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Chapter 1: Problem 61

Select the lesser of the two given numbers. $$ -|-6|,-|-4| $$

Short Answer

Expert verified
-6 is the lesser number.

Step by step solution

01

- Understand the Absolute Value

Absolute value \( |x| \) represents the distance of a number from 0 on the number line, without considering direction. For instance, \(|-6| = 6 \) and \(|-4| = 4\).
02

- Calculate the Absolute Values

Find the absolute values of the numbers inside the given expression. \(|-6| = 6\) and \(|-4| = 4\).
03

- Determine the Negative of the Absolute Values

Calculate the negative of the absolute values obtained. \(-|-6| = -6\) and \(-|-4| = -4\).
04

- Compare the Results

Compare the values obtained: -6 and -4. Since -6 is less than -4, -6 is the lesser number.

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Key Concepts

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

Negative Values
Negative values are numbers less than zero. They are often represented with a minus sign (-) in front of them. For instance, -3, -7, and -10 are all negative values. Negative values are simply the opposite of positive values.
When calculating with negative numbers, keep in mind:
* Subtracting a negative number is the same as adding its positive counterpart
* For example, \( -(-6) = 6 \) turns into \( 6 \)
Negative values are crucial in understanding how they behave in relation to one another, especially when comparing their magnitudes.
Number Line
A number line is a visual representation of numbers placed in order on a straight line. It helps to see the relative position of different values, including how values compare to each other. Positive numbers are found to the right of zero, while negative numbers are to the left. Each step on the number line represents an equal increase or decrease in value.
    * Zero is the midpoint of the number line for both positive and negative numbers
    * Numbers increase to the right and decrease to the left
    * Negative numbers are always less than zero and positive numbers
    For example, \( -4 \) is located four steps to the left of zero, whereas \( 6 \) is six steps to the right of zero.
Comparison of Numbers
When comparing numbers, we look at their position on the number line.
* If a number is to the left of another, it is lesser
* If a number is to the right of another, it is greater
Using the example \( -|-6| \) and \( -|-4| \), first calculate their absolute values:
* \( |-6| = 6 \)
* \( |-4| = 4 \)
Negate the absolute values:
* \( -|-6| = -6 \)
* \( -|-4| = -4 \)
When comparing \( -6 \) and \( -4 \) on the number line, \( -6 \) is to the left of \( -4 \). Therefore, \( -6 \) is the lesser number.

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Most popular questions from this chapter

Nadine Blackwood enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were \(-19,28,-5,\) and \(13 .\) What was her final score for the four turns?

Write a numerical expression for each phrase and simplify. \(20 \%\) of the product of \(-5\) and 6

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. $$ -17,34,9,-2 $$

Simplify each expression. $$ -\frac{5}{6}+8 x+\frac{1}{6} x-7-\frac{7}{6} $$

Simplify each expression. $$ -9 m^{3}+3 m^{3}-7 m^{3} $$
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