Developmental mathematics.

1410 Pages·2019·73.022 MB·English

by  K. Elayn Martin-Gay

Developmental
Mathematics
Fourth Edition
University of New Orleans
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Library of Congress Cataloging-in-Publication Data
Names: Martin-Gay, K. Elayn, 1955- author.
Title: Developmental mathematics.
Description: Fourth edition. | Boston : Pearson Education, Inc., [2019]
Identifiers: LCCN 2018016536 (print) | LCCN 2018018680 (ebook) | ISBN
9780135161715 (epub) | ISBN 9780135164419 (etext 2) | ISBN 9780134896014
(student ed : alk. paper) | ISBN 9780135162286 (instructor ed : alk. paper)
Subjects: LCSH: Mathematics—Textbooks. | Arithmetic—Textbooks. |
Algebra—Textbooks. | Problem solving—Textbooks.
Classification: LCC QA107.2 (ebook) | LCC QA107.2 .M368 2019 (print) | DDC
510—dc23
LC record available at https://lccn.loc.gov/2018016536
ISBN-13: 978-0-13-489601-4 (Student Edition)
ISBN-10: 0-13-489601-7
This book is dedicated to students everywhere—
and we should all be students. After all, is there anyone among
us who truly knows too much? Take that hint and continue
to learn something new every day of your life.
Best wishes from a fellow student:
Elayn Martin-Gay
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Contents
Preface xiii
Applications Index xxiii
1
The Whole Numbers
1
1.1 Study Skill Tips for Success in Mathematics 2
1.2 Place Value, Names for Numbers, and Reading Tables 8
1.3 Adding Whole Numbers and Perimeter 17
1.4 Subtracting Whole Numbers 28
1.5 Rounding and Estimating 39
1.6 Multiplying Whole Numbers and Area 48
1.7 Dividing Whole Numbers 61
Integrated Review— Operations on Whole Numbers 75
1.8 An Introduction to Problem Solving 77
1.9 Exponents, Square Roots, and Order of Operations 87
Vocabulary Check 97
Chapter Highlights 97
Chapter Review 101
Getting Ready for the Test 108
Chapter Test 109
2
Multiplying and Dividing Fractions
111
2.1 Introduction to Fractions and Mixed Numbers 112
2.2 Factors and Prime Factorization 124
2.3 Simplest Form of a Fraction 131
Integrated Review—Summary on Fractions, Mixed Numbers, and Factors 141
2.4 Multiplying Fractions and Mixed Numbers 143
2.5 Dividing Fractions and Mixed Numbers 154
Vocabulary Check 163
Chapter Highlights 163
Chapter Review 166
Getting Ready for the Test 169
Chapter Test 170
Cumulative Review 172
v
vi Contents
3
Adding and Subtracting Fractions
175
3.1 Adding and Subtracting Like Fractions 176
3.2 Least Common Multiple 185
3.3 Adding and Subtracting Unlike Fractions 192
Integrated Review—Operations on Fractions and Mixed Numbers 203
3.4 Adding and Subtracting Mixed Numbers 205
3.5 Order, Exponents, and the Order of Operations 216
3.6 Fractions and Problem Solving 223
Vocabulary Check 234
Chapter Highlights 234
Chapter Review 237
Getting Ready for the Test 242
Chapter Test 243
Cumulative Review 245
4
Decimals
248
4.1 Introduction to Decimals 249
4.2 Order and Rounding 256
4.3 Adding and Subtracting Decimals 265
4.4 Multiplying Decimals and Circumference of a Circle 276
Integrated Review—Operations on Decimals 286
4.5 Dividing Decimals and Order of Operations 288
4.6 Fractions and Decimals 299
Vocabulary Check 308
Chapter Highlights 308
Chapter Review 310
Getting Ready for the Test 315
Chapter Test 316
Cumulative Review 318
5
Ratio, Proportion, and Percent
321
5.1 Ratio and Proportion 322
5.2 Introduction to Percent 338
5.3 Percents and Fractions 345
5.4 Solving Percent Problems Using Equations 352
5.5 Solving Percent Problems Using Proportions 360
Integrated Review—Ratio, Proportion, and Percent 368
5.6 Applications of Percent 370
5.7 Percent and Problem Solving: Sales Tax, Commission, and Discount 381
5.8 Percent and Problem Solving: Interest 388
Vocabulary Check 395
Chapter Highlights 396
Chapter Review 400
Contents vii
Getting Ready for the Test 404
Chapter Test 405
Cumulative Review 407
6
Geometry
409
6.1 Lines and Angles 410
6.2 Plane Figures and Solids 421
6.3 Perimeter 430
6.4 Area 440
6.5 Volume 450
Integrated Review—Geometry Concepts 458
6.6 Square Roots and the Pythagorean Theorem 459
6.7 Congruent and Similar Triangles 466
Vocabulary Check 476
Chapter Highlights 476
Chapter Review 480
Getting Ready for the Test 487
Chapter Test 488
Cumulative Review 490
7
Reading Graphs and Introduction to Statistics
and Probability
492
7.1 Pictographs, Bar Graphs, Histograms, and Line Graphs 493
7.2 Circle Graphs 507
Integrated Review—Reading Graphs 515
7.3 Mean, Median, Mode, and Range 517
7.4 Counting and Introduction to Probability 528
Vocabulary Check 535
Chapter Highlights 536
Chapter Review 538
Getting Ready for the Test 544
Chapter Test 546
Cumulative Review 551
8
Real Numbers and Introduction to Algebra
554
8.1 Symbols and Sets of Numbers 555
8.2 Exponents, Order of Operations, and Variable Expressions 565
8.3 Adding Real Numbers 576
8.4 Subtracting Real Numbers 585
Integrated Review—Operations on Real Numbers 595
8.5 Multiplying and Dividing Real Numbers 597
8.6 Properties of Real Numbers 610
8.7 Simplifying Expressions 618
viii Contents
Vocabulary Check 627
Chapter Highlights 627
Chapter Review 631
Getting Ready for the Test 635
Chapter Test 636
Cumulative Review 638
9
Equations, Inequalities, and Problem Solving
640
9.1 The Addition Property of Equality 641
9.2 The Multiplication Property of Equality 650
9.3 Further Solving Linear Equations 659
Integrated Review—Solving Linear Equations 668
9.4 Further Problem Solving 670
9.5 Formulas and Problem Solving 684
9.6 Percent and Mixture Problem Solving 697
9.7 Linear Inequalities and Problem Solving 710
Vocabulary Check 721
Chapter Highlights 722
Chapter Review 725
Getting Ready for the Test 730
Chapter Test 731
Cumulative Review 733
10
Graphing Equations and Inequalities
736
10.1 The Rectangular Coordinate System 737
10.2 Graphing Linear Equations 750
10.3 Intercepts 760
10.4 Slope and Rate of Change 770
10.5 Equations of Lines 787
Integrated Review—Summary on Linear Equations 799
10.6 Introduction to Functions 801
10.7 Graphing Linear Inequalities in Two Variables 813
10.8 Direct and Inverse Variation 822
Vocabulary Check 833
Chapter Highlights 833
Chapter Review 837
Getting Ready for the Test 844
Chapter Test 845
Cumulative Review 848
Contents ix
11
Systems of Equations
851
11.1 Solving Systems of Linear Equations by Graphing 852
11.2 Solving Systems of Linear Equations by Substitution 863
11.3 Solving Systems of Linear Equations by Addition 871
Integrated Review—Summary on Solving Systems of Equations 879
11.4 Systems of Linear Equations and Problem Solving 880
Vocabulary Check 893
Chapter Highlights 893
Chapter Review 896
Getting Ready for the Test 899
Chapter Test 900
Cumulative Review 902
12
Exponents and Polynomials
904
12.1 Exponents 905
12.2 Negative Exponents and Scientific Notation 917
12.3 Introduction to Polynomials 927
12.4 Adding and Subtracting Polynomials 937
12.5 Multiplying Polynomials 944
12.6 Special Products 951
Integrated Review—Exponents and Operations on Polynomials 959
12.7 Dividing Polynomials 961
Vocabulary Check 968
Chapter Highlights 969
Chapter Review 972
Getting Ready for the Test 977
Chapter Test 978
Cumulative Review 980
13
Factoring Polynomials
983
13.1 The Greatest Common Factor and Factoring by Grouping 984
13.2 Factoring Trinomials of the Form x2 + bx + c 994
13.3 Factoring Trinomials of the Form ax2 + bx + c 1001
13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping 1008
13.5 Factoring Perfect Square Trinomials and the Diffe rence of Two Squares 1013
Integrated Review—Choosing a Factoring Strategy 1022
13.6 Solving Quadratic Equations by Factoring 1024
13.7 Quadratic Equations and Problem Solving 1032
Vocabulary Check 1042
Chapter Highlights 1042