics. It is often represented by two vertical bars around a number, like this: \(|a|\). The absolute value of a number refers to its distance from zero on a number line, without considering the direction. This means it is always a non-negative number, whether the original number is positive, negative, or zero.

For example, \(|-5|\) is 5 because -5 is 5 units away from zero. Likewise, \(|5|\) is also 5 because it is 5 units away from zero in the positive direction. Absolute value helps in understanding distances and magnitudes without worrying about direction.

Positive Numbers

Understanding positive numbers is essential for grasping the concept of absolute value. A positive number is any number greater than zero. These numbers lie to the right of zero on a number line. Examples include 1, 2, 3, and so on.

When finding the absolute value of a positive number, like in the exercise \( |25| \), you simply get the same number because it is already a distance from zero without needing to change its sign. Therefore, \( |25| = 25 \). Positive numbers, by definition, are straightforward when dealing with absolute values because they do not need to change anything about their nature.

Number Line Distance

A number line is a visual representation of numbers placed at equal intervals on a straight line. It helps in understanding the concept of absolute value through the idea of distance. The number line extends infinitely in both positive and negative directions from zero.

To find the absolute value using a number line, you measure how far a number is from zero. Distance on a number line is always positive since it's a measure of how much space is between two points without regard to direction. For instance, the distance of 25 from zero is 25 units, hence \(|25| = 25\). Practicing with a number line can improve your grasp of absolute values and positions of numbers.