Algebra Foundations

About our author Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment” (as they prepare for a test) along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 13 published textbooks and a new Interactive Assignment MyLab® Math course, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across the broadest range of educational materials: textbooks, videos, tutorial software, and courseware. This provides an opportunity of various combinations for an integrated teaching and learning package offering great consistency for the student.

Table of Contents

The Whole Numbers

1.1 Study Skill Tips for Success in Mathematics
1.2 Place Value, Names for Numbers, and Reading Tables
1.3 Adding and Subtracting Whole Numbers, and Perimeter
1.4 Rounding and Estimating
1.5 Multiplying Whole Numbers and Area
1.6 Dividing Whole Numbers

Integrated Review–Operations on Whole Numbers


1.7 Exponents and Order of Operations
1.8 Introduction to Variables, Algebraic Expressions, and Equations


Integers and Introduction to Solving Equations

2.1 Introduction to Integers
2.2 Adding Integers
2.3 Subtracting Integers
2.4 Multiplying and Dividing Integers

Integrated Review–Integers


2.5 Order of Operations
2.6 Solving Equations: The Addition and Multiplication Properties


Solving Equations and Problem Solving

3.1 Simplifying Algebraic Expressions
3.2 Solving Equations: Review of the Addition and Multiplication Properties

Integrated Review–Expressions and Equations


3.3 Solving Linear Equations in One Variable
3.4 Linear Equations in One Variable and Problem Solving


Fractions and Mixed Numbers

4.1 Introduction to Fractions and Mixed Numbers
4.2 Factors and Simplest Form
4.3 Multiplying and Dividing Fractions
4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions
4.5 Adding and Subtracting Unlike Fractions

Integrated Review–Summary on Fractions and Operations on Fractions


4.6 Complex Fractions and Review of Order of Operations
4.7 Operations on Mixed Numbers
4.8 Solving Equations Containing Fractions


Decimals

5.1 Introduction to Decimals
5.2 Adding and Subtracting Decimals
5.3 Multiplying Decimals and Circumference of a Circle
5.4 Dividing Decimals

Integrated Review–Operations on Decimals


5.5 Fractions, Decimals, and Order of Operations
5.6 Solving Equations Containing Decimals
5.7 Decimal Applications: Mean, Median, and Mode


Ratio, Proportion, and Percent

6.1 Ratio and Proportion
6.2 Percents, Decimals, and Fractions
6.3 Solving Percent Problems with Equations
6.4 Solving Percent Problems with Proportions

Integrated Review–Ratio, Proportion, and Percent


6.5 Applications of Percent
6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount
6.7 Percent and Problem Solving: Interest


Graphs, Triangle Applications, and Introduction to Statistics and Probability

7.1 Pictographs, Bar Graphs, Histograms, Line Graphs, and Introduction to Statistics
7.2 Circle Graphs

Integrated Review–Reading Graphs


7.3 Square Roots and the Pythagorean Theorem
7.4 Congruent and Similar Triangles
7.5 Counting and Introduction to Probability


Geometry and Measurement

8.1 Lines and Angles
8.2 Perimeter
8.3 Area, Volume, and Surface Area

Integrated Review–Geometry Concepts


8.4 Linear Measurement
8.5 Weight and Mass
8.6 Capacity
8.7 Temperature and Conversions Between the U.S. and Metric Systems


Equations, Inequalities, and Problem Solving

9.1 Symbols and Sets of Numbers
9.2 Properties of Real Numbers
9.3 Further Solving Linear Equations

Integrated Review–Real Numbers and Solving Linear Equations


9.4 Further Problem Solving
9.5 Formulas and Problem Solving
9.6 Linear Inequalities and Problem Solving


Graphing

10.1 The Rectangular Coordinate System
10.2 Graphing Linear Equations
10.3 Intercepts
10.4 Slope and Rate of Change

Integrated Review–Summary on Slope and Graphing Linear Equations


10.5 Equation of Lines
10.6 Functions


Solving Systems of Linear Equations

11.1 Solving Systems of Linear Equations by Graphing
11.2 Solving Systems of Linear Equations by Substitution
11.3 Solving Systems of Linear Equations by Addition

Integrated Review–Solving Systems of Equations


11.4 Solving Systems of Linear Equations in Three Variables
11.5 Systems of Linear Equations and Problem Solving


Exponents and Polynomials

12.1 Exponents
12.2 Polynomial Functions and Adding and Subtracting Polynomials
12.3 Multiplying Polynomials
12.4 Special Products

Integrated Review–Exponents and Operations on Polynomials


12.5 Negative Exponents and Scientific Notation
12.6 Dividing Polynomials
12.7 Synthetic Division and the Remainder Theorem


Factoring Polynomials

13.1 The Greatest Common Factor and Factoring by Grouping
13.2 Factoring Trinomials of the Form x2 + bx + c
13.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials
13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping
13.5 Factoring Binomials

Integrated Review–Choosing a Factoring Strategy


13.6 Solving Quadratic Equations by Factoring
13.7 Quadratic Equations and Problem Solving


Rational Expressions

14.1 Rational Functions and Simplifying Rational Expressions
14.2 Multiplying and Dividing Rational Expressions
14.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator
14.4 Adding and Subtracting Rational Expressions with Unlike Denominators
14.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions


14.6 Problem Solving with Proportions and Rational Equations
14.7 Simplifying Complex Fractions


More on Functions and Graphs

15.1 Graphing and Writing Linear Functions
15.2 Reviewing Function Notation and Graphing Nonlinear Functions

Integrated Review–Summary on Functions and Equations of Lines


15.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions
15.4 Variation and Problem Solving


Inequalities and Absolute Value

16.1 Compound Inequalities
16.2 Absolute Value Equations
16.3 Absolute Value Inequalities

Integrated Review–Solving Compound Inequalities and Absolute Value Equations and Inequalities


16.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities


Rational Exponents, Radicals, and Complex Numbers

17.1 Radicals and Radical Functions
17.2 Rational Exponents
17.3 Simplifying Radical Expressions
17.4 Adding, Subtracting, and Multiplying Radical Expressions
17.5 Rationalizing Denominators and Numerators of Radical Expressions

Integrated Review–Radicals and Rational Exponents


17.6 Radical Equations and Problem Solving
17.7 Complex Numbers


Quadratic Equations and Functions

18.1 Solving Quadratic Equations by Completing the Square
18.2 Solving Quadratic Equations by the Quadratic Formula
18.3 Solving Equations by Using Quadratic Methods

Integrated Review–Summary on Solving Quadratic Equations


18.4 Nonlinear Inequalities in One Variable
18.5 Quadratic Functions and Their Graphs
18.6 Further Graphing of Quadratic Functions


Exponential and Logarithmic Functions

19.1 The Algebra of Functions: Composite Functions
19.2 Inverse Functions
19.3 Exponential Functions
19.4 Exponential Growth and Decay Functions
19.5 Logarithmic Functions
19.6 Properties of Logarithms

Integrated Review–Functions and Properties of Logarithms


19.7 Common Logarithms, Natural Logarithms, and Change of Base
19.8 Exponential and Logarithmic Equations and Problem Solving


Conic Sections

20.1 The Parabola and the Circle
20.2 The Ellipse and the Hyperbola

Integrated Review–Graphing Conic Sections


20.3 Solving Nonlinear Systems of Equations
20.4 Nonlinear Inequalities and Systems of Inequalities


Sequences, Series, and the Binomial Theorem

21.1 Sequences
21.2 Arithmetic and Geometric Sequences
21.3 Series

Integrated Review–Sequences and Series


21.4 Partial Sums of Arithmetic and Geometric Sequences
21.5 The Binomial Theorem



APPENDICES

Appendix A. Tables

A.1 Table of Geometric Figures
A.2 Table of Percents, Decimals, and Fraction Equivalents
A.3 Table on Finding Common Percents of a Number
A.4 Table of Squares and Square Roots
A.5 Geometric Formulas


Appendix B. Review of Algebra Topics

B.1 Equations (Linear and Quadratic Solved by Factoring)
B.2 Mixture and Uniform Motion Problem Solving
B.3 Graphing
B.4 Polynomials and Factoring
B.5 Rational Expressions


Appendix C. Stretching and Compressing Graphs of Absolute Value Functions
Appendix D. An Introduction to Using a Graphing Utility
Appendix E. Solving Systems of Equations by Matrices
Appendix F. Solving Systems of Equations by Determinants