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Chapter 2: Problem 23

The following sets of integers, perform the following tasks: 1\. Plot each of the integers on a numberline. 2\. List the numbers in order, from smallest to largest. \(-2,-4,3\), and \(-6\)

Short Answer

Expert verified
Order: -6, -4, -2, 3.

Step by step solution

01

Understanding the Integers

We have the set of integers: \(-2, -4, 3, -6\). These numbers include both negative and positive integers.
02

Plotting on a Number Line

To plot these integers, we draw a horizontal line (a number line). Mark each integer's position relative to zero:- Start with \(-6\) on the far left, as it's the smallest.- Next, place \(-4\) to the right of \(-6\).- Then, plot \(-2\) further to the right.- Finally, \(3\) is placed further to the right as it's positive.
03

Listing the Integers in Order

Now, to arrange the integers from smallest to largest:- Start with \(-6\).- Follow with \(-4\).- Then \(-2\).- Finish with \(3\).Thus, the ordered list is \(-6, -4, -2, 3\).

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Key Concepts

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

Number Line
A number line is a visual tool that helps us understand the arrangement of numbers, especially when dealing with both positive and negative integers. Imagine it as a horizontal line, stretching infinitely in both directions. On this line:
  • Zero (0) is usually at the center, acting as a neutral point.
  • Numbers to the right of zero are positive (e.g., 1, 2, 3).
  • Numbers to the left of zero are negative (e.g., -1, -2, -3).
A number line helps illustrate the relative size of numbers. For example, -6 is placed much further to the left compared to 3. This spatial representation aids our understanding of how numbers compare to one another in value. Consider using a number line whenever you need to visualize negative and positive integers together.
Negative Numbers
Negative numbers are values less than zero, represented with a minus sign (-). They appear on the left side of zero on a number line, indicating that they are 'less than' any positive number. In practical terms:
  • Negative numbers often represent a deficiency or loss, like debt or temperature below zero.
  • The more negative a number is, the further it is from zero and the smaller its value. For instance, -6 is less than -4.
When visualizing negative numbers, always remember that they can sometimes be counterintuitive. They express a size in reverse, growing larger in their negative impact as they move leftward on the number line. Understanding negative numbers is crucial as they have wide-ranging applications in various fields, from finance to science.
Ordering Numbers
Ordering numbers involves placing them in a sequence based on their value. For integers, both positive and negative, the process involves comparing how they relate to zero and each other. Here are some key points to remember:
  • Negative numbers will always be smaller than positive numbers.
  • Among negative numbers, the number with the higher absolute value is considered smaller. For example, -6 is smaller than -4 because 6 is larger than 4.
  • While ordering, start with the smallest (most negative) number and move towards the largest (most positive) one.
With our given set, the numbers -6, -4, -2, and 3 were ordered from smallest to largest based on these principles. This skill is essential for handling data effectively and making informed observations in mathematics and other real-life scenarios.

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Most popular questions from this chapter

A student's bank account is overdrawn. After making a deposit of $$\$ 360$$, he finds that his account is still overdrawn by an amount of $$\$ 90 .$$ What was his balance before he made his deposit?

Solve the given equation for \(\mathrm{x}\). \( .-19 x-17=-36\)

The number \(-5\) is 8 more than an unknown number. Find the unknown number.

The number \(-6\) is 8 more than an unknown number. Find the unknown number.

Is 12 a solution of \(4 x+5=-8\) ?
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