Elementary Algebra
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E LE ME NTARY A LG EB R A
Authors
AUTHOR
John Redden
COLLEGE OF THE SEQUOIAS
REVIEWERS
Katherine Adams
EASTERN MICHIGAN UNIVERSITY
Sheri Berger
LOS ANGELES VALLEY COLLEGE
Seung Choi
NORTHERN VIRGINIA COMMUNITY COLLEGE
Stephen DeLong
COLORADO MOUNTAIN COLLEGE
Keith Eddy
COLLEGE OF THE SEQUOIAS
Solomon Emeghara
WILLIAM PATERSON UNIVERSITY
Audrey Gillant
SUNY–MARITIME
Barbara Goldner
NORTH SEATTLE COMMUNITY COLLEGE
Joseph Grich
WILLIAM PATERSON UNIVERSITY
Caroll Hobbs
PENSACOLA STATE COLLEGE
Clark Ingham
MOTT COMMUNITY COLLEGE
Valerie LaVoice
NHTI, CONCORD’S COMMUNITY COLLEGE
Sandra Martin
BREVARD SCHOOLS
Bethany Mueller
PENSACOLA STATE COLLEGE
Tracy Redden
COLLEGE OF THE SEQUOIAS
James Riley
NORTHERN ARIZONA UNIVERSITY
Bamdad Samii
CALIFORNIA STATE UNIVERSITY–NORTHRIDGE
Michael Scott
CALIFORNIA STATE UNIVERSITY–MONTEREY BAY
Nora Wheeler
SANTA ROSA JUNIOR COLLEGE
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E LE ME NTARY A LG EB R A
Table of Contents
Chapter 1: Real Numbers and
Their Operations
DECIMALS AND PERCENTS
Understand and Manipulate Decimals
• Convert between fractions and decimals
WHOLE NUMBERS AND INTEGERS
• Perform operations with decimals
Number Lines and Absolute Value
• Compare round and order decimals
• Identify points on the number line
• Use the number line to order and compare real
numbers
Understand and Manipulate Percents
• Define percents
• Understand opposites and evaluate absolute value
• Convert between percents and decimals
• Convert between percents and fractions
Operations with Whole Numbers
• Perform addition with whole numbers
EXPONENTS AND SQUARE ROOTS
• Perform subtraction with whole numbers
Understand and Evaluate Exponents and Square
Roots
• Perform multiplication with whole numbers
• Understand exponential notation and evaluate
exponents
• Perform multiplication with whole numbers
Operations with Integers
• Determine the square root of a real number
• Add integers
• Multiply and divide integers
Chapter 2: Linear Equations and
Inequalities
• Factor a number into primes
SIMPLIFY AND SOLVE ALGEBRAIC EXPRESSIONS
• Subtract integers
AND EQUATIONS
FRACTIONS
Distribute and Combine Like Terms
Multiply and Divide Fractions
• Simplify expressions using order of operations
• Perform multiplication with fractions
• Simplify expressions with distribution
• Find reciprocal fractions
• Simplify expressions by combining like terms
• Perform division with fractions
Solve Linear Equations with Integers
Add and Subtract Fractions
• Determine if a given value is a solution to a linear
equation
• Add and subtract fractions with like denominators
• Add and subtract fractions with unlike
denominators
• Solve linear equations in one step
• Solve linear equations in two steps
Equivalent Fractions
Solve Linear Equations with Fractions and Decimals
• Find equivalent fractions by reducing to lowest
terms
• Solve equations involving fractions
• Solve equations involving decimals
• Convert between mixed numbers and improper
fractions
Solve Literal Equations
• Solve a formula for a given variable
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E LE ME NTARY A LG EB R A : : TA B L E OF CON T E N T S
Chapter 5: Exponents and Polynomials
LINEAR INEQUALITIES
Solve Single Variable Inequalities
EXPONENTS
• Use interval notation and number line graphs to
model linear inequalities in one variable
Exponent Rules and Scientific Notation
• Use the product rule to multiply exponents
• Solve a linear inequality in one variable
• Use integer exponents
• Solve a compound linear inequality in one variable
• Write numbers in scientific notation
Chapter 3: Graphing Lines
Operations with Exponents
GRAPHING
• Use operations with scientific notation
Introduction to Graphing
• Use the quotient rule to divide exponents
• Plot and identify points on 4 quadrants
• Use the power rule for exponents
• Determine if a point is a solution to an equation
with two variables
POLYNOMIALS
Operations with Polynomials
Graph Linear Equations by Plotting Points and
Intercepts
• Perform addition and subtraction with
polynomials
• Graph linear equations by plotting points
• Use the distributive property to multiply
monomials by polynomials
• Use intercepts to graph linear equations
• Multiply binomials using FOIL
Graph Linear Equations Using Slope
• Find the slope given a line or given two points
• Multiply trinomials or higher
• Graph linear equations using slope-intercept form
• Divide polynomials by monomials
• Graph linear equations using point-slope form
Long Division of Polynomials
• Graph parallel and perpendicular lines
• Divide polynomials using long division
Solve and Graph Linear Inequalities
Greatest Common Factor and Factor by Grouping
• Solve linear inequalities in two variables
• Factor the greatest common factor of polynomials
• Graph a solution set for linear inequalities in two
variables
• Factor polynomials by grouping
Factor Trinomials
Chapter 4: Solving Linear Systems
• Factor trinomials using the “b-c method”
• Factor trinomials where leading coefficient
is not 1
SYSTEMS OF LINEAR EQUATIONS AND
INEQUALITIES
Solve Systems of Linear Equations
Factor Special Products and Solve Quadratic
Equations by Factoring
• Determine if an ordered pair is a solution to a
system of linear equations
• Factor difference of squares
• Solve systems of equations by graphing
• Factor perfect square trinomials
• Solve a system of equations using the substitution
method
• Factor sum and difference of cubes
• Solve quadratic equations by factoring
• Solve a system of linear equations using the
elimination method
Solve Systems of Linear Inequalities
• Solve a system of linear inequalities in two
variables
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E LE ME NTARY A LG EB R A : : TA B L E OF CON T E N T S
Chapter 6: Rational Expressions and
Equations
Simplify Radical Expressions and Add and Subtract
Radicals
• Simplify radical expressions
RATIONAL EXPRESSIONS
• Add and subtract like radicals
Evaluate and Simplify Rational Expressions
• Add and subtract unlike radicals
• Evaluate rational expressions
• Simplify a rational expression
QUADRATIC EQUATIONS
Completing the Square and the Quadratic Formula
Multiply and Divide Rational Expressions
• Evaluate rational expressions
• Perform multiplication with rational expressions
• Simplify a rational expression
• Perform division with rational expressions
Multiply and Divide Rational Expressions
Add and Subtract Rational Expressions and Complex
Fractions
• Solve quadratic equations using the square root
property
• Add and subtract rational expressions with like
denominators
• Solve quadratic equations using completing the
square
• Add and subtract rational expressions with unlike
denominators
• Solve quadratic equations by using the quadratic
formula, rational solutions
• Simplify complex fractions containing variables
• Solve quadratic equations by using the quadratic
formula, irrational solutions
RATIONAL EQUATIONS
Solve Rational Equations
Introduction to Complex Numbers
• Solve rational equations, no extraneous solutions
• Understand and simplify complex numbers
• Solve rational equations with extraneous solutions
or no solution
• Perform addition and subtraction with complex
numbers
Direct and Inverse Variation
Multiply and Divide Complex Numbers
• Solve problems that involve direct variation
• Multiply complex numbers
• Solve problems that involve inverse variation
• Divide complex numbers and rationalize
denominators
RADICAL EXPRESSIONS
Cube and nth Roots
The Quadratic Formula with Imaginary Solutions
• Evaluate cube and nth roots
• Solve quadratic equations by completing the
square, complex solutions
• Simplify an expression with an nth root
• Solve quadratic equations using the quadratic
formula, complex solutions
Simplify Radical Expressions and Add and Subtract
Radicals
• Simplify radical expressions
PARABOL AS
• Add and subtract like radicals
Graph Quadratic Equations
• Graph a quadratic equation by plotting points
• Add and subtract unlike radicals
• Find the x and y intercepts of a quadratic equation
Multiply and Divide Radical Expressions
• Graph a quadratic equation using intercepts
• Multiply radical expressions
• Multiply binomial radical expressions
• Multiply radical conjugates
• Rationalize monomial denominators
• Rationalize binomial denominators
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