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Chapter 7: Problem 10

Find the absolute value. $$|-15|$$

Short Answer

Expert verified
The absolute value of \(-15\) is 15.

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always a non-negative number. In mathematical terms, the absolute value of a number \( a \) is represented as \( |a| \).
02

Apply Absolute Value Definition

For the number \(-15\), the absolute value \(|-15|\) is simply the distance from 0, which means you remove the negative sign to get a positive value. Thus, \(|-15| = 15\).
03

Verify Your Solution

To verify, ensure that when you take the absolute value of \(-15\), you have followed the rule of making the result non-negative. Since \(15\) is the positive equivalent, \(|-15| \) indeed equals 15.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Number Line
The number line is a simple yet powerful visual tool used to represent numbers. It is a straight line where each point corresponds to a number.
This line extends infinitely in both directions, with zero positioned in the center.
To the right of zero are positive numbers, and to the left are negative numbers.
  • Zero acts as a critical reference point on the number line.
  • Each unit on the number line signifies an equal distance away from the previous number.
  • Numbers increase as you move right and decrease as you move left.
When calculating the absolute value, we are primarily concerned with the number's position relative to zero on this line.
Whether a number is positive or negative, the absolute value represents how far it is from zero along the number line.
What is a Non-Negative Number?
Non-negative numbers are figures that are greater than or equal to zero.
This group includes all positive numbers and zero itself.
They do not include any negative values, which is a key characteristic when talking about absolute values.
  • Examples of non-negative numbers include: 0, 3, 27, and 145.
  • Non-negative numbers are central to the concept of absolute value, as the result of an absolute value is always non-negative.
By understanding non-negative values, you grasp that when we calculate an absolute value, we're ensuring no negative sign affects our outcome.
This transformation is why the absolute value of "-15" becomes "15".
Exploring the Distance from Zero
The term "distance from zero" is central to understanding absolute values.
In mathematics, distance is always non-negative, which means it can be zero or positive but never negative.
This applies to how we measure a number's absolute value: it is a measure of how far a number is from zero on the number line.
  • Consider the number "-15"; its position is 15 units to the left of zero.
  • Its absolute value ignores direction, simply reflecting the numeric distance, which is 15.
  • This process underscores that absolute value only concerns itself with a number's magnitude, not its sign.
Whenever you see \(|-15|\), know that you're only finding how far \(-15\) is from zero, making the answer a positive 15.

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