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ALGEBRA
Essentials Practice
WORKBOOK
with Answers
Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations
Improve Your Math Fluency Series
2x – 3x = –1 2
Chris McMullen, Ph.D.
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com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@
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_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Algebra Essentials Practice Workbook with Answers:
Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations
Improve Your Math Fluency Series
Copyright © 2010, 2014 Chris McMullen, Ph.D.
Updated on March 31, 2014
All rights reserved. This includes the right to reproduce any portion of this book in any form.
However, teachers who purchase one copy of this book, or borrow one physical copy from a
library, may make and distribute photocopies of selected pages for instructional purposes for
their own classes only. Also, parents who purchase one copy of this book, or borrow one
physical copy from a library, may make and distribute photocopies of selected pages for use by
their own children only.
CreateSpace
Professional & Technical / Science / Mathematics / Algebra
Professional & Technical / Education / Specific Skills / Mathematics / Algebra
ISBN: 1453661387
EAN-13: 9781453661383
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com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@
9/25/2026, 3:17:54 PM_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@
,@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Contents
Making the Most of this Workbook 4
Chapter 1: Linear Equations with Integral Coefficients 5
Chapter 2: Linear Equations with Fractional Coefficients 28
Chapter 3: Simple Quadratic Equations 51
Chapter 4: Factoring Quadratic Equations 76
Chapter 5: Formula for the Quadratic Equation 109
Chapter 6: Cross Multiplying 132
Chapter 7: Systems of Linear Equations 158
Answer Key 193
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9/25/2026, 3:17:54 PM_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@
,@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Improve Your Math Fluency Series
Making the Most of this Workbook
Mathematics is a language. You can’t hold a decent conversation in any language if you
have a limited vocabulary or if you are not fluent. In order to become successful in
mathematics, you need to practice until you have mastered the fundamentals and
developed fluency in the subject. This Algebra Essentials Practice Workbook with
Answers: Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations will
help you improve the fluency with which you apply fundamental techniques to solve for
unknowns.
This book is conveniently divided into 7 chapters so that you can focus on one basic skill
at a time. The exercises of Chapters 1 and 2 are linear equations with a single unknown,
which entail using arithmetic operations to collect and isolate the unknowns. The
coefficients are all integers in Chapter 1, while Chapter 2 features fractional coefficients.
Quadratic equations are the focus of Chapters 3 thru 5. Chapter 3 is limited to quadratic
equations that either do not have a constant term or do not have a term of the first
power in the unknown, while Chapters 4 and 5 are focused on techniques for solving the
full quadratic equation. The quadratic equations of Chapter 4 are reasonably
straightforward to factor into a product of linear factors with integral coefficients,
whereas the focus of Chapter 5 is how to apply the quadratic formula. Chapter 6 is
dedicated to cross multiplying. Systems of linear equations with two unknowns are the
subject of Chapter 7.
Each chapter begins with a few pages of instructions describing a basic algebraic skill –
such as how to factor the quadratic equation. These instructions are followed by a few
examples. Use these examples as a guide until you become fluent in the technique.
After you complete a page, check your answers with the answer key in the back of the
book. Practice makes permanent, but not necessarily perfect: If you practice making
mistakes, you will learn your mistakes. Check your answers and learn from your
mistakes such that you practice solving the problems correctly. This way your practice
will make perfect.
Math can be fun. Make a game of your practice by recording your times and trying to
improve on your times, and recording your scores and trying to improve on your scores.
Doing this will help you see how much you are improving, and this sign of improvement
can give you the confidence to succeed in math, which can help you learn to enjoy this
subject more.
4
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_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
ALGEBRA
Essentials Practice
WORKBOOK
with Answers
Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations
Improve Your Math Fluency Series
2x – 3x = –1 2
Chris McMullen, Ph.D.
@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@
9/25/2026, 3:17:54 PM_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@
,@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Algebra Essentials Practice Workbook with Answers:
Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations
Improve Your Math Fluency Series
Copyright © 2010, 2014 Chris McMullen, Ph.D.
Updated on March 31, 2014
All rights reserved. This includes the right to reproduce any portion of this book in any form.
However, teachers who purchase one copy of this book, or borrow one physical copy from a
library, may make and distribute photocopies of selected pages for instructional purposes for
their own classes only. Also, parents who purchase one copy of this book, or borrow one
physical copy from a library, may make and distribute photocopies of selected pages for use by
their own children only.
CreateSpace
Professional & Technical / Science / Mathematics / Algebra
Professional & Technical / Education / Specific Skills / Mathematics / Algebra
ISBN: 1453661387
EAN-13: 9781453661383
@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@
9/25/2026, 3:17:54 PM_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@
,@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Contents
Making the Most of this Workbook 4
Chapter 1: Linear Equations with Integral Coefficients 5
Chapter 2: Linear Equations with Fractional Coefficients 28
Chapter 3: Simple Quadratic Equations 51
Chapter 4: Factoring Quadratic Equations 76
Chapter 5: Formula for the Quadratic Equation 109
Chapter 6: Cross Multiplying 132
Chapter 7: Systems of Linear Equations 158
Answer Key 193
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com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@
9/25/2026, 3:17:54 PM_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@
,@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
_with_Answers_-_Chris_McMullen.pdf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!!
_OceanofPDF.com_Algebra_Essentials_Practice_Workbook_with_Answers_-_Chris_McMullen.pdf@@@@@@_OceanofP
Improve Your Math Fluency Series
Making the Most of this Workbook
Mathematics is a language. You can’t hold a decent conversation in any language if you
have a limited vocabulary or if you are not fluent. In order to become successful in
mathematics, you need to practice until you have mastered the fundamentals and
developed fluency in the subject. This Algebra Essentials Practice Workbook with
Answers: Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations will
help you improve the fluency with which you apply fundamental techniques to solve for
unknowns.
This book is conveniently divided into 7 chapters so that you can focus on one basic skill
at a time. The exercises of Chapters 1 and 2 are linear equations with a single unknown,
which entail using arithmetic operations to collect and isolate the unknowns. The
coefficients are all integers in Chapter 1, while Chapter 2 features fractional coefficients.
Quadratic equations are the focus of Chapters 3 thru 5. Chapter 3 is limited to quadratic
equations that either do not have a constant term or do not have a term of the first
power in the unknown, while Chapters 4 and 5 are focused on techniques for solving the
full quadratic equation. The quadratic equations of Chapter 4 are reasonably
straightforward to factor into a product of linear factors with integral coefficients,
whereas the focus of Chapter 5 is how to apply the quadratic formula. Chapter 6 is
dedicated to cross multiplying. Systems of linear equations with two unknowns are the
subject of Chapter 7.
Each chapter begins with a few pages of instructions describing a basic algebraic skill –
such as how to factor the quadratic equation. These instructions are followed by a few
examples. Use these examples as a guide until you become fluent in the technique.
After you complete a page, check your answers with the answer key in the back of the
book. Practice makes permanent, but not necessarily perfect: If you practice making
mistakes, you will learn your mistakes. Check your answers and learn from your
mistakes such that you practice solving the problems correctly. This way your practice
will make perfect.
Math can be fun. Make a game of your practice by recording your times and trying to
improve on your times, and recording your scores and trying to improve on your scores.
Doing this will help you see how much you are improving, and this sign of improvement
can give you the confidence to succeed in math, which can help you learn to enjoy this
subject more.
4
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