Problem 79 Find the absolute value of the n... [FREE SOLUTION]

Chapter 3: Problem 79

Find the absolute value of the number. $$-4$$

Short Answer

Expert verified

The absolute value of -4 is 4.

Step by step solution

Understand the concept of absolute value

The absolute value of a number is its distance from zero on a number line. It's always positive or zero as distance cannot be negative.

Identify the number and its sign

As -4 is a negative number, its absolute value will be found by removing the negative sign.

Find the absolute value

The absolute value of -4, which is denoted as $|-4|$, is 4. This is because the distance of -4 from zero on the number line is 4 units.

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Key Concepts

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

Understanding the Number Line

A number line is a visual representation that helps us easily understand numbers and their relationships. It stretches infinitely in both directions with a zero in the center.

On the right side of zero, we have positive numbers, and on the left, negative numbers. This layout helps us to see how numbers relate to one another.

Zero serves as the starting point or the origin.
Each number is evenly spaced, making it easy to compare different values.
The number line is a tool to visualize the absolute value, which is the distance between any number and zero.

By using a number line, you can easily see that negative and positive numbers are equidistant from zero, providing a clear understanding of absolute values.

Decoding Negative Numbers

Negative numbers are values less than zero, and they are written with a minus sign in front. They appear on the left side of the zero on the number line. Understanding negative numbers is key to grasping the concept of absolute value.

Negative numbers represent things like debt, temperatures below freezing, or losing points in a game.
They allow us to express values less than nothing, which is essential in various applications and real-life situations.
On the number line, negative numbers are opposite their positive counterparts, but at the same distance from zero.

By removing the negative sign, we find their absolute value, which is always positive or zero.

Grasping Distance from Zero

Distance from zero is a fundamental idea in understanding absolute values. It measures how far a number is from zero on the number line. This distance is always positive because distance itself cannot be negative.

For any number $ x $, the absolute value is written as $|x|$.
For example, the absolute value of $-4$ is $|-4| = 4$, as it is 4 units away from zero.
This concept helps us simplify the comparison of numbers, regardless of whether they are positive or negative.

By focusing on the distance from zero, students can better understand why absolute values aim to express non-negative measurements.

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91影视

Find the absolute value of the number. $$-4$$

Short Answer

Step by step solution

Understand the concept of absolute value

Identify the number and its sign

Find the absolute value

Key Concepts

Understanding the Number Line

Decoding Negative Numbers

Grasping Distance from Zero

One App. One Place for Learning.

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