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Chapter 1: Problem 45

Simplify by finding the absolute value. $$ -|12| $$

Short Answer

Expert verified
-12

Step by step solution

01

Understand Absolute Value

The absolute value of a number is its distance from 0 on the number line, regardless of direction. This means that the absolute value of a positive number is the number itself, and the absolute value of a negative number is its positive counterpart.
02

Find the Absolute Value

Identify the absolute value of 12. Since 12 is already positive, \( |12| = 12 \).
03

Apply the Negative Sign

Now, apply the negative sign to the absolute value found in the previous step, \( -|12| = -12 \).

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Key Concepts

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

absolute value properties
The absolute value of a number refers to how far it is from zero on the number line, without considering its direction. Think of it as measuring the number鈥檚 distance from zero. Absolute values have a few key properties:

鈥� The absolute value of a positive number is the number itself (e.g., \( |5| = 5 \)).
鈥� The absolute value of a negative number is its positive counterpart (e.g., \( |-7| = 7 \)).
鈥� The absolute value of zero is zero (e.g., \( |0| = 0 \)).

Knowing these properties helps us solve and simplify expressions that involve absolute values efficiently.
number line
A number line is a visual tool used to understand the placement and order of numbers. It is a straight horizontal line where each point corresponds to a number, and the distance between the points is consistent.

On a number line:

鈥� Positive numbers are located to the right of zero.
鈥� Negative numbers are located to the left of zero.
鈥� Zero is the central point.

Using a number line can simplify the process of finding absolute values by visually representing the distances from zero. For example, on a number line, you can clearly see that both \( 12 \) and \( -12 \) are 12 units away from zero, helping you understand why \( |-12| = 12 \).
simplifying expressions
Simplifying expressions often involves combining like terms and following the order of operations, which can include using the properties of absolute values.

In the given exercise, the steps to simplify \( -|12| \) were:

1. Determine the absolute value of \( 12 \). Since \( 12 \) is positive, \( |12| = 12 \).
2. Apply the negative sign to the absolute value found: \( -|12| = -12 \).

By understanding and applying these steps, you break down complex expressions into simpler parts, making them easier to solve.

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Most popular questions from this chapter

Simplify each expression. $$ -\frac{7}{5}(t-15)-\frac{1}{2} t $$

Write a numerical expression for each phrase and simplify. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number, added to the sum of the number and six

Write a numerical expression for each phrase and simplify. The quotient of \(-12\) and the sum of \(-5\) and \(-1\)

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. All even integers between \(-18\) and \(4,\) inclusive
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