Introduction: Connecting your Learning

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Mathematics is generally referred to as the universal language. Through the overwhelming popularity of society media, this is coming to be increasingly clear. You cannot interact with others from miscellaneous walks of life there is no the usual language of math driving your web connection, moving satellites, or translating words.

Furthermore, civilization cannot map the planet from smartphones without computer programmers to create mathematical algorithms to administer this technology. If you pick to go after a career in details technology, whether it is in security, networking, cell phone applications, or geospatial technology, you will need a details level of mathematics knowledge.

In this lesson, you will certainly learn how real numbers space ordered, how countless categories of numbers exist, and mathematical symbolism that enables you to easily compare or categorize numbers.

concentrating Your Learning


Lesson Objectives

By the finish of this lesson, you should be maybe to:

Distinguish between variables and also constants. Divide numbers right into their proper sets/subsets. Order real numbers.

Presentation

Variables and also Constants

A basic distinction between algebra and also arithmetic is the usage of symbols. In algebra, icons (usually letters) are supplied to stand for numbers. To solve math problems, girlfriend should recognize what variables and constants are. Right here is an advent to the terms variables and constants.


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

You are watching: What does n mean in algebra

What"s a Variable?


A continuous can it is in a letter or a symbol that represents a fixed number.

What"s a Constant?


Look in ~ two examples of instances in i m sorry letters space substituted for numbers.


Example 1

Suppose the a student is taking 3 technology-related classes.

Each specific class deserve to have one test per week in ~ most. Therefore, in any kind of one-week period, the college student may have actually 0, 1, 2, or 3 exams for the 3 classes. In algebra, the letter X have the right to represent the number of exams the student may have in a one-week period. The letter X is a variable due to the fact that it deserve to represent any of the numbers: 0, 1, 2, 3.

Example 2

Suppose you must report the total variety of software programs provided in the computer lab throughout the spring semester at your college.

due to the fact that you execute not recognize this number off the height of her head, you decision to stand for it (at least temporarily) v the letter S. Later, you make a perform of the obtainable software programs and include up the total number. You find there room a full of seven computer software programs gift used. The letter S, which represents this number then, is 7. due to the fact that S cannot represent any other values, the value S is constant.

Watch the complying with videos about variables and also constants. You will certainly see extr examples that can help you acquire a far better understanding that these new concepts.

Math video clip Toolkit

Variables and Constants

Variables, Expressions, and also Equations


Real Numbers

prior to learning around real numbers and the aspects that make up real numbers, you will an initial learn about the real number line.

The study of mathematics requires the usage of several collections the numbers. The real number line allows you to visually display (graph) the numbers you are interested in.

A heat is written of infinitely plenty of points. Come each allude you have the right to associate a unique number, and with every number, you deserve to associate a specific point.

The complying with words are supplied to explain points ~ above a genuine number line.


Coordinate The number linked with a point on the number heat is dubbed the coordinate of the point.


Graph

The point on a number line that is connected with a certain number is dubbed the graph of the number.


How do I construct a genuine Number Line?

here are three procedures to monitor to develop a actual number line.

draw a horizontal line.

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mark the origin.

Choose any allude on the line and label it 0. This suggest is called the origin.

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select a practically length. Starting at 0, note this length off in both direc­tions, being careful to do the lengths around the same size.

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Now that you have developed a number line, that is time see just how points ~ above a number line room defined.


Real Numbers

A actual number is any kind of number the is the name: coordinates of a suggest on the actual number line.


Positive Numbers, an adverse Numbers

actual numbers whose graphs room to the ideal of 0 are dubbed positive real numbers, or much more simply, hopeful numbers. Actual numbers who graphs appear to the left of 0 space called an unfavorable real numbers, or an adverse numbers.

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The number 0 is neither optimistic nor negative.


clock the video clip for a basic explanation of positive and negative numbers top top a genuine number line.

What Are confident and negative Numbers?


Subsets of genuine Numbers

The collection of real numbers has numerous subsets. Below is a chart of genuine numbers. Friend will see the state natural, whole, integers, rational, and also irrational numbers which are sets of actual numbers.


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Natural Numbers, count Numbers

The letter (N) is the symbol used to represent natural numbers. Organic numbers are likewise known together counting numbers, and they begin with the number 1 and continue come infinity (never ending), i beg your pardon is represented by 3 dots (...).

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

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Whole number

The letter (W) is the symbol supplied to represent totality numbers. Totality numbers space counting numbers from 0 come infinity.

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

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Notice the every natural number is a totality number.


Integers

The letter (Z) is the symbol used to represent integers. An integer can be 0, a confident number come infinity, or a an adverse number to negative infinity.

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

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Notice that every entirety number is an integer.


Watch the following video to gain a better understanding of integers.

What Is an Integer?


Rational Numbers (Fractions)

The letter (Q) is the symbol the is provided to stand for rational numbers. Reasonable numbers are sometimes referred to as fractions. They are numbers that have the right to be composed as the quotient of 2 integers. They have actually decimal representations that one of two people terminate or perform not terminate but contain a repeating block the digits. Some examples are below:

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= − 0.75 Terminating

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some rational numbers are graphed below.

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Notice the every creature is a reasonable number.


You will notification a good many point out on the number line that space not discussed. These numbers comprise the irrational numbers. They will certainly be check in information in one algebra course. An example of one irrational number is π (pi), who decimal representation does no terminate no one contain a repeating block of digits. An approximation for π is 3.14.


Example: genuine Numbers

Is every whole number a natural number?

No. The number 0 is a whole number, however it is not a natural number.

Is there an integer the is not a herbal number?

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

Is there an integer that is a whole number?

Yes. In fact, every entirety number is an integer.


Now that is your rotate to practice. Try answering the adhering to questions on your own and also then pick Check Answers come see just how well friend did.


Practice

Is every herbal number a totality number? Is every whole number one integer? Is every integer a genuine number? Is there an integer that is a entirety number? Is over there an integer the is not a natural number?

Check Answers


correctly Yes correct Yes correct

Watch the following video for a an easy overview of the subsets of actual numbers with examples to help you apply your new knowledge.

Subsets of genuine Numbers


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complete the following interactive task to test her knowledge.

genuine Numbers practice Exercise


Ordering actual Numbers

Equality Symbols

You recognize what the same symbol method and looks like.

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

to learn about ordering real numbers, think around it this way.

If a genuine number b is greater than a real number a, their partnership would look prefer this:

b > a, and also b is come the ideal of a top top the number line

right here is an example:

5 > 2 since 5 is to the appropriate of 2 top top the number line

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

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


Inequality Symbols

it is crucial to find out what each inequality symbol method because they are used to order numbers. Take a look at the graph below.

Inequality signs

What does the symbol mean?

Example 1

Example 2

Example 3

>

is better than

a > b

a is higher than b

(8 > 5)

b.


Example 1

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

−3 ≤ x attract a number line that extends from −4 to 4.

place points in ~ all whole numbers between and also including −1 and 4.

Check Answers


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Practice attract a number line the extends indigenous −4 come 3.

place points at all whole numbers between and including −2 and 2.

See more: What Would Happen If Nobody Voted For President, Frequently Asked Questions

Check Answers


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It is time to exercise on her own. Choose the link listed below to work-related on practice problems and then choose the attach to the remedies to see exactly how well girlfriend did.

Variables, Constants, genuine Number practice Problems

Solutions: Variables, Constants, real Numbers exercise Problems


Watch the following videos come see extr examples the can aid you gain a better understanding the these brand-new concepts.

What Is one Inequality?

Inequalities: bespeak on a actual Number Line

Summarizing Your discovering

In this lesson, you have been introduced to straightforward components that a valuable link in between societies called mathematics. You have actually seen the difference between variables (ever-changing contents in math) and constants. Friend have also seen the numbers are categorized, and much more importantly, you have seen that some numbers fall into lot of categories. In ~ the conclusion of this lesson you were presented to the inequality symbol (, ≥).

As you progress through mathematics you will view how vital these symbols are to the human being of details technology, particularly to procedures that require algorithms, a step-by-step procedure, or straight programming.

Lastly, as you end up being acquainted with new symbols or terms, you are encouraged to take it time to research just how each particular concept relates to the ar of research you have actually chosen.

Assessing your Learning

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Now that you have actually read end the lesson carefully and attempted the practice problems, that is time because that a understanding check. Please note that this is a graded part of this module therefore be sure you have actually prepared yourself prior to starting.