Practical Algebra: A Self-Teaching Guide by Peter H. Selby

A Self-Teaching Guide by Peter H. Selby

If you studied algebra years ago and now need a refresher course in order to use algebraic principles on the job, or if you’re a student who needs an introduction to the subject, here’s the perfect book for you. Practical Algebra is an easy and fun-to-use workout program that quickly puts you in command of all the basic concepts and tools of algebra. With the aid of practical, real-life examples and applications, you’ll learn

  • the basic approach and application of algebra to problem solving
  • the number system (in a much broader way than you have known it from arithmetic)
  • Monomials and polynomials; factoring algebraic expressions; how to handle algebraic fractions; exponents, roots, and radicals; linear and fractional equations
  • Functions and graphs; quadratic equations; inequalities; ratio, proportion, and variation; how to solve word problems, and more.

Autors Peter Selby and Steve Slavin emphasize pratical algebra throughout by providing you with techniques for solving problems in a wide range of disciplines – from engineering, biology, chemistry, and the physical sciences, to psychology and even sociology and business administration. Step by step, Practical Algebra shows you how to solve algebraic problems in each of these areas, then allows you to tackle similar problems on your own, at your own pace. Self-tests are provided at the end of each chapter so you can measure your mastery.

Peter Selby (deceased) was Director of Educational Technology at Man Factors Associates, a human factors engineering consulting firm. He is the author of two other self-teaching guides: Quick Algebra Review: A Self-Teaching Guide and Geometry and Trigonometry for Calculus: A Self-Teaching Guide, both published by Wiley.

Steve Slavin, PhD, is Associate Professor of Economics at Union County College, Cranford, New Jersey. He has written over 300 newspaper and magazine articles, and is the author of four other books, including All the Math You’ll Ever Need: A Self-Teaching Guide and Economics: A Self-Teaching Guide, both published by Wiley.

An excerpt from the book:

To achieve maximum benefit from this program you need to proceed logically from where you are now in your knowledge of mathematics to where you should be at the end of this program. And since we have assumed that you are familiar with the subject of arithmetic, we will start there.

Algebra is a logical outgrowth of arithmetic and many of the methods of arithmetic are used in algebra, although in modified, expanded, or original form. This chapter will provide a bridge from arithmetic to algebra for the reader who has not studied algebra before. It will also furnish a review for those who, although they perhaps had a first-year high school course in algebra, have largely forgotten what they once knew.

When you complete this chapter you should be able to:

  • express the product of factors without the use of multiplication signs;
  • identify the literal factors in an algebraic term;
  • use letters and symbols to change simple word statements into algebraic expressions;
  • determine what value of the letter(s) in the denominator of an algebraic fraction would result in an undefined division;
  • use parentheses correctly to express multiplication or grouping of terms;
  • evaluate algebraic expressions;
  • correctly identify terms in an algebraic expression;
  • use exponents to indicate repeated multiplication;
  • simplify elementary algebraic expressions.

… Buy this book to read it in full

Postulates for the natural numbers

natural number

Every natural number a has a successor a + 1. (For example, the successor of 5 if 6, the successor of 10 is 11, and so on.)

Every natural number a (except 1) has a predecessor a – 1. (The predecessor of 4 is 3, the predecessor of 9 is 8, and so on.)

The natural numbers can be put in order. In other words, if a and b are two natural numbers, then either a is greater than b (written a > b), a is less than b (a < b), or a is equal to b (a = b.)

The order doesn’t make a difference (commutative) property of addition: a + b = b + a (for any two given numbers a and b).

The order doesn’t make a difference (commutative) property of multiplication: a x b = b x a (for any two given numbers a and b).

The where you put the parentheses doesn’t make a difference property of addition: (a + b) + c = a + (b + c). For any three numbers a, b, and c. (This property is known as the associative property of addition, because it says that it doesn’t matter which numbers associate with each other.) For example,

(5 + 4) + 3 = 5 + (4 + 3)
(9) + 3 = 5 + (7)
12 = 12

The where you put the parentheses doesn’t make a difference (associative) property of multiplication: (a x b) x c = a x (b x c). For any three numbers, a b, and c. For example,

(2 x 6) x 4 = 2 x (6 x 4)
(12) x 4 = 2 + (24)
48 = 48

Precedence rules for arithmetic expressions

When an expression contains more than one type of operation, perform the operations in the following order:

Top priority: an operation inside parentheses. For example, in the expression 8 x (7 + 6), perform the addition before the multiplication, 8 x (7 + 6) = 8 x 13 = 104.

Second priority: exponentiations. For example, in the expression 4 x 32, perform the exponentiation before the multiplication. 4 x 32 = 4 x 9 = 36

Third priority: multiplications and divisions. For example, in the expression 8 + 7 x 6, perform the multiplication before the addition. 8 + 7 x 6 = 8 + 42 = 50.

Fourth priority: additions and subtractions.

When an expression contains more than one operation with the same priority, perform the operations in order from left to right. For example, here is how we work out this expressions:

7 + 3 x 6 – 4 x 2 + 9

Calculate 3 x 6 first:

7 + 18 – 4 x 2 + 9

Next, calculate 4 x 2:

7 + 18 – 8 + 9

Next, calculate 7 + 18:

25 – 8 + 9

Next, calculate 25 – 8:

17 + 9

The final result is 17 + 9 = 26.

Algebra I for Dummies by Mary Jane Sterling

Algebra I for Dummies by Mary Jane Sterling

Algebra I for Dummies is a book by Mary Jane Sterling who has taught mathematics at Bradley University since 1979, and has also taught math at the high school and junior high school levels. Algebra I for Dummies provides a pain-free way to explore algebra and believe the reviewers, you would come out smiling. Does the word polynomial make your hair stand on end? Relax! Let Mary Jane Sterling show you the easy way to tackle algebra. This friendly guide explains the basic – and the toughest stuff – in easy-to understand, no-nonsense language. Whether you want to brush up on your math skills or help your children with their homework, this book gives you power – to the nth degree.

Algebra I for Dummies helps you discover how to:

  • Find out about fractions and explore exponents
  • Figure out factoring
  • Solve linear equations
  • Factor quadratic equations
  • Graph equations
  • Solve story problems

If you’re looking for help with some of the basic tools of algebra, you can find that type of information in the first part of the book. Think of these tools as being like what a cook needs. You can’t cook a couffle unless you know how to whisk the eggs and turn on the oven. Your success later depends on your preparation. Of course, you may be beyond these basics. Great! How about the second part?

In the second part, the writer spends a lot of time explaining factoring. Factoring is really no more than changing what the expression looks like. And the factored form is one where everything is all multiplied together. You can find which of the factoring techniques you need to brush up on if you get stuck with a problem.

And where are the equations, you may ask. In Part III, the author gives you any type of equation you desire, in order from simplest to most complex. More rules and methods are added as the equations get more difficult. The author also throws in inequalities for good measure.

Part IV covers a good deal of the answer to the question, “What is this algebra stuff used for?” The applications in these chapters are more on the practical side – discussing things you may actually experience.

The Part of Tens serves as a nice set of lists of game plans. You may need only one thing in the list, or you may run down through the whole thing, in order. Use them as you wish.

Have fun with this. Think of this book as being like a computer’s “Help” button. If you have a problem, you can find the answer (hopefully, better explained than some of those computer “helps”).

Algebra I for Dummies by Mary Jane Stering is available from at US$ 13.59.

How are expressions formed?

Algebra 2

We know very well what a variable is. We use letters x, y, l, m, … etc. to denote variables. A variable can take various values. Its value is not fixed. On the other hand a constant has a fixed value. Examples of constant are: 4, 100, -17, etc.

We combine variables and constants to make algebraic expressions. For this we use the operations of addition, subtraction, multiplication and division. We have already come across expressions like 4x + 5, 10y -20. The expression 4x + 5 is obtained from the variable x, first by multiplying x by the constant 4 and then adding the constant 5 to the product. Similarly, 10y – 20 is obtained by multiplying constant 10 with variable y and then subtracting 20 from the product.

The above expressions were obtained by combining variables with constants. We can also obtain expressions by combining variables with themselves or with other variables.

Look at how the following expressions are obtained:

x2, 2y2, 3x2 – 5, xy, 4xy + 7

  • The expression x2 is obtained by multiplying the variable x by itself;
    x x x = x2Just as 4 x 4 = 42, we write x x x = x2. It is commonly read as x squared. In the same manner, we can write
    x x x x x = x3

    Commonly, x3 is read as x cubed which can also be read as x raised to the power 3.

  • The expression 2y2 is obtained from y: 2y2 = 2 x y x y
    Here by multiplying y with y we obtained y2 and then we multiply y2 by the constant 2.
  • In (3x2 – 5) we first obtain x2 and multiply it by 3 to get 3x2. From 3x2, we subtract 5 to finally arrive at 3x2 = 5.
  • In xy, we multiply the variable x with another variable y. Thus, x x y = xy.
  • In 4xy + 7, we first obtain xy, multiply it by 4 to get 4xy and add 7 to 4xy to get the expression.

Algebra Survival Guide by Josh Rappaport

The Algebra Survival Guide

The Algebra Survival Guide comes with an Algebra Wilderness “Bored Game” that gives children a fun way to practice their lessons and also with a tear-out Emergency Fact Sheet poster with all of algebra’s secret rules and formulas at your fingertips. The book has been written by Josh Rappaport who has been a winner of the Outstanding Young Educator award, is a teacher and a tutor in Santa Fe, New Mexico. Josh runs an online community at to help students and parents to overcome the fears of algebra.

Algebra Survival Guide begins its conversation with What is algebra?, its Properties & Sets of Numbers and gradually steps further to Positive & Negative Numbers, Order of Operations & Like Terms, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Equations, Coordinate Plane & Word Problems.

The book very well defines algebra as a branch of mathematics that performs the magic trick – it takes something that’s unknown and poof! – turns it into something known. Algebra does this by using letters (variables) to stand for mystery numbers, and giving you a process to let you discover the value of the variables. The book lays the following reasons to study & learn algebra:

  • Studying algebra boosts your chances of going to college and succeeding in today’s world. Studies show that taking algebra, and following it with geometry, dramatically boosts a student’s chance of going to college. In fact, a 1990 College Board study found that students who take algebra and geometry stand a much greater chance of attending college than students who don’t take these courses. And, of course, to succeed in today’s high-tech/information-age economy, you must have a good education.
  • Learning algebra can help you find a good-paying job. Anyone who wants to work in any field of science – computer science, astronomy, medicine, psychology, genetics, etc – needs to know algebra. That’s because all the science rely on algebra and on the higher maths.
  • Knowing algebra will help you survive the “big, bad world.” Understanding algebraic ratios helps you become a smart comparison shopper; understanding percentages helps you make sense of the statistics thrown at you by the media. The ways to use algebra are numerous.
  • Algebra teaches you to solve difficult problems. By developing your algebraic mental muscles, you strengthen your ability to tackle problems in life, for learning algebra improves your ability to think clearly.
  • Learning algebra teaches you about yourself. Since algebra is a product of the human mind, studying algebra gives you insight into how your own mind works. Learning this subject shows the logical thought patterns that are part of you just because you’re human.

Find below some reviews given by journals & magazines for The Algebra Survival Guide:

  • What the Survival Guide does is make algebra approachable, even without a teacher. In some ways, it even makes algebra simple. – Shasta Parent Magazine
  • The unique and user-friendly Algebra Survival Guide is here to save the day! It is well organized, and easy to understand. – Bay Area Parent Magazine
  • The Algebra Survival Guide will help calm the nerves of any student lost in the letters and numbers of algebra. – Mathematics Teacher, a journal of the National Council of Teachers of Mathematics
  • The Algebra Survival Guide will help students navigate the sea of confusion many find in the ‘Algebra Wilderness.’ – L. A. Parent Magazine

The Algebra Survival Guide by Josh Rappaport can be bought in US$ 13.57 from

A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1 by Rong Yang


The A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1 by Rong Yang includes topics on Algebra such as Real Numbers, Decimals, Number Theory, Fractions, Percents, Equations, Functions & Graphs, Factoring, Inequalties & Absolute Value, Systems of Equations, Systems of Inequalities, Radicals, Quadratic Equations, Quadratic Functions, Rational Expressions and Statistics & Probability along with standardized sample questions & tests.

The book can be best used for SAT, ACT, NTE, CBEST, STAR TEST & HS EXIT and outlines the concepts, formulas & theorems in Algebra. With over 18,000 simple & complex examples and exercises, the book facilitates the learning process in problem solving. Rong Yang, the author of A-Plus Notes for Beginning Algebra, has written other books as well such as A-Plus Notes for Algebra, A-Plus Notes for Algebra 2 and Pre-Calculus and A-Plus Notes for SAT Math.

An excerpt from the book:

Real numbers are the one which can be located on the number line. Each point on the number line is called the graph of the number on the line. The number is called the coordinate of the point. The coordinate of point A is -5. The graph of -5 is point A. The graph of 0 is the point called origin. The coordinate of the origin is 0. Real numbers include rational numbers and irrational numbers.

Rational numbers can be written as the ratio of two integers. 0.1 = 1/10, 0.5 = 5/10, 1.2 = 12/10 = 6/5, 0.1 = 1/9, 0.54 = 54/99 = 6/11. Every rational number can be expressed as either a terminating decimal or as a repeating decimal.

Irrational numbers cannot be written as the ratio of two integers. They are nonterminating (infinite), nonrepeating decimals.

Integers are positive integers, negative integers & zero. Zero is an integer, neither positive nor negative.

Positive Integers are numbers which we use to count objects such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. They are also called natural numbers or counting numbers.

Whole numbers: They are 0 and positive integers. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …)

Prime numbers are whole numbers, other than 0 and 1, which are only divisible by 1 and themselves. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41…)

Composite numbers are whole numbers other than 0 and 1 which are not prime numbers. (4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30,…)

On a number line, the numbers to the right of the origin are positive, and the numbers to the left of the origin are negative. On a number line, the number on the right is greater than the number on the left.

Rule of rounding: When an exact computation is not needed for the answer of a problem, we use the rules of rounding to estimate numbers. We can round each number to the nearest 10, 100, 1000,… It depends on how accurate the answer we need. If the digit to the right of the digit to be rounded is 5 or more, we round up by increasing the digit to be rounded by 1 and replacing the digits to the right with zeros. If the digit to the right of the digit to be rounded is less than 5, we round down by leaving the digit to be rounded the same and replacing the digits to the right with zeros.

The book can be bought in US$ 13.26 from

How to Find the Best Algebra II Tutor Online Tutoring Service

Algebra 3

Find qualified and reliable Algebra II tutor can be a daunting task for any parent. This short article will describe what you as a parent should look for when hiring an Algebra II tutor for your child.

The Tutor really know the subject?

The first thing to find a tutor in Algebra II is a person who is familiar with the material and whose background includes a vast pre-calculus and calculus. The reason is that the teacher needs to understand mathematics or Algebra II students to adequately assist with problems and challenges him. The ultimate goal is to prepare students for future assignments, quizzes, tests, and finals, plus more complex math courses. For this reason, peer tutoring is not always as effective as professionals to teach tutoring.

The Guardian “click” with students?

It is essential that the guardian may be relevant to the student. This should be done in two ways. First, the teacher be able to convey difficult material to students in a way that he or she will be easy to understand. The guardian must be able to use technology and the graphing calculator to help students understand the equations and inequalities, and various types of functions, including the second degree polynomials, reciprocity, radical, exponential and logarithmic. Secondly, the teacher can talk to students in an attractive manner that encourages him to solve problems and work independently in the long term. This result is obtained when the tutor is to strengthen the confidence of students by strengthening weaknesses which may include fractions, rational functions, or even negative numbers. Unless the student weaknesses to be addressed, he or she will have a tough time to shine with more complex issues in the future.

What to know about your child’s Tutor

It is extremely important that the guardian must be informed about the strengths and weaknesses before the student tutoring are held. They are not only the ability of mathematics, but also for potential learning problems or other things that students learn the new materials can affect. Of course, the instructor teaches a lot about the progress of the student in the tutoring. An expert teacher will be able to gain the confidence of the student and the organization of aid and the workload of each day before strategist.


Finally, in finding the best tutor Algebra II, the parent must choose a guardian who is very familiar with the subject well and works well with the student. In addition, the parents also make sure to talk to the teacher about the learning style of students and all the strong points or zwakke, he or she be make in mathematics.

Math Tutoring – Problems Need to be Divided Or it Would Be Multiply

Algebra 4

Mathematics is the most common topic that students need a mentor. Not everyone has a mathematical ability, so teachers are often needed in this area. When a child to school they begin to learn the basics of addition, subtraction, multiplication, division, and the majority of children, these areas very well. Then there are fractions, decimals and percentages.

But the areas that most students need help to algebra, geometry, trigonometry and calculus. These are the areas most requested for a mentor. What’s so great about this problem is the need for teachers. It’s a supply and demand, your child needs help with the subject and because the demand is so high, teachers in mathematics, more than ever.

When your child to help in such areas as algebra needs, they receive the help they need. The basis for a good leader will start from the beginning, although they may be beyond that point in the school. Return to the top of the child, their time to the concept of algebra to understand. It is very important because if one guardian picks up where your child is learning at school, you might as well money out the window. The reason why your child has difficulty because they do not understand the full concept of the object. At the beginning and slowly explain that your child really understand why X + Y = Z

Without understanding the basics of the subject especially in mathematics, you’re never enough to understand the object to pass. At some point you wonder if you ask a parent, I want my child to get one in the subject or I want them to pass gewoon. The latter is what many parents choose to do so. But she can not understand why the right choice to leave, it gives the child the idea as long as I play enough, I can pass. They must learn to excel in everything they do.

It has to be understood that not all kids have an aptitude for math but you want your child to try as hard as they can to do the best that they can. When you send out the message as a parent you can get tutoring to help you pass then when the child moves onto the next subject they will again study just to pass

Tutoring is a long way from a teacher to help their students after school. There is so much help available for your child. You teachers of local colleges and universities, a tutor of a service or even register your child for a learning center after school. The help is there for the taking.

Homework help and Online Algebra Assignments

Algebra 6

Do you need help with algebra? We know how we can help! Our online help is the algebra for you. We will respond to your request promptly and with pleasure. Algebra help is needed throughout the world. And we believe our customers are always satisfied with our online help algebra and we only get positive feedback.

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Algebra is considered one of the main branches and more important in the mathematics that covers areas such as the structure, relation and quantity.

Algebra covers not only the number but also the atmosphere of symbols, variables and elements shown.

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Learn Algebra With Algebra Games

Algebra Games

One of the best ways to teach children and they think they are just playing through games. Algebra is an easy subject, but the children quickly understand the basics. Some children just do not want to do because it is difficult and boring. Many parents have this problem with their children.

Play Games algebra is a great way to teach kids to count on a playful and fun way. This will allow them to spend time on the subject and also keep their interest high. In this lens you can find information about the various games that you can use algebra to help your child improve their math exams.

There are some great equation solving games on the Internet. Here is a list of some of them I found. I’ll add more as I find.

1) Comparison Buster – This is a very interesting game that will surely help you get the concepts of solving equations to obtain. You will also learn to solve equations in the minimal steps. There are four levels in this game according to the difficulty. Level 1 is the easiest and Level 4 is the hardest.

2) These equations by balancing – You have to decide which mathematical symbol. After determining the symbol write the value you think the comparison easier. It is similar to previous game. You can even create your own equations and solve them.

3) Solve the equation and post letters – This is a simple game. You’re a mailman and your letters to supply houses. A comparison will be written on the door and a dog comes out of the window holding the value “a”. Replacement of the value, finding the correct number and click on the appropriate letter. There are three levels of hardness in this game.

4) Plot Equations – Write the equation that you want to plot and plot key hit. You get a good understanding of how the various equations plot. If you can not think of a comparison and then press the random button, then plot that equation.

5) Equations and a millionaire quiz game – where you must type the correct answer from four choices to choose. You get some money if you give the right answer.

6) Math succeed – In Internet-based Software Program Subscriptions Create Personalized Tutoring Plans for each student to improve Math Skills, Increase Grades and test scores. The bilingual program creates a solid foundation in Math Fundamentals Middle school.
Problem Solving Games

Here are some interesting problems solving games:

1) Algebra Puzzle – A good puzzle game to test your algebra resolution. You need the value of the three objects in the puzzle.

2) Find two numbers -, You will definitely like this. First you are shown an example problem is solved for you. It shows step by step audio and video. Then you get a similar problem.

3) Gamequarium – Algebra interactive games.

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