Introduction: Connecting Your Learning

Mathematics is commonly described as the global language. With the overwhelming popularity of social media, this is ending up being increasingly clear. You cannot communicate via others from various walks of life without the common language of mathematics driving your Internet connection, relocating satellites, or translating words.

Additionally, human being cannot map the earth from smartphones without computer system programmers to generate mathematical algorithms to administer this modern technology. If you pick to go after a career in information modern technology, whether it is in security, netfunctioning, mobile applications, or geospatial innovation, you will need a details level of mathematical understanding.

In this leschild, you will learn how real numbers are ordered, just how many type of categories of numbers exist, and mathematical symbolism that enables you to conveniently compare or categorize numbers.

Focusing Your Learning

Leskid Objectives

By the end of this leskid, you must be able to:

Distinguish in between variables and also constants. Classify numbers into their appropriate sets/subsets. Order genuine numbers.


Variables and Constants

A basic difference in between algebra and arithmetic is the use of icons. In algebra, icons (normally letters) are supplied to recurrent numbers. To solve math troubles, you should recognize what variables and also constants are. Here is an introduction to the terms variables and constants.

A variable is a letter or symbol supplied as a placeholder for an unrecognized value.

You are watching: A symbol used to represent a number

What"s a Variable?

A constant can be a letter or a symbol that represents a fixed number.

What"s a Constant?

Look at 2 examples of cases in which letters are substituted for numbers.

Example 1

Suppose that a student is taking 3 technology-associated classes.

Each specific class can have one exam per week at a lot of. Thus, in any kind of one-week period, the student might have 0, 1, 2, or 3 exams for the 3 classes. In algebra, the letter X deserve to recurrent the number of exams the student may have in a one-week duration. The letter X is a variable because it have the right to recurrent any kind of of the numbers: 0, 1, 2, 3.

Example 2

Suppose you have to report the complete variety of software program programs used in the computer system lab during the spring semester at your college.

Because you carry out not know this number off the top of your head, you decide to recurrent it (at leastern temporarily) through the letter S. Later, you make a list of the obtainable software programs and include up the total number. You discover tbelow are a complete of salso computer software application programs being used. The letter S, which represents this number then, is 7. Since S cannot recurrent any other values, the worth S is continuous.

Watch the following videos about variables and also constants. You will check out added examples that deserve to help you get a far better expertise of these brand-new principles.

Math Video Toolkit

Variables and Constants

Variables, Expressions, and Equations

Real Numbers

Before learning about actual numbers and the aspects that comprise genuine numbers, you will certainly first learn around the genuine number line.

The research of math calls for the use of numerous collections of numbers. The genuine number line enables you to visually display screen (graph) the numbers you are interested in.

A line is created of infinitely many type of points. To each suggest you can associate a distinctive number, and also via each number, you deserve to associate a details allude.

The adhering to words are used to define points on a actual number line.

Coordinate The number connected through a point on the number line is referred to as the coordinate of the point.


The point on a number line that is linked through a certain number is dubbed the graph of that number.

How Do I Construct a Real Number Line?

Here are 3 procedures to follow to create a real number line.

Draw a horizontal line.


Mark the beginning.

Choose any type of allude on the line and also label it 0. This point is referred to as the beginning.


Choose a convenient length. Starting at 0, note this size off in both direc­tions, being mindful to make the lengths around the very same size.


Now that you have produced a number line, it is time check out just how points on a number line are defined.

Real Numbers

A genuine number is any type of number that is the coordinate of a point on the actual number line.

Positive Numbers, Negative Numbers

Real numbers whose graphs are to the ideal of 0 are dubbed positive genuine numbers, or more simply, positive numbers. Real numbers whose graphs show up to the left of 0 are referred to as negative real numbers, or negative numbers.


The number 0 is neither positive nor negative.

Watch the video for an easy explacountry of positive and also negative numbers on a genuine number line.

What Are Positive and also Negative Numbers?

Subsets of Real Numbers

The collection of actual numbers has actually many kind of subsets. Below is a diagram of genuine numbers. You will watch the terms natural, totality, integers, rational, and irrational numbers which are sets of genuine numbers.


Natural Numbers, Counting Numbers

The letter (N) is the symbol used to reexisting organic numbers. Natural numbers are additionally known as counting numbers, and they start with the number 1 and also proceed to infinity (never before ending), which is represented by 3 dots (...).

The herbal or counting numbers (N): 1, 2, 3, 4 . . . "and so on."


Whole Numbers

The letter (W) is the symbol supplied to recurrent totality numbers. Whole numbers are counting numbers from 0 to infinity.

The entirety numbers (W): 0, 1, 2, 3, 4 . . .


Notice that eextremely herbal number is a totality number.


The letter (Z) is the symbol supplied to represent integers. An integer have the right to be 0, a positive number to infinity, or an unfavorable number to negative infinity.

The integers (Z): . . . -3, -2, -1, 0, 1, 2, 3 . . .


Notice that eexceptionally entirety number is an integer.

Watch the adhering to video to get a far better expertise of integers.

What Is an Integer?

Rational Numbers (Fractions)

The letter (Q) is the symbol that is provided to reexisting rational numbers. Rational numbers are occasionally called fractions. They are numbers that can be written as the quotient of 2 integers. They have actually decimal depictions that either terminate or execute not terminate however contain a repeating block of digits. Some examples are below:

= − 0.75 Terminating


Some rational numbers are graphed listed below.


Notice that eincredibly integer is a rational number.

You will certainly alert a great many type of points on the number line that are not questioned. These numbers comprise the irrational numbers. They will certainly be examined in detail in an algebra course. An instance of an irrational number is π (pi), whose decimal depiction does not terminate nor contain a repeating block of digits. An approximation for π is 3.14.

Example: Real Numbers

Is eextremely whole number a herbal number?

No. The number 0 is a entirety number, yet it is not a natural number.

Is tbelow an integer that is not a natural number?

Yes. Some examples are 0, −1, −2, −3, and −4.

Is tright here an integer that is a whole number?

Yes. In truth, eincredibly whole number is an integer.

Now it is your revolve to exercise. Try answering the adhering to inquiries on your very own and then choose Check Answers to view just how well you did.


Is every natural number a whole number? Is eexceptionally totality number an integer? Is every integer a real number? Is tright here an integer that is a whole number? Is tright here an integer that is not a organic number?

Check Answers

Yes Yes Yes Yes Yes

Watch the adhering to video for an easy overview of the subsets of genuine numbers through examples to assist you use your brand-new understanding.

Subsets of Real Numbers


Complete the complying with interactive task to test your knowledge.

Real Numbers Practice Exercise

Ordering Real Numbers

Etop quality Symbols

You know what the equal symbol indicates and looks choose.

If a = b, then a and b are equal, (8 = 8).

To learn around ordering actual numbers, think about it this way.

If a genuine number b is higher than a real number a, their partnership would look like this:

b > a, and b is to the appropriate of a on the number line

Here is an example:

5 > 2 because 5 is to the best of 2 on the number line

−2 > −5 since −2 is to the right of −5 on the number line.

-5, and also on the left side is 5 > 2.">

Inetop quality Symbols

It is necessary to learn what each inequality symbol means because they are offered to order numbers. Take a look at the chart listed below.

Inehigh quality Symbols

What does the symbol mean?

Example 1

Example 2

Example 3


is higher than

a > b

a is higher than b

(8 > 5)


Example 1

What integers can replace x so that the adhering to statement is true?

−3 ≤ x Draw a number line that exhas a tendency from −4 to 4.

Place points at all whole numbers in between and consisting of −1 and also 4.

Check Answers


Practice Draw a number line that exoften tends from −4 to 3.

Place points at all whole numbers between and also consisting of −2 and also 2.

See more: Things Get A Little Easier Once You Understand Song, Think (Band)

Check Answers



It is time to practice on your own. Select the connect below to occupational on exercise troubles and then select the connect to the options to see just how well you did.

Variables, Constants, Real Number Practice Problems

Solutions: Variables, Constants, Real Numbers Practice Problems

Watch the adhering to videos to view additional examples that have the right to help you acquire a much better knowledge of these new concepts.

What Is an Inequality?

Inequalities: Order on a Real Number Line

Summarizing Your Learning

In this leschild, you have actually been presented to basic components of an useful link in between societies referred to as mathematics. You have actually watched the distinction in between variables (ever-transforming components in math) and also constants. You have also checked out that numbers are categorized, and also even more importantly, you have checked out that some numbers autumn right into multiple categories. At the conclusion of this leskid you were presented to the inetop quality symbol (, ≥).

As you progression with mathematics you will see how crucial these symbols are to the people of information modern technology, particularly to procedures that call for algorithms, a step-by-step procedure, or direct programming.

Lastly, as you end up being acquainted with new signs or terms, you are motivated to take time to research just how each specific principle relates to the field of study you have chosen.

Assessing Your Learning


Now that you have actually check out over the lesson very closely and attempted the exercise problems, it is time for a expertise inspect. Please note that this is a graded component of this module so be sure you have ready yourself prior to beginning.