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Chapter 2: Problem 37

Which is greater, \(-5\) or \(|-5| ?\)

Short Answer

Expert verified
\(|-5|\) is greater than \-5\

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. Denoted as \(|a|\), it is always non-negative. For example, the absolute value of \-5\ is 5.
02

- Calculate Absolute Value

Calculate \(|-5|\). Since \-5\ is 5 units away from zero on the number line, \(|-5| = 5\).
03

- Compare Numbers

Compare \-5\ and \(|-5| \) using their values. \-5\ is negative, while \(|-5|\) is positive, making 5 greater. Therefore, \(|-5|\) is greater than \-5\

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of the number. For example, -5a lies 5 units to the left of zero on the number line.
Negative numbers are used to represent values below zero, such as temperatures below freezing, depths below sea level, or financial debts.
When comparing negative numbers, the number that is less negative is greater. For example,-3is greater than -5, because -3 is closer to zero on the number line.
Number Line
A number line is a straight, horizontal line with numbers placed at intervals along its length. It is commonly used to visualize numbers and their relationships.
On a number line, zero is the central point. Positive numbers are located to the right of zero, and negative numbers are to the left.
Here are some key points about the number line:
  • Zero is the origin and is neither positive nor negative.
  • Positive numbers get larger as you move to the right.
  • Negative numbers get smaller as you move to the left.
  • The further a number is from zero, the greater its absolute value.
Distance from Zero
The distance from zero is a way to measure how far a number is from zero on the number line. This distance is always non-negative and is known as the absolute value.
For instance, the absolute value of -5 is written as |-5| , and its value is 5. This is because -5 is 5 units away from zero, irrespective of direction.
Absolute value is essential when comparing the magnitude of numbers, especially when dealing with negative numbers. Example:
  • The absolute value of -3 is | -3 | = 3
  • The absolute value of 6 is | 6 | = 6
  • Therefore, | -3 | is greater than -3
  • so -3 is less than 6.

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Most popular questions from this chapter

A submarine descended from a depth of \(-528 \mathrm{m}\) to \(-1804 \mathrm{m}\) in a 2 -hr period. What was the average change in depth per hour during this time?

Simplify. $$-4^{4}$$

Subtract the integers using a calculator. \(104,839-(-24,938)\)

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-(b)$$

Simplify using the order of operations. $$-7+(1-5)^{2} \div 4$$
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