This is a virtual edition of an elementary algebra textbook with some review of real numbers and arithmetic. It is intended to be used online, although portions, such as the exercises and summaries, may be printed. When printing, please reduce the zoom level to avoid printing excessive pages. The font size is large for ease of online classroom use. It is too large for the printed page.




  Each Module (B through H) is broken down into various sections in much the same way as a textbook’s chapters are segmented into sections. Each section has a main lesson titled after the section name, a supplementary lesson providing students with additional examples and practice, an exercise section intended for student homework and a section with answers to those homework problems. Some sections have additional lessons, summaries and supplements. The last section in each module contains review exercises, answers to the review exercises, a practice test and answers to the practice test. These are intended for student use in test preparation.


Detailed Table of Contents (TOC) Hierarchy


Algebra is Vital

by Leslie Elizabeth Buck is licensed under a

Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License




To the Student


To the Instructor


A. Why study Algebra?

An optional, motivational presentation or argument for the necessity of the algebra experience is provided here.


B. Review of the Fundamental Operations of Real Numbers


1. Mathematical symbols and notation

One lesson reviewing basic symbols and notation; no exercises or supplement


1.7 Whole numbers

Whole numbers

Supplementary examples




2. Sets of numbers

Sets of numbers

Supplementary examples




Most sections appear as the above two examples; only those sections that differ from this format will be detailed below;


3. Basic properties of real numbers


Includes an additional section:

Summary of the properties of Reals – a printable summary or a quick web reference for students


4. Operations of signed numbers


5. Graphing of signed numbers

    No supplement;

5.3 Arithmetic with decimals


5.5 Percents


5.7 Arithmetic with fractions


6. Order of operations


7. Absolute value

No supplement;

8. Review

Review exercises

Answers to review exercises

Practice test

Answers to practice test


All review sections appear as above;


C. Linear Equations and Inequalities


1. Solving linear equations


Includes an additional/optional lesson:

Like terms


1.7 Units of measurements

Includes an additional, printable section:

Summary of conversion factors and prefixes


1.9 Basic geometry

Includes an additional, printable section:

Summary of formulas


2. Solving verbal problems and applications

Includes two additional, printable sections:


Problem solving procedure

English to math translation


3. Solving simple linear inequalities


4. Basic formula manipulations


5. Review


D. Graphing and Systems of Linear Equations


1. The Cartesian coordinate system


2. Graphs of linear equations


3. Definition of slope, parallel and perpendicular lines


4. Using slope-intercept form of a linear equation to graph lines


5. Solving linear systems by graphing, addition and substitution methods


6. Applications involving linear systems


7. Review


E. Operations with Polynomials


1. Naming and evaluation of polynomials

    No supplement;

2. Addition and subtraction of polynomials


3. Properties of exponents and scientific notation

Includes an additional, printable section:

Summary of the properties of exponents

The lesson is broken down into two sections:

Properties of exponents

Scientific notation


4. Multiplication of polynomials


5. Division of polynomials by monomials

No supplement;

6. Division of polynomials by binomials


7. Review


F. Factoring Polynomials and Solving Quadratic Equations by Factoring


1. Common factors

The lesson is broken down into two sections:

Common factors

Factoring by grouping


2. Factoring trinomials


3. Difference of two squares

No supplement;

4. Solving quadratic equations by factoring


5. Review


G. Algebraic Fractions


1. Simplifying algebraic fractions


2. Multiplication and division


3. Addition and subtraction


4. Solving equations containing algebraic fractions


5. Solving applied problems

The lesson is broken down into two sections:


Solving applied problems


6. Review


H. Common Roots and Radicals

1. Definitions

No supplement;

2. Properties

Includes an additional, printable section:

Summary of Radical Properties


3. Simplification of a single radical


  Ideally, the lessons should be viewed in a top-down order. This hierarchy follows the syllabus for the Algebra I course (MAT007) approved by the Mathematics department of Suffolk County Community College as of this writing (July, 2013). There are additional topics added to facilitate this books’ use in MAT006 and MAT001. Please see the suggested topics outline below for use in different courses.

  Most pages have TOC icons on the bottom left for return to the table of contents. Within each section, pages allow for the return to the front page of the module via a Unit# icon on the bottom right.

  Each lesson and supplemental lesson is in flash format. The lessons may be navigated in several ways:

a) by using the right/left keyboard arrows

b) by mouse-clicking the screen to advance

c) by using the scroll-bar to advance or reverse

d) by advancing to the next/previous slide by using the arrows on the bottom left of the flash screen.

The left arrow key may be used for reverse. The scroll-bar allows for rapid advancement or reversal. The current slide number and the total number of slides are visible on the bottom left of the flash screen. Additional adjustments to volume and screen size are available on the bottom right side of the flash screen.

 It is important to remember that each lesson is animated. If the mouse is clicked prematurely or the right arrow is applied to soon, important aspects of the animation may be missed. Try to wait until all animation has ceased before advancing. It is always possible to reverse using the left arrow key when it appears that the lesson has ‘skipped’ (advanced too quickly).





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