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Chapter 1: Problem 56

Select the lesser of the two given numbers. $$ -16,-17 $$

Short Answer

Expert verified
-17

Step by step solution

01

- Understand the Concept of Negative Numbers

In the number line, numbers to the left are less than numbers to the right. This also means that for negative numbers; the one with a larger absolute value is actually smaller.
02

- Compare the Given Numbers

Compare the two numbers given: -16 and -17. Among negative numbers, the number with the smaller absolute value (-16 has a smaller absolute value than -17) is greater.
03

- Select the Lesser Number

Since -17 has a larger absolute value than -16, it is actually the lesser number. Hence, -17 is less than -16.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers that are less than zero. They are represented with a minus sign (-). Negative numbers are found to the left of zero on a number line.
For example, -1, -5, and -100 are all negative numbers. In everyday life, you might think of negative numbers when considering temperatures below zero or finances indicating debt.
It is important to understand that the more negative the number, the smaller its value. Thus, -17 is smaller than -16 because -17 is further left on the number line.
Number Line
A number line is a visual representation of numbers placed on a straight line. It helps in understanding the order and value of different numbers.
On a number line, numbers increase as you move to the right and decrease as you move to the left. Here is how it looks:
-20,..., -3, -2, -1, 0, 1, 2, 3,..., 20.
Zero is the central point, with positive numbers to the right and negative numbers to the left. To compare negative numbers, remember that the further to the left a number is, the smaller it is. This makes it easier to compare numbers like -16 and -17 by simply checking their positions on the number line.
Absolute Value
The absolute value of a number is its distance from zero on a number line, without considering direction.
The absolute value is always a non-negative number. For example, the absolute value of both -5 and 5 is 5, denoted as \(|-5| = 5\).
Comparing negative numbers with absolute values can help understand their sizes. For instance, \(|-17| = 17\) and \(|-16| = 16\).
Although 16 is less than 17, because -17 has a larger absolute value, it is actually the smaller number in a negative context. This is an important principle when comparing and ordering negative numbers.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 3 is \(-3\)

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. \(23,18,13,-4,\) and \(-8\)

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. $$ -15,29,8,-6 $$

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

Write a numerical expression for each phrase and simplify. The sum of \(-18\) and \(-6,\) divided by the product of 2 and \(-4\)
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