Elementary algebra: concepts and applications
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Munich [u.a.]
Addison-Wesley
2010
|
| Edition: | 8th ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes indexes. |
| Physical Description: | xviii, 600, [59] p. ill. (chiefly col.) 29 cm. + 1 CD-ROM (12 cm) |
| ISBN: | 9780321557179 0321557174 0321593790 |
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| 245 | 1 | 0 | |a Elementary algebra |b concepts and applications |c Marvin L. Bittinger ; David J. Ellenbogen |
| 250 | |a 8th ed. | ||
| 264 | 1 | |a Boston ; Munich [u.a.] |b Addison-Wesley |c 2010 | |
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| adam_text | Contents
Introduction
to Algebraic Expressions
I.I Introduction to Algebra
2
Algebraic Expressions
·
Translating to Algebraic Expressions
Translating to Equations
hAÍ . -¿LAT
1
¡G. cGR
SUCCESS
9
1.2
The Commutative, Associative, and Distributive Laws
13
Equivalent Expressions
·
The Commutative Laws
·
The Associative Laws
·
The Distributive Law
·
The Distributive Law and Factoring
1.3
Fraction Notation
21
Factors and Prime Factorizations
·
Fraction Notation
·
Multiplication,
Division, and Simplification
·
More Simplifying
·
Addition and Subtraction
1.4
Positive and Negative Real Numbers
29
The Integers
·
The Rational Numbers
·
Real Numbers and Order
·
Absolute Value
1.5
Addition of Real Numbers
37
Adding with the Number Line
·
Adding Without the Number Line
·
Problem Solving
·
Combining Like Terms
1.6
Subtraction of Real Numbers
43
Opposites and Additive Inverses
·
Subtraction
·
Problem Solving
1.7
Multiplication and Division of Real Numbers
51
Multiplication
·
Division
CONNECTING THE CONCEPTS
59
1.8
Exponential Notation and Order of Operations
60
Exponential Notation
·
Order of Operations
·
Simplifying and the Distributive Law
·
The Opposite of a Sum
STUDY SUMMARY
69
REVIEW EXERCISES
73
TEST
75
Equations, Inequalities, and Problem Solving
77
2.1
Solving Equations
78
Equations and Solutions
·
The Addition Principle
·
The Multiplication Principle
·
Selecting the Correct Approach
III
IV
CONTENTS
2.2
Using the Principles Together
85
Applying Both Principles
·
Combining Like Terms
·
Clearing Fractions and Decimals
23
Formulas
92
Evaluating Formulas
·
Solving for a Variable
2.4
Applications with Percent
99
Converting Between Percent Notation and Decimal Notation
·
Solving Percent Problems
2.5
Problem Solving
109
Five Steps for Problem Solving
·
Applying the Five Steps
2.6
Solving Inequalities
120
Solutions of Inequalities
·
Graphs of Inequalities
·
Solving Inequalities
Using the Addition Principle
·
Solving Inequalities Using the
Multiplication Principle
·
Using the Principles Together
CONNECTING THE CONCEPTS
128
2.7
Solving Applications with Inequalities
129
Translating to Inequalities
·
Solving Problems
TRANSLATING FOR SUCCESS
132
STUDY SUMMARY
137
REVIEW EXERCISES
140
TEST
142
CUMULATIVE REVIEW: CHAPTERS
1-2 143
Introduction to Graphing
145
3.1
Reading Graphs, Plotting Points, and Scaling Graphs
146
Problem Solving with Bar, Circle, and Line Graphs
·
Points and Ordered Pairs
·
Numbering the Axes Appropriately
3.2
Graphing Linear Equations
156
Solutions of Equations
·
Graphing Linear Equations
·
Applications
3.3
Graphing and Intercepts
166
Intercepts
·
Using Intercepts to Graph
·
Graphing Horizontal or Vertical Lines
ЗА
Rates
174
Rates of Change
·
Visualizing Rates
3.5
Slope
183
Rate and Slope
·
Horizontal and Vertical Lines
·
Applications
3.6
Slope-Intercept Form
194
Using the y-Intercept and the Slope to Graph a Line
·
Equations in Slope-Intercept Form
·
Graphing and Slope-Intercept Form
CONNECTING THE CONCEPTS
202
CONTENTS
3.7
Point-Slope Form
203
Writing Equations in Point-Slope Form
·
Graphing and Point-Slope Form
Estimations and Predictions Using Two Points
VISUALIZING FOR SUCCESS
208
CONNECTING THE CONCEPTS
21 2
STUDY SUMMARY
214
REVIEW EXERCISES
21
В
TEST
218
CUMULATIVE REVIEW: CHAPTERS
1-3 219
Polynomials
221
4.1
Exponents and Their Properties
222
Multiplying Powers with Like Bases
·
Dividing Powers with Like Bases
·
Zero as an Exponent
·
Raising a Power to a Power
·
Raising a Product or a Quotient to a Power
4.2
Polynomials
230
Terms
·
Types of Polynomials
·
Degree and Coefficients
·
Combining Like Terms
·
Evaluating Polynomials and Applications
4.3
Addition and Subtraction of Polynomials
238
Addition of Polynomials
·
Opposites of Polynomials
·
Subtraction of Polynomials
·
Problem Solving
4.4
Multiplication of Polynomials
246
Multiplying Monomials
·
Multiplying a Monomial and a Polynomial
·
Multiplying Any Two Polynomials
·
Checking by Evaluating
4.5
Special Products
253
Products of Two Binomials
·
Multiplying Sums and Differences of
Two Terms
·
Squaring Binomials
·
Multiplications of Various Types
VISUALIZING FOR SUCCESS
259
CONNECTING THE CONCEPTS
263
4.6
Polynomials in Several Variables
264
Evaluating Polynomials
·
Like Terms and Degree
·
Addition and Subtraction
·
Multiplication
4.7
Division of Polynomials
272
Dividing by a Monomial
·
Dividing by a Binomial
4.8
Negative Exponents and Scientific Notation
278
Negative Integers as Exponents
·
Scientific Notation
·
Multiplying and Dividing Using Scientific Notation
CONNECTING THE CONCEPTS
287
STUDY SUMMARY
288
REVIEW EXERCISES
291
TEST
293
CUMULATIVE REVIEW: CHAPTERS
1-4 294
VÍ
CONTENTS
Polynomials and Factoring
297
5.1
Introduction to Factoring
298
Factoring Monomials
·
Factoring When Terms Have a Common Factor
·
Factoring by Grouping
·
Checking by Evaluating
5.2
Factoring Trinomials of the Type x2
■+■
bx
с
306
When the Constant Term Is Positive
·
When the Constant Term Is Negative
·
Prime Polynomials
5.3
Factoring Trinomials of the Type ax2 bx
с
314
Factoring with FOIL
·
The Grouping Method
CONNECTING THE CONCEPTS
322
5.4
Factoring Perfect-Square Trinomials
and Differences of Squares
323
Recognizing Perfect-Square Trinomials
·
Factoring Perfect-Square
Trinomials
·
Recognizing Differences of Squares
·
Factoring Differences of Squares
·
Factoring Completely
5.5
Factoring: A General Strategy
330
Choosing the Right Method
5.6
Solving Quadratic Equations by Factoring
335
The Principle of Zero Products
·
Factoring to Solve Equations
CONNECTING THE CONCEPTS
343
5.7
Solving Applications
344
Applications
·
The Pythagorean Theorem
TRANSLATING FOR SUCCESS
350
STUDY SUMMARY 35B
REVIEW EXERCISES
358
TEST 3BO
CUMULATIVE REVIEW: CHAPTERS
1-5 361
Rational Expressions and Equations
363
6.1 Rational Expressions
364
Simplifying Rational Expressions
·
Factors That Are Opposites
6.2
Multiplication and Division
371
Multiplication
·
Division
6.3
Addition, Subtraction, and Least Common Denominators
377
Addition When Denominators Are the Same
·
Subtraction When
Denominators Are the Same
·
Least Common Multiples and Denominators
6.4
Addition and Subtraction with Unlike Denominators
385
Adding and Subtracting with LCDs
·
When Factors Are Opposites
CONNECTING THE CONCEPTS
392
CONTENTS
VII
6.5
Complex Rational Expressions
393
Using Division to Simplify
·
Multiplying by the LCD
6.6
Solving Rational Equations
399
Solving a New Type of Equation
·
A Visual Interpretation
CONNECTING THE CONCEPTS
406
6.7
Applications Using Rational Equations and Proportions
407
Problems Involving Work
·
Problems Involving Motion
·
Problems Involving Proportions
РПДМЅ1
AT!( IG FOR
SUCŒSy
4 ]
h
STUDY SUMMARY
422
REVIEW EXERCISES
425
TEST
426
CUMULATIVE REVIEW: CHAPTERS
1-6 427
Systems and More Graphing
429
7.1
Systems of Equations and Graphing
430
Solutions of Systems
·
Solving Systems of Equations by Graphing
7.2
Systems of Equations and Substitution
436
The Substitution Method
·
Solving for the Variable First
·
Problem Solving
7.3
Systems of Equations and Elimination
443
Solving by the Elimination Method
·
Problem Solving
CONNECTING THE CONCEPTS
451
7.4
More Applications Using Systems
452
Total-Value Problems
·
Mixture Problems
7.5
Linear Inequalities in Two Variables 461
Graphing Linear Inequalities
·
Linear Inequalities in One Variable
7.6
Systems of Linear Inequalities
466
Graphing Systems of Inequalities
·
Locating Solution Sets
VISUALIZING
Γ
U R
SIAXlbS
4UÖ
7.7
Direct and Inverse Variation
470
Equations of Direct Variation
·
Problem Solving with Direct Variation
·
Equations of Inverse Variation
·
Problem Solving with Inverse Variation
STUDY SUMMARY
476
REVIEW EXERCISES
478
TEST
480
CUMULATIVE REVIEW: CHAPTERS
1-7 481
VIU
CONTENTS
Radical Expressions and Equations
483
8.1
Introduction to Square Roots and Radical Expressions 48A
Square Roots
·
Radicands and Radical Expressions
·
Irrational
Numbers
·
Square Roots and Absolute Value
·
Problem Solving
8.2
Multiplying and Simplifying Radical Expressions
491
Multiplying
·
Simplifying and Factoring
·
Simplifying Square Roots
of Powers
·
Multiplying and Simplifying
8.3
Quotients Involving Square Roots
497
Dividing Radical Expressions
·
Rationalizing Denominators
8.4
Radical Expressions with Several Terms
501
Adding and Subtracting
Radica]
Expressions
·
More with Multiplication
·
More with Rationalizing Denominators
8.5
Radical Equations
506
Solving Radical Equations
·
Problem Solving and Applications
CONNECTING THE CONCEPTS
511
8.6
Applications Using Right Triangles
512
Right Triangles
·
Problem Solving
·
The Distance Formula
TRANSLATING FOR SUCCESS
517
8.7
Higher Roots and Rational Exponents
522
Higher Roots
·
Products and Quotients Involving Higher Roots
·
Rational Exponents
·
Calculators
STUDY SUMMARY
528
REVIEW EXERCISES
530
TEST
532
CUMULATIVE REVIEW: CHAPTERS
1-8 533
Quadratic Equations
535
9.1
Solving Quadratic Equations:
The Principle of Square Roots
536
The Principle of Square Roots
·
Solving Quadratic Equations of the Type
(x
+
k)2
=
ρ
9.2
Solving Quadratic Equations: Completing the Square
541
Completing the Square
·
Solving by Completing the Square
9.3
The Quadratic Formula and Applications
546
The Quadratic Formula
·
Problem Solving
CONNECTING THE CONCEPTS
555
CONTENTS
IX
9.4
Formulas
556
Solving Formulas
9.5
Complex Numbers as Solutions of Quadratic Equations
560
The Complex-Number System
·
Solutions of Equations
CONNECTING THE CONCEPTS
563
9.6
Graphs of Quadratic Equations
564
Graphing Equations of the Form
y
=
ax2
·
Graphing Equations of the
Form
ƒ =
ax2
+
bx
+
с
VISUALIZING FOR SUCCESS
569
9.7
Functions
571
Identifying Functions
·
Functions Written as Formulas
·
Function
Notation
·
Graphs of Functions
·
Recognizing Graphs of Functions
STUDY SUMMARY
581
REVIEW EXERCISES
583
TEST
585
CUMULATIVE REVIEW/FINAL EXAM: CHAPTERS
1-9 586
Appendixes
A Factoring Sums or Differences of Cubes
589
Factoring a Sum of Two Cubes
·
Factoring a Difference of Two Cubes
В
Mean, Median, and Mode
591
Mean
·
Median
·
Mode
С
Sets
595
Naming Sets
·
Membership
·
Subsets
·
Intersections
·
Unions
Tables
1
Fraction and Decimal Equivalents
599
2
Squares and Square Roots with Approximations to
Three Decimal Places
600
Answers A-1
Glossary G-1
Index
1-1
Index of Applications
1-7
Concepts
&
Applications
MARVIN L. BITTINGER,
Indiana
University Purdue University
Indianapolis-
DAVID
J.
ELLENBOGEN, Community College
of
Vermont
EXCELLENCE THROUGH
INNOVATION—
BITTINGER S CONCEPTS
& APPLICATIONS
SERIES
The Bittinger/Ellenbogen
author team has one goal: to help you succeed in your mathematics course. The
time-tested pedagogy, exceptional applications, and well-crafted exercises of the Concepts
&
Applications
series set the standard for excellence through innovation, explaining both how mathematics works and
why it matters.
Designed with your learning experience in mind, here are some of the new and updated features in
this text. Please see the Preface for more information on these important features and additional
supplemental resources.
New! Translating for Success and Visualizing for Success are matching
exercises that help you learn to associate word problems (through
translation) and graphs (through visualization) with their appropriate
mathematical equations.
Revised! Connecting the Concepts
Revised and expanded to include new
Mixed Review exercises, this midchapter
review helps you understand the big
picture and prepare for chapter and
cumulative tests by relating the concept
at hand to previously learned and
upcoming concepts.
Revised! Student Summary Found
at the end of each chapter and now
presented in a two-column format
organized by section, this synopsis gives
you a fast and effective review of key
chapter terms and concepts paired with
accompanying examples.
ISBN-13:
978-0-321-55717-9
ISBN-10:
0-321-55717-4
Addison-Wesley
is an imprint of
[СНС
Pearson is the proud sponsor of the
International Conference on Technology in Collegiate Mathematics.
Please visit www.ictcm.com
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|
| any_adam_object | 1 |
| author | Bittinger, Marvin L. Ellenbogen, David |
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| author_sort | Bittinger, Marvin L. |
| author_variant | m l b ml mlb d e de |
| building | Verbundindex |
| bvnumber | BV035769147 |
| callnumber-first | Q - Science |
| callnumber-label | QA152 |
| callnumber-raw | QA152.3 |
| callnumber-search | QA152.3 |
| callnumber-sort | QA 3152.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SM 340 |
| ctrlnum | (OCoLC)229750506 (DE-599)BVBBV035769147 |
| dewey-full | 512.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9 |
| dewey-search | 512.9 |
| dewey-sort | 3512.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 8th ed. |
| format | Book |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | xviii, 600, [59] p. ill. (chiefly col.) 29 cm. + 1 CD-ROM (12 cm) |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Addison-Wesley |
| record_format | marc |
| spelling | Bittinger, Marvin L. Verfasser aut Elementary algebra concepts and applications Marvin L. Bittinger ; David J. Ellenbogen 8th ed. Boston ; Munich [u.a.] Addison-Wesley 2010 xviii, 600, [59] p. ill. (chiefly col.) 29 cm. + 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes indexes. Algebra Textbooks Algebra (DE-588)4001156-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Algebra (DE-588)4001156-2 s DE-604 Ellenbogen, David Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628879&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628879&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bittinger, Marvin L. Ellenbogen, David Elementary algebra concepts and applications Algebra Textbooks Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4143389-0 |
| title | Elementary algebra concepts and applications |
| title_auth | Elementary algebra concepts and applications |
| title_exact_search | Elementary algebra concepts and applications |
| title_full | Elementary algebra concepts and applications Marvin L. Bittinger ; David J. Ellenbogen |
| title_fullStr | Elementary algebra concepts and applications Marvin L. Bittinger ; David J. Ellenbogen |
| title_full_unstemmed | Elementary algebra concepts and applications Marvin L. Bittinger ; David J. Ellenbogen |
| title_short | Elementary algebra |
| title_sort | elementary algebra concepts and applications |
| title_sub | concepts and applications |
| topic | Algebra Textbooks Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra Textbooks Algebra Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628879&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628879&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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