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Chapter 3: Problem 6

Simplify the following problems. $$ |8| $$

Short Answer

Expert verified
Answer: The absolute value of 8 is 8.

Step by step solution

01

Recognize the Absolute Value notation

In the given expression, the "|" symbol represents the absolute value. The expression asks for the absolute value of the number 8.
02

Find the distance from zero

The number 8 is already a positive number, and its distance from zero is 8 units. There is no need to change the sign of the number.
03

Write the simplified expression

Since the number 8 is already a positive number, its absolute value remains the same. Thus, the simplified expression is: $$ 8 $$

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Key Concepts

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

Positive Numbers
Positive numbers are numbers greater than zero. They can be thought of as having a value that is added to zero, moving to the right on a number line. For example, in the exercise above, the number 8 is a straightforward example of a positive number, as it lies to the right of zero.

Positive numbers are often used in everyday situations, such as when measuring quantities like distance, time, and money. When dealing with absolute values, if the number inside the absolute value symbols is positive, the result remains the same, because the absolute value of a positive number is the number itself.

  • Always consider positive numbers as adding value or moving forward on a scale.
  • The absolute value operation is straightforward for positive numbers because it doesn't change their value.
Distance from Zero
The concept of distance from zero is integral when understanding absolute value. Absolute value measures how far a number is from zero on a number line, regardless of direction. For example, both 8 and -8 are 8 units away from zero, so their absolute values are both 8.

This distance is always a non-negative number, as distance cannot be negative. In the given exercise, since 8 is already a positive number, its distance from zero is simply 8 units.

  • Distance from zero helps determine the absolute value of both positive and negative numbers.
  • Understanding this makes it easier to visualize number placement on a number line.
Simplifying Expressions
Simplifying expressions involves reducing complex expressions to their simplest form. In the case of absolute values, it means finding the simplified result. If the expression is in the form |x| and x is positive or zero, the simplification is essentially x itself.

The goal is to make the expression easier to understand and work with, showing the absolute value directly without additional operations. In the exercise, |8| is simplified to 8 because 8 is already a positive number, meaning it is its own absolute value.

  • Look for opportunities to simplify expressions by recognizing patterns and basic mathematical rules.
  • An expression is fully simplified when no more arithmetic operations can be performed.

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Most popular questions from this chapter

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