/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 Find each absolute value and sim... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 52

Find each absolute value and simplify if needed. $$ -|12.4| $$

Short Answer

Expert verified
-12.4

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, the absolute value of both positive and negative numbers will be positive.
02

- Calculate the Absolute Value

Find the absolute value of 12.4. Since 12.4 is a positive number, its absolute value is simply 12.4. Hence, \(|12.4| = 12.4\).
03

- Apply the Negative Sign

The original problem has a negative sign outside the absolute value. Thus, we apply this negative sign to the absolute value we calculated: \(-|12.4| = -12.4\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

number line
To fully understand absolute value, it's important to grasp the concept of a number line. A number line is a straight, horizontal line with numbers placed at intervals along its length. The center of the line is typically marked with zero. Positive numbers are located to the right of zero, and negative numbers are to the left. The further you move from zero, the larger the absolute value of the number becomes. For example:
  • Numbers like 1, 2, and 3 are positive and are placed to the right of zero.
  • Numbers like -1, -2, and -3 are negative and are to the left of zero.
Understanding this layout helps in visualizing the concept of 'absolute value.' Whether a number is positive or negative, its absolute value is simply its distance from zero, without considering direction.
positive numbers
Positive numbers are those greater than zero and appear on the right side of the number line. They do not have a negative sign in front of them. For example, 5 is a positive number, while -5 is not. When considering the absolute value of a positive number, it remains unchanged. For instance:
  • The absolute value of 3 is written as \(|3| = 3\).
  • Even for decimal numbers, like 12.4, the absolute value remains the same: \(|12.4| = 12.4\).
Positive numbers are straightforward in terms of absolute value, as their distance from zero is exactly their numerical value.
negative sign
A negative sign, denoted by '-', indicates a value is less than zero and is located to the left of zero on the number line. For example, -2 is two units to the left of zero. When calculating the absolute value, the negative sign is ignored because we're only interested in the distance from zero. However, if there is a negative sign outside an absolute value, it must be considered after finding the absolute value.
Let's consider the step-by-step solution for the given problem, \(-|12.4|\):
  • First, find the absolute value of 12.4, which is 12.4 (since it's positive).
  • Next, apply the negative sign outside the absolute value: \-|12.4| = -12.4\.
By following these steps, you can correctly apply the negative sign after calculating the absolute value.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each expression. $$ 6|4-5|-24 \div 3 $$

Find each square root. If it is not a real number, say so. $$ -\sqrt{400} $$

Simplify each expression. $$ |-6-5|(-8)-3^{2} $$

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 47 \% $$

Use an inequality symbol to write each statement. $$ 5+14 \text { is greater than or equal to } 19 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.