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Chapter 1: Problem 61

Select the lesser of the two given numbers. \(-|-6|,-|-4|\)

Short Answer

Expert verified
-6 is lesser than -4. Hence, \(-|-6|\) is lesser.

Step by step solution

01

Identify the Absolute Values

First, find the absolute values of the given numbers. The absolute value of \(-6\) is \(|-6| = 6\), and the absolute value of \(-4\) is \(|-4| = 4\).
02

Negate the Absolute Values

Next, negate the absolute values obtained in the previous step. This gives \(-|6| = -6\) and \(-|4| = -4\).
03

Compare the Negative Values

Compare the two negative values: \(-6\) and \(-4\). A smaller number in terms of value is \(-6\), because it is further left on the number line.

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Key Concepts

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

absolute values
Absolute values indicate how far a number is from zero on the number line, regardless of direction. They are always non-negative. For any number, whether it is positive or negative, the absolute value will be positive.
For example, the absolute value of \(-9\) is \(|-9| = 9\).
When we work with absolute values, we often use these steps:
  • Identify the given number.
  • Ignore the negative sign if there is one.
  • The result is the absolute value.
So, the absolute value of a negative number like \(-4\) is just \(|-4| = 4\). In the same way, the absolute value of a positive number like 5 is \(|5| = 5\).
This helps when comparing the magnitude of numbers without worrying about their sign.
negative numbers
Negative numbers are numbers less than zero. They are very important in understanding mathematical concepts, especially for comparisons.
When comparing negative numbers, the one that is further from zero is considered smaller. This is because on the number line, numbers get smaller as they move left.
  • For instance, \(-6\) is less than \(-4\) because it is further to the left on the number line.
  • Thus, in the given exercise, \(-6\) is smaller than \(-4\).
Negative numbers are used to represent values below a certain point, like temperatures below freezing or elevations below sea level.
number line
A number line is a visual representation of numbers placed in order along a straight line. It is a useful tool for understanding number relationships and operations.
Here are some key features:
  • Zero is usually placed in the center.
  • Positive numbers are placed to the right of zero.
  • Negative numbers are placed to the left of zero.
When comparing numbers on a number line, the position to the left indicates a smaller value, and the position to the right indicates a larger value.
Therefore, if we look at \(-6\) and \(-4\) on a number line, \(-6\) is to the left of \(-4\), meaning it is the lesser number by value.

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Most popular questions from this chapter

Solve each problem. 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?

In August, Susan Goodman began with a checking account balance of \(\$ 904.89\). Her checks and deposits for August are as follows: $$ \begin{array}{|r|r|} \hline \text { Checks } & \text { Deposits } \\ \hline \$ 35.84 & \$ 85.00 \\ \$ 26.14 & \$ 120.76 \\ \$ 3.12 & \\ \hline \end{array} $$ Assuming no other transactions, what was her account balance at the end of August?

Find each difference. $$ 3.4-(-8.2) $$

Write a numerical expression for each phrase and simplify. The sum of 12 and \(-7,\) decreased by 14

To find the average (mean) of a group 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. \(-15,29,8,-6\)
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