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Chapter 1: Problem 101

Simplify. $$ |20| $$

Short Answer

Expert verified
The absolute value of 20 is 20.

Step by step solution

01

Identify the Absolute Value

Observe that you are asked to calculate the absolute value of 20. Absolute value is the distance of a number from zero on the number line, regardless of direction. Therefore, \(|20|\) represents the absolute value of 20.
02

Simplify the Absolute Value

For positive numbers, the absolute value is the number itself because the distance from zero is simply the number. Therefore, \(|20| = 20\).

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Key Concepts

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

Number Line
The number line is a visual representation that helps us understand the position and relationships between numbers. It's like an imaginary tape measure for math, where each point on the line corresponds to a real number. This line extends infinitely in both directions, with zero typically placed in the center.

Here's how the number line can be broken down:
  • To the right of zero, we have positive numbers.
  • To the left of zero, we find negative numbers.
  • The further right you move, the larger the number gets.
  • Conversely, moving left means numbers become smaller.
The number line is essential for understanding absolute values, as it visually shows how far a number is from zero, regardless of what direction you're going.
Positive Numbers
Positive numbers are more than just numbers bigger than zero; they represent quantities, values, or magnitudes. Everyday examples include counting objects, measuring heights, and recording temperatures above zero. On the number line, positive numbers are situated to the right of the zero.

Characteristics of positive numbers include:
  • They have no negative signs.
  • They're used in addition and multiplication to show gain or increase.
  • They reflect positive movement on the number line, or progress.
In the context of absolute value, positive numbers make it easy because their distance from zero is their own value, allowing quick simplification like \(|20| = 20\).
Distance from Zero
The concept of distance from zero is crucial in understanding absolute value. It refers to how far a number is from the point marked as zero on the number line. Absolute value, denoted by vertical bars like \(|x|\), measures this distance without considering direction. This means:

  • A positive number's absolute value is the number itself.
  • A negative number's absolute value is its positive counterpart.
  • Zero has an absolute value of zero, as it is at its own starting point.
Using distance from zero tells us that no matter if you move left or right from zero, what matters is the magnitude of that move. For example, both \(|20|\) and \(|-20|\) equal 20, illustrating the distance focus of absolute value.

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