Elementary technical mathematics

642 Pages·2015·44.406 MB·English

by  Ewen, Dale, Nelson, C. Robert

ELEvEnTTIhT L EEdITIon
Elementary Technical
Mathematics
Dale Ewen
Parkland Community College
C. Robert Nelson
Champaign Centennial High School
Australia Brazil Japan Korea Mexico Singapore Spain United Kingdom United States
i
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Elementary Technical Mathematics, © 2015, 2011, 2007 Cengage Learning
Eleventh Edition
WCN: 02-200-203
Dale Ewen / C. Robert Nelson
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Co n T En T S
List of Applications ix
Preface xiii
1
C h A P T E R Basic Concepts 1
Unit 1A
Review of opeRations with whole numBeRs 2
1.1 Review of Basic Operations 2
1.2 Order of Operations 11
1.3 Area and Volume 14
1.4 Formulas 19
1.5 Prime Factorization 22
Unit 1A: Review 26
Unit 1B
Review of opeRations with fRaCtions 26
1.6 introduction to Fractions 26
1.7 Addition and Subtraction of Fractions 31
1.8 Multiplication and Division of Fractions 43
1.9 the U.S. System of Weights and Measures 51
Unit 1B: Review 54
Unit 1C
Review of opeRations with DeCimal fRaCtions anD peRCent 55
1.10 Addition and Subtraction of Decimal Fractions 55
1.11 Rounding numbers 64
1.12 Multiplication and Division of Decimal Fractions 67
1.13 Percent 74
1.14 Rate, Base, and Part 79
1.15 Powers and Roots 87
1.16 Applications involving Percent: Business and Personal Finance 90
Unit 1C: Review 96
Chapter 1: Group Activities 97
Chapter 1: Summary 97
Chapter 1: Review 100
Chapter 1: test 102
iii
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iv Contents
2
C h A P T E R signed numbers and powers of 10 105
2.1 Addition of Signed numbers 106
2.2 Subtraction of Signed numbers 110
2.3 Multiplication and Division of Signed numbers 112
2.4 Signed Fractions 115
2.5 Powers of 10 119
2.6 Scientific notation 123
2.7 Engineering notation 128
Chapter 2: Group Activities 131
Chapter 2: Summary 131
Chapter 2: Review 132
Chapter 2: test 133
Chapters 1–2: Cumulative Review 134
3
C h A P T E R the metric system 135
3.1 introduction to the Metric System 136
3.2 Length 139
3.3 Mass and Weight 142
3.4 Volume and Area 144
3.5 time, Current, and Other Units 147
3.6 temperature 150
3.7 Metric and U.S. Conversion 152
Chapter 3: Group Activities 156
Chapter 3: Summary 157
Chapter 3: Review 157
Chapter 3: test 158
4
C h A P T E R measurement 159
4.1 Approximate numbers and Accuracy 160
4.2 Precision and Greatest Possible Error 163
4.3 the Vernier Caliper 167
4.4 the Micrometer Caliper 174
4.5 Addition and Subtraction of Measurements 182
4.6 Multiplication and Division of Measurements 186
4.7 Relative Error and Percent of Error 189
4.8 Color Code of Electrical Resistors 193
4.9 Reading Scales 197
Chapter 4: Group Activities 205
Chapter 4: Summary 206
Chapter 4: Review 207
Chapter 4: test 208
Chapters 1–4: Cumulative Review 209
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Contents v
5
C h A P T E R polynomials: an introduction to algebra 211
5.1 Fundamental Operations 212
5.2 Simplifying Algebraic Expressions 214
5.3 Addition and Subtraction of Polynomials 218
5.4 Multiplication of Monomials 221
5.5 Multiplication of Polynomials 224
5.6 Division by a Monomial 226
5.7 Division by a Polynomial 228
Chapter 5: Group Activities 230
Chapter 5: Summary 230
Chapter 5: Review 232
Chapter 5: test 232
6
C h A P T E R equations and formulas 233
6.1 Equations 234
6.2 Equations with Variables in Both Members 238
6.3 Equations with Parentheses 240
6.4 Equations with Fractions 243
6.5 translating Words into Algebraic Symbols 247
6.6 Applications involving Equations 248
6.7 Formulas 253
6.8 Substituting Data into Formulas 256
6.9 Reciprocal Formulas Using a Calculator 259
Chapter 6: Group Activities 262
Chapter 6: Summary 262
Chapter 6: Review 263
Chapter 6: test 264
Chapters 1–6: Cumulative Review 264
7
C h A P T E R Ratio and proportion 267
7.1 Ratio 268
7.2 Proportion 272
7.3 Direct Variation 279
7.4 inverse Variation 285
Chapter 7: Group Activities 289
Chapter 7: Summary 289
Chapter 7: Review 289
Chapter 7: test 290
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vi Contents
8
C h A P T E R Graphing linear equations 291
8.1 Linear Equations with two Variables 292
8.2 Graphing Linear Equations 297
8.3 the Slope of a Line 304
8.4 the Equation of a Line 310
Chapter 8: Group Activities 315
Chapter 8: Summary 315
Chapter 8: Review 317
Chapter 8: test 318
Chapters 1–8: Cumulative Review 318
9
C h A P T E R systems of linear equations 321
9.1 Solving Pairs of Linear Equations by Graphing 322
9.2 Solving Pairs of Linear Equations by Addition 328
9.3 Solving Pairs of Linear Equations by Substitution 333
9.4 Applications involving Pairs of Linear Equations 334
Chapter 9: Group Activities 340
Chapter 9: Summary 340
Chapter 9: Review 341
Chapter 9: test 342
10
C h A P T E R factoring algebraic expressions 343
10.1 Finding Monomial Factors 344
10.2 Finding the Product of two Binomials Mentally 345
10.3 Finding Binomial Factors 348
10.4 Special Products 350
10.5 Finding Factors of Special Products 352
10.6 Factoring General trinomials 354
Chapter 10: Group Activities 357
Chapter 10: Summary 357
Chapter 10: Review 358
Chapter 10: test 358
Chapters 1–10: Cumulative Review 358
11
C h A P T E R Quadratic equations 361
11.1 Solving Quadratic Equations by Factoring 362
11.2 the Quadratic Formula 365
11.3 Applications involving Quadratic Equations 367
11.4 Graphs of Quadratic Equations 371
11.5 imaginary numbers 375
Chapter 11: Group Activities 379
Chapter 11: Summary 379
Chapter 11: Review 380
Chapter 11: test 380
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Contents vii
12
C h A P T E R Geometry 381
12.1 Angles and Polygons 382
12.2 Quadrilaterals 389
12.3 triangles 393
12.4 Similar Polygons 402
12.5 Circles 406
12.6 Radian Measure 414
12.7 Prisms 419
12.8 Cylinders 424
12.9 Pyramids and Cones 430
12.10 Spheres 437
Chapter 12: Group Activities 439
Chapter 12: Summary 440
Chapter 12: Review 443
Chapter 12: test 445
Chapters 1–12: Cumulative Review 446
13
C h A P T E R Right triangle trigonometry 449
13.1 trigonometric Ratios 450
13.2 Using trigonometric Ratios to Find Angles 454
13.3 Using trigonometric Ratios to Find Sides 457
13.4 Solving Right triangles 458
13.5 Applications involving trigonometric Ratios 460
Chapter 13: Group Activities 468
Chapter 13: Summary 468
Chapter 13: Review 469
Chapter 13: test 470
14
C h A P T E R trigonometry with any angle 473
14.1 Sine and Cosine Graphs 474
14.2 Period and Phase Shift 480
14.3 Solving Oblique triangles: Law of Sines 484
14.4 Law of Sines: the Ambiguous Case 487
14.5 Solving Oblique triangles: Law of Cosines 493
Chapter 14: Group Activities 498
Chapter 14: Summary 499
Chapter 14: Review 500
Chapter 14: test 500
Chapters 1–14: Cumulative Review 501
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
viii Contents
15
C h A P T E R Basic statistics 503
15.1 Bar Graphs 504
15.2 Circle Graphs 507
15.3 Line Graphs 510
15.4 Other Graphs 513
15.5 Mean Measurement 514
15.6 Other Average Measurements and Percentiles 516
15.7 Range and Standard Deviation 519
15.8 Grouped Data 521
15.9 Standard Deviation for Grouped Data 528
15.10 Statistical Process Control 530
15.11 Other Graphs for Statistical Data 534
15.12 normal Distribution 537
15.13 Probability 540
15.14 independent Events 542
Chapter 15: Group Activities 543
Chapter 15: Summary 544
Chapter 15: Review 545
Chapter 15: test 546
16
C h A P T E R Binary and hexadecimal numbers 549
16.1 introduction to Binary numbers 550
16.2 Addition of Binary numbers 552
16.3 Subtraction of Binary numbers 553
16.4 Multiplication of Binary numbers 554
16.5 Conversion from Decimal to Binary System 555
16.6 Conversion from Binary to Decimal System 557
16.7 Hexadecimal System 558
16.8 Addition and Subtraction of Hexadecimal numbers 560
16.9 Binary to Hexadecimal Conversion 563
16.10 Hexadecimal Code for Colors 564
Chapter 16: Group Activities 565
Chapter 16: Summary 566
Chapter 16: Review 567
Chapter 16: test 567
Chapters 1–16: Cumulative Review 568
A P P E n d I C E S
APPEndIx A: tables 569
table 1: Formulas from Geometry 569
table 2: Electrical Symbols 571
APPEndIx B: Exponential Equations 573
APPEndIx C: Simple inequalities 579
APPEndIx D: Answers to Odd-numbered Exercises and All Chapter Review
and Cumulative Review Exercises 585
IndEx 613
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