Elementary Technical Mathematics (10th Edition)

651 Pages·2010·16.66 MB·English

by  Dale Ewen

Elementary Technical
Mathematics
T E N T H E D I T I O N
Dale Ewen
Parkland Community College
C. Robert Nelson
Champaign Centennial High School
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Contents
List of Applications ix
Preface xiii
1
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 Divisibility 23
Unit 1A: Review 27
Unit 1B
REVIEW OF OPERATIONS WITH FRACTIONS 27
1.6 Introduction to Fractions 27
1.7 Addition and Subtraction of Fractions 33
1.8 Multiplication and Division of Fractions 45
1.9 The U.S. System of Weights and Measures 53
Unit 1B: Review 56
Unit 1C
REVIEW OF OPERATIONS WITH DECIMAL FRACTIONS AND PERCENT 57
1.10 Addition and Subtraction of Decimal Fractions 57
1.11 Rounding Numbers 66
1.12 Multiplication and Division of Decimal Fractions 69
1.13 Percent 75
1.14 Rate, Base, and Part 80
1.15 Powers and Roots 89
1.16 Applications Involving Percent: Personal Finance (Optional) 93
Unit 1C: Review 97
Chapter 1: Group Activities 98
Chapter 1: Summary 99
Chapter 1: Review 102
Chapter 1: Test 104
iii
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iv Contents
2
Signed Numbers and Powers of 10 107
2.1 Addition of Signed Numbers 108
2.2 Subtraction of Signed Numbers 112
2.3 Multiplication and Division of Signed Numbers 114
2.4 Signed Fractions 117
2.5 Powers of 10 122
2.6 Scientific Notation 125
2.7 Engineering Notation 131
Chapter 2: Group Activities 134
Chapter 2: Summary 134
Chapter 2: Review 136
Chapter 2: Test 137
Chapter 1-2: Cumulative Review 138
3
The Metric System 139
3.1 Introduction to the Metric System 140
3.2 Length 143
3.3 Mass and Weight 146
3.4 Volume and Area 148
3.5 Time, Current, and Other Units 152
3.6 Temperature 154
3.7 Metric and U.S. Conversion 156
Chapter 3: Group Activities 161
Chapter 3: Summary 161
Chapter 3: Review 162
Chapter 3: Test 163
4
Measurement 165
4.1 Approximate Numbers and Accuracy 166
4.2 Precision and Greatest Possible Error 169
4.3 The Vernier Caliper 173
4.4 The Micrometer Caliper 181
4.5 Addition and Subtraction of Measurements 189
4.6 Multiplication and Division of Measurements 193
4.7 Relative Error and Percent of Error 196
4.8 Color Code of Electrical Resistors 200
4.9 Reading Scales 204
Chapter 4: Group Activities 213
Chapter 4: Summary 213
Chapter 4: Review 214
Chapter 4: Test 216
Chapter 1-4: Cumulative Review 217
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Contents v
5
Polynomials: An Introduction to Algebra 219
5.1 Fundamental Operations 220
5.2 Simplifying Algebraic Expressions 222
5.3 Addition and Subtraction of Polynomials 226
5.4 Multiplication of Monomials 230
5.5 Multiplication of Polynomials 232
5.6 Division by a Monomial 234
5.7 Division by a Polynomial 236
Chapter 5: Group Activities 239
Chapter 5: Summary 239
Chapter 5: Review 241
Chapter 5: Test 241
6
Equations and Formulas 243
6.1 Equations 244
6.2 Equations with Variables in Both Members 249
6.3 Equations with Parentheses 251
6.4 Equations with Fractions 254
6.5 Translating Words into Algebraic Symbols 259
6.6 Applications Involving Equations 260
6.7 Formulas 265
6.8 Substituting Data into Formulas 268
6.9 Reciprocal Formulas Using a Calculator 272
Chapter 6: Group Activities 275
Chapter 6: Summary 275
Chapter 6: Review 276
Chapter 6: Test 277
Chapter 1-6: Cumulative Review 278
7
Ratio and Proportion 279
7.1 Ratio 280
7.2 Proportion 284
7.3 Direct Variation 290
7.4 Inverse Variation 295
Chapter 7: Group Activities 299
Chapter 7: Summary 299
Chapter 7: Review 300
Chapter 7: Test 301
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vi Contents
8
Graphing Linear Equations 303
8.1 Linear Equations with Two Variables 304
8.2 Graphing Linear Equations 310
8.3 The Slope of a Line 317
8.4 The Equation of a Line 323
Chapter 8: Group Activities 328
Chapter 8: Summary 329
Chapter 8: Review 330
Chapter 8: Test 331
Chapter 1-8: Cumulative Review 332
9
Systems of Linear Equations 333
9.1 Solving Pairs of Linear Equations by Graphing 334
9.2 Solving Pairs of Linear Equations by Addition 340
9.3 Solving Pairs of Linear Equations by Substitution 345
9.4 Applications Involving Pairs of Linear Equations 347
Chapter 9: Group Activities 353
Chapter 9: Summary 354
Chapter 9: Review 355
Chapter 9: Test 356
10
Factoring Algebraic Expressions 357
10.1 Finding Monomial Factors 358
10.2 Finding the Product of Two Binomials Mentally 360
10.3 Finding Binomial Factors 362
10.4 Special Products 365
10.5 Finding Factors of Special Products 367
10.6 Factoring General Trinomials 369
Chapter 10: Group Activities 372
Chapter 10: Summary 372
Chapter 10: Review 373
Chapter 10: Test 373
Chapter 1-10: Cumulative Review 374
11
Quadratic Equations 375
11.1 Solving Quadratic Equations by Factoring 376
11.2 The Quadratic Formula 379
11.3 Applications Involving Quadratic Equations 381
11.4 Graphs of Quadratic Equations 386
11.5 Imaginary Numbers 390
Chapter 11: Group Activities 393
Chapter 11: Summary 393
Chapter 11: Review 394
Chapter 11: Test 395
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Contents vii
12
Geometry 397
12.1 Angles and Polygons 398
12.2 Quadrilaterals 405
12.3 Triangles 410
12.4 Similar Polygons 419
12.5 Circles 423
12.6 Radian Measure 430
12.7 Prisms 435
12.8 Cylinders 441
12.9 Pyramids and Cones 446
12.10 Spheres 453
Chapter 12: Group Activities 455
Chapter 12: Summary 456
Chapter 12: Review 460
Chapter 12: Test 462
Chapter 1-12: Cumulative Review 463
13
Right Triangle Trigonometry 465
13.1 Trigonometric Ratios 466
13.2 Using Trigonometric Ratios to Find Angles 470
13.3 Using Trigonometric Ratios to Find Sides 473
13.4 Solving Right Triangles 474
13.5 Applications Involving Trigonometric Ratios 476
Chapter 13: Group Activities 484
Chapter 13: Summary 485
Chapter 13: Review 486
Chapter 13: Test 487
14
Trigonometry with Any Angle 489
14.1 Sine and Cosine Graphs 490
14.2 Period and Phase Shift 496
14.3 Solving Oblique Triangles: Law of Sines 500
14.4 Law of Sines: The Ambiguous Case 503
14.5 Solving Oblique Triangles: Law of Cosines 509
Chapter 14: Group Activities 514
Chapter 14: Summary 515
Chapter 14: Review 516
Chapter 14: Test 516
Chapter 1-14: Cumulative Review 517
15
Basic Statistics 519
15.1 Bar Graphs 520
15.2 Circle Graphs 523
15.3 Line Graphs 526
15.4 Other Graphs 529
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viii Contents
15.5 Mean Measurement 530
15.6 Other Average Measurements and Percentiles 532
15.7 Range and Standard Deviation 535
15.8 Grouped Data 537
15.9 Standard Deviation for Grouped Data 544
15.10 Statistical Process Control 546
15.11 Other Graphs for Statistical Data 550
15.12 Normal Distribution 553
15.13 Probability 556
15.14 Independent Events 558
Chapter 15: Group Activities 559
Chapter 15: Summary 560
Chapter 15: Review 562
Chapter 15: Test 563
16
Binary and Hexadecimal Numbers 565
16.1 Introduction to Binary Numbers 566
16.2 Addition of Binary Numbers 568
16.3 Subtraction of Binary Numbers 569
16.4 Multiplication of Binary Numbers 571
16.5 Conversion from Decimal to Binary System 572
16.6 Conversion from Binary to Decimal System 573
16.7 Hexadecimal System 574
16.8 Addition and Subtraction of Hexadecimal Numbers 576
16.9 Binary to Hexadecimal Conversion 579
16.10 Hexadecimal Code for Colors 581
Chapter 16: Group Activities 582
Chapter 16: Summary 583
Chapter 16: Review 584
Chapter 16: Test 584
Chapter 1-16: Cumulative Review 585
Appendixes
Appendix A: Tables 587
Table 1: Formulas from Geometry 587
Table 2: Electrical Symbols 589
Appendix B: Exponential Equations 591
Appendix C: Answers to Odd-Numbered Exercises and All Chapter Review
and Cumulative Review Exercises 597
Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
List of Applications
Agriculture Painting a silo, 444 Mixing saline solution, 352 VFR use, 84
Paving a feed lot, 51 Potassium solution, 289 VOR (very high frequency
Acreage of a ranch, 409
Percentage of a herd lost in Preparing medication, 289 omnidirectional range),
Antifreeze in tractor, 289
winter, 84 Storeroom capacity, 408 408, 418
Applying fertilizer, 85, 283
Pesticide spraying, 51, 74 X-ray film, 408 Volume of baggage
Area of cross section of
Profit on feeder cattle, 74 compartment, 439
pipe, 427
Aviation
Soil nutrient depletion, 288
Area of a ranch, 409
Auto/Diesel
Total yield per acre, 10, Area/size of a runway/
Border around a garden,
Mechanics
288 taxiway, 17, 422, 475
385
Tractor depreciation, 9 Area of a military Alternator, 283
Butterfat in milk, 85, 351
Tractor purchase, 97 operating zone, 17, 408 Amount of oil used, 42
Calculating storage
Volume of bin, 429 Area of airspeed indicator, Amount of time servicing a
requirements, 10
Volume of wagon box, 427 car, 42, 51, 74
Capacity of conical bin,
429 Baggage volume, 192 Antifreeze, 193
451
Volume of cotton bales, 10, Cost of fuel, 73 Auto damage, 512
Chemical requirement, 84,
51 Difference of fuel used, 42 Area occupied by an
288
Weight of dry hay, 104 Dimensions of wing, 384 automobile, 17
Corn and soybean harvest,
Weight of grain, 283 Distance flown, 9 Area of side of tire, 427
351
Weight of hay bales, 10 Distance from base airport, Area/size of mirror, 409,
Depreciation of a corn
Weight of a hog, 289 480 422
planter, 10
Weight of protein, 85 Flight distance, 74 Area of windshield, 195
Diameter of pipes, 427
Yield per acre of corn, 51, Flight time, 9, 19, 52, 63, Car seat dimensions, 512
Diameter of a silo, 427
195, 283 83, 352 Calculating displacement,
Fat in beef, 289
Yield per acre of oats, 10 Fuel used, 42, 195, 288 9, 74
Feed consumption of
Yield per acre of soybeans, IFR (instrument flight Capacity of a fuel tank, 56,
steers, 10
10 rules), 84 289
Feed invoice, 87
Lateral surface area of Changing tires, 51
Feed lot construction, 51
Allied Health
airplane nose, 451 Circumference of rim, 427
Feed mix, 351
Alcohol content of Length of side of hexagon- Converting dimensions, 58
Freight car capacity, 10
medication, 51 shaped landing pad, 422 Cost of labor, 9
Harvesting hay, 104
Calculating dosages, 10, Length of taxiway, 475 Cost of tires, 9, 73
Herbicide application, 51,
51, 52, 74, 85, 283, 288 Percent of rental time, 84 Distance driven, 193
74, 283
Calculating a patient’s Plane height, 9, 55 Fan belt arrangement, 422
Land purchase, 56
input and output, 9 Plane rental, 84 Fuel consumption, 9, 288
Making a trough, 445
Floor space per hospital Remaining fuel, 42, 173 Fuel pump, 288
Manifold diameter, 427
bed, 408 Search time, 50 Grinding a valve, 65
Mixing feed, 56
Fluid intake, 9 Speed of plane, 50, 73 Horsepower of an engine,
Mixing insecticide, 74
Intravenous (IV), 283, 352 Surface area of hemispheri- 195, 288
Mixing pesticide, 10, 74,
Medication vials, 283, 352 cal cockpit cover, 454 Labor cost per hour, 9
351, 352
ix
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