Schaum's outline of elementary algebra

384 Pages·6.653 MB·English

by  Rich, Barnett;Schmidt, Philip A

SCHAUM’S
OUTLINE OF
ELEMENTARY
ALGEBRA
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SCHAUM’S
OUTLINE OF
Theory and Problems of
ELEMENTARY
ALGEBRA
Third Edition
BARNETT RICH, Ph.D.
PHILIP A. SCHMIDT, Ph.D.
Program Coordinator, Mathematics and Science Education
The Teachers College,Western Governors University
Salt Lake City, Utah
Schaum’s Outline Series
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DR. BARNETT RICHheld a doctor of philosophy degree (Ph.D.) from Columbia University and a doctor of
jurisprudence (J.D.) from New York University. He began his professional career at Townsend Harris Hall High
School of New York City and was one of the prominent organizers of the High School of Music and Art,where
he served as the Administrative Assistant. Later he taught at CUNY and Columbia University and held the post
of Chairman of Mathematics at Brooklyn Technical High School for 14 years. Among his many achievements
are the six degrees that he earned and the 23 books that he wrote,among them Schaum’s Outlines of Review of
Elementary Mathematicsand Geometry.
PHILIP A. SCHMIDT,Ph.D.,has a B.S. from Brooklyn College (with a major in mathematics),an M.A. in
mathematics, and a Ph.D. in mathematics education from Syracuse University. He is currently Program
Coordinator in Mathematics and Science Education at The Teachers College of Western Governors University
in Salt Lake City,Utah. He is also the coauthor of the Schaum’s Outlines of College Mathematicsas well as the
reviser of Schaum’s Outlines of Geometryand Review of Elementary Mathematics. Among his many achieve-
ments are numerous grants and scholarly publications in mathematics education.
Copyright © 2004,1993,1960 by Barnett Rich and Philip A. Schmidt.All rights reserved. Manufactured in the United States of America.
Except as permitted under the Unite States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form
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DOI: 10.1036/0071431098
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PREFACE
In the third edition of Elementary Algebra,I have maintained the pacing,philosophy,and point of view of the
prior two editions. Students who are interested in learning algebra for the first time,or who are engaged in the
study of algebra and are seeking a study guide or supplementary problems and solutions,will find virtually all
major topics in elementary algebra in this text. In addition,there is an ample review of arithmetic,as well as a
serious introduction to geometry,trigonometry,problem solving,and mathematical modeling.
In crafting this edition,I have removed material that is no longer a part of the standard algebra curriculum,
added topics as part of that effort as well,modernized terminology and notation when necessary,and incorpo-
rated the use of calculators throughout the text. Mathematical modeling is introduced as an important compo-
nent to problem solving in mathematics. Pedagogy has been revamped to match current teaching methods.
My thanks must be expressed to Barbara Gilson and Andrew Littell of McGraw-Hill. They have been
supportive of this project from its earliest stages. I must also thank Dr. Marti Garlett, Dean of the Teachers
College of Western Governors University,for her professional support as I worked to meet important publish-
ing deadlines. I thank my wife, Dr. Jan Zlotnik Schmidt, for her love and support during this project. And I
dedicate this edition to the late Jean (Mrs. Barnett) Rich. Her drive to make certain that this volume was writ-
ten was a substantial part of my own drive to do this work.
PHILIPA. SCHMIDT
New Paltz,NY
v
Copyright © 2004,1993,1960 by Barnett Rich and Philip A. Schmidt. Click here for terms of use.
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CONTENTS
CHAPTER 1 From Arithemetic to Algebra 1
1. Representing Numbers by Letters 1
2. Interchanging Numbers in Addition 2
3. Interchanging Numbers in Multiplication 3
4. Symbolizing the Operations in Algebra 4
5. Expressing Addition and Subtraction Algebraically 5
6. Expressing Multiplication and Division Algebraically 6
7. Expressing Two or More Operations Algebraically 6
8. Order in Which Fundamental Operations Are Performed 8
9. The Uses of Parentheses: Changing the Order of Operations 9
10. Multiplying Factors in Terms: Numerical and Literal Coefficients 10
11. Repeated Multiplying of a Factor: Base, Exponent, and Power 11
12. Combining Like and Unlike Terms 13
CHAPTER 2 Simple Equations and Their Solutions 21
1. Kinds of Equalities: Equations and Identities 21
2. Translating Verbal Statements into Equations 22
3. Solving Simple Equations by Using Inverse Operations 23
4. Rules of Equality for Solving Equations 25
5. Using Division to Solve an Equation 26
6. Using Multiplication to Solve an Equation 28
7. Using Subtraction to Solve an Equation 30
8. Using Addition to Solve an Equation 31
9. Using Two or More Operations to Solve an Equation 32
CHAPTER 3 Signed Numbers 43
1. Understanding Signed Numbers: Positive and Negative Numbers 43
2. Using Number Scales for Signed Numbers 44
3. Adding Signed Numbers 48
4. Simplifying the Addition of Signed Numbers 50
5. Subtracting Signed Numbers 51
6. Multiplying Signed Numbers 53
7. Finding Powers of Signed Numbers 55
8. Dividing Signed Numbers 56
9. Evaluating Expressions Having Signed Numbers 58
vii
viii CONTENTS
CHAPTER 4 Introduction to Monomials and Polynomials 64
1. Understanding Monomials and Polynomials 64
2. Adding Monomials 65
3. Arranging and Adding Polynomials 66
4. Subtracting Monomials 67
5. Subtracting Polynomials 68
6. Using Parentheses and Other Grouping Symbols to Add or Subtract
Polynomials 69
7. Multiplying Monomials and Powers of the Same Base 71
8. Multiplying a Polynomial by a Monomial 72
9. Multiplying Polynomials 73
10. Dividing Powers and Monomials 74
11. Dividing a Polynomial by a Monomial 76
12. Dividing a Polynomial by a Polynomial 77
CHAPTER 5 First-Degree Equations 86
1. Reviewing the Solution of First-Degree Equations Having Positive
Roots 86
2. Solving First-Degree Equations Having Negative Solutions 88
3. Solving Equations by Transposing 90
4. Solving Equations Containing Parentheses 91
5. Solving Equations Containing One Fraction or Fractions Having the
Same Denominator 92
6. Solving Equations Containing Fractions Having Different
Denominators: Lowest Common Denominator 93
7. Solving Equations Containing Decimals 95
8. Solving Literal Equations 96
9. The Graphing Calculator 97
CHAPTER 6 Formulas 105
1. Points and Lines 105
2. Understanding Polygons, Circles, and Solids 106
3. Formulas for Perimeters and Circumferences: Linear Measure 111
4. Formulas for Areas: Square Measure 115
5. Formulas for Volumes: Cubic Measure 120
6. Deriving Formulas 124
7. Transforming Formulas 126
8. Finding the Value of an Unknown in a Formula 128
CHAPTER 7 Graphs of Linear Equations 137
1. Understanding Graphs 137
2. Graphing Linear Equations 141
3. Solving a Pair of Linear Equations Graphically 147
4. Deriving a Linear Equation from a Table of Values 150
5. Midpoint of a Segment 152
6. Distance between Two Points 153