Introductory Technical Mathematics

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ISBN: 9781418015435 | 1418015431
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Copyright: 6/9/2006

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Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math.Enhancements to the fifth edition include improved algebra coverage, a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing.

Preface

xvii

SECTION I Fundamentals of General Mathematics

(196)

Unit 1 Whole Numbers

(31)

Place Value

(1)

Expanding Whole Numbers

(1)

Estimating (Approximating)

(1)

Addition of Whole Numbers

(2)

Subtraction of Whole Numbers

(1)

Problem Solving---Word Problem Practical Applications

(1)

Adding and Subtracting Whole Numbers in Practical Applications

(2)

Multiplication of Whole Numbers

(4)

Division of Whole Numbers

(3)

Multiplying and Dividing Whole Numbers in Practical Applications

(2)

Combined Operations of Whole Numbers

(2)

Combined Operations of Whole Numbers in Practical Applications

(7)

Unit Exercise and Problem Review

(4)

Computing with a Calculator: Whole Numbers

(4)

Unit 2 Common Fractions

(48)

Definitions

(1)

Fractional Parts

(1)

A Fraction as an Indicated Division

(1)

Equivalent Fractions

(1)

Expressing Fractions in Lowest Terms

(1)

Expressing Mixed Numbers as Improper Fractions

(1)

Expressing Improper Fractions as Mixed Numbers

(1)

Division of Whole Numbers: Quotients as Mixed Numbers

(1)

Use of Common Fractions in Practical Applications

(2)

Addition of Common Fractions

(5)

Subtraction of Common Fractions

(3)

Adding and Subtracting Common Fractions in Practical Applications

(4)

Multiplication of Common Fractions

(4)

Multiplying Common Fractions in Practical Applications

(3)

Division of Common Fractions

(3)

Dividing Common Fractions in Practical Applications

(3)

Combined Operations with Common Fractions

(2)

Combined Operations of Common Fractions in Practical Applications

(7)

Unit Exercise and Problem Review

(5)

Computing with a Calculator: Fractions and Mixed Numbers

(7)

Unit 3 Decimal Fractions

(50)

Meaning of Fractional Parts

(1)

Reading Decimal Fractions

(1)

Simplified Method of Reading Decimal Fractions

(1)

Writing Decimal Fractions

(1)

Rounding Decimal Fractions

(1)

Expressing Common Fractions as Decimal Fractions

(1)

Expressing Decimal Fractions as Common Fractions

(1)

Expressing Decimal Fractions in Practical Applications

(2)

Adding Decimal Fractions

(1)

Subtracting Decimal Fractions

(1)

Adding and Subtracting Decimal Fractions in Practical Applications

(3)

Multiplying Decimal Fractions

(3)

Multiplying Decimal Fractions in Practical Applications

(2)

Dividing Decimal Fractions

(3)

Dividing Decimal Fractions in Practical Applications

100

(3)

Powers and Roots of Decimal Fractions

103

(3)

Decimal Fraction Powers and Roots in Practical Applications

106

(3)

Table of Decimal Equivalents

109

(3)

Combined Operations of Decimal Fractions

112

(2)

Combined Operations of Decimal Fractions in Practical Applications

114

(11)

Unit Exercise and Problem Review

118

(7)

Computing with a Calculator: Decimals

125

(6)

Unit 4 Ratio and Proportion

131

(15)

Description of Ratios

131

(1)

Order of Terms of Ratios

132

(2)

Description of Proportions

134

(3)

Direct Proportions

137

(2)

Inverse Proportions

139

(7)

Unit Exercise and Problem Review

142

(4)

Unit 5 Percents

146

(18)

Definition of Percent

146

(1)

Expressing Decimal Fractions as Percents

147

(1)

Expressing Common Fractions and Mixed Numbers as Percents

147

(1)

Expressing Percents as Decimal Fractions

148

(1)

Expressing Percents as Common Fractions

149

(1)

Types of Simple Percent Problems

149

(3)

Finding Percentage in Practical Applications

152

(2)

Finding Percent (Rate) in Practical Applications

154

(2)

Finding the Base in Practical Applications

156

(1)

More Complex Percentage Practical Applications

157

(7)

Unit Exercise and Problem Review

160

(4)

Unit 6 Signed Numbers

164

(33)

Meaning of Signed Numbers

164

(2)

The Number Line

166

(1)

Operations Using Signed Numbers

167

(1)

Absolute Value

167

(1)

Addition of Signed Numbers

168

(3)

Subtraction of Signed Numbers

171

(1)

Multiplication of Signed Numbers

172

(2)

Division of Signed Numbers

174

(1)

Powers of Signed Numbers

175

(2)

Roots of Signed Numbers

177

(3)

Combined Operations of Signed Numbers

180

(2)

Scientific Notation

182

(6)

Engineering Notation

188

(9)

Unit Exercise and Problem Review

191

(6)

SECTION II Measurement

197

(96)

Unit 7 Precision, Accuracy, and Tolerance

198

(16)

Exact and Approximate (Measurement) Numbers

198

(1)

Degree of Precision of Measuring Instruments

199

(1)

Common Linear Measuring Instruments

199

(1)

Degree of Precision of a Measurement Number

200

(1)

Degrees of Precision in Adding and Subtracting Measurement Numbers

201

(1)

Significant Digits

202

(1)

Accuracy

203

(1)

Accuracy in Multiplying and Dividing Measurement Numbers

204

(1)

Absolute and Relative Error

204

(1)

Tolerance (Linear)

205

(2)

Unilateral and Bilateral Tolerance with Clearance and Interference Fits

207

(7)

Unit Exercise and Problem Review

209

(5)

Unit 8 Customary Measurement Units

214

(26)

Customary Linear Units

214

(1)

Expressing Equivalent Units of Measure

215

(3)

Arithmetic Operations with Compound Numbers

218

(4)

Customary Linear Measure Practical Applications

222

(3)

Customary Units of Surface Measure (Area)

225

(2)

Customary Area Measure Practical Applications

227

(1)

Customary Units of Volume (Cubic Measure)

228

(1)

Customary Volume Practical Applications

229

(1)

Customary Units of Capacity

230

(1)

Customary Capacity Practical Applications

231

(1)

Customary Units of Weight (Mass)

232

(1)

Customary Weight Practical Applications

233

(1)

Compound Units

233

(2)

Compound Units Practical Applications

235

(5)

Unit Exercise and Problem Review

237

(3)

Unit 9 Metric Measurement Units

240

(28)

Metric Units of Linear Measure

240

(2)

Expressing Equivalent Units within the Metric System

242

(2)

Arithmetic Operations with Metric Lengths

244

(1)

Metric Linear Measure Practical Applications

244

(2)

Metric Units of Surface Measure (Area)

246

(1)

Arithmetic Operations with Metric Area Units

247

(1)

Metric Area Measure Practical Applications

248

(1)

Metric Units of Volume (Cubic Measure)

248

(2)

Arithmetic Operations with Metric Volume Units

250

(1)

Metric Volume Practical Applications

250

(1)

Metric Units of Capacity

251

(1)

Metric Capacity Practical Applications

252

(1)

Metric Units of Weight (Mass)

253

(1)

Metric Weight Practical Applications

254

(1)

Compound Units

254

(2)

Compound Units Practical Applications

256

(1)

Metric Prefixes Applied to Very Large and Very Small Numbers

257

(4)

Conversion Between Metric and Customary Systems

261

(7)

Unit Exercise and Problem Review

264

(4)

Unit 10 Steel Rules and Vernier Calipers

268

(13)

Types of Steel Rules

268

(1)

Reading Fractional Measurements

268

(2)

Measurements that Do Not Fall on Rule Graduations

270

(1)

Reading Decimal-Inch Measurements

271

(1)

Reading Metric Measurements

272

(1)

Vernier Calipers: Types and Description

273

(2)

Reading Measurements on a Customary Vernier Caliper

275

(2)

Reading Measurements on a Metric Vernier Caliper

277

(4)

Unit Exercise and Problem Review

279

(2)

Unit 11 Micrometers

281

(12)

Description of a Customary Outside Micrometer

281

(1)

Reading a Customary Micrometer

282

(1)

The Customary Vernier Micrometer

283

(1)

Reading a Customary Vernier Micrometer

284

(2)

Description of a Metric Micrometer

286

(1)

Reading a Metric Micrometer

286

(1)

The Metric Vernier Micrometer

287

(1)

Reading a Metric Vernier Micrometer

288

(5)

Unit Exercise and Problem Review

290

(3)

SECTION III Fundamentals of Algebra

293

(130)

Unit 12 Introduction to Algebra

294

(11)

Symbolism

294

(1)

Algebraic Expressions

294

(3)

Evaluation of Algebraic Expressions

297

(8)

Unit Exercise and Problem Review

302

(3)

Unit 13 Basic Algebraic Operations

305

(31)

Definitions

305

(1)

Addition

306

(2)

Subtraction

308

(3)

Multiplication

311

(3)

Division

314

(4)

Powers

318

(3)

Roots

321

(3)

Removal of Parentheses

324

(1)

Combined Operations

325

(1)

Basic Structure of the Binary Numeration System

326

(10)

Unit Exercise and Problem Review

330

(6)

Unit 14 Simple Equations

336

(23)

Expression of Equality

336

(1)

Writing Equations from Word Statements

337

(2)

Checking the Equation

339

(2)

Principles of Equality

341

(1)

Solution of Equations by the Subtraction Principle of Equality

341

(3)

Solution of Equations by the Addition Principle of Equality

344

(3)

Solution of Equations by the Division Principle of Equality

347

(2)

Solution of Equations by the Multiplication Principle of Equality

349

(3)

Solution of Equations by the Root Principle of Equality

352

(2)

Solution of Equations by the Power Principle of Equality

354

(5)

Unit Exercise and Problem Review

356

(3)

Unit 15 Complex Equations

359

(14)

Equations Consisting of Combined Operations

359

(4)

Solving for the Unknown in Formulas

363

(1)

Substituting Values Directly in Given Formulas

363

(3)

Rearranging Formulas

366

(7)

Unit Exercise and Problem Review

370

(3)

Unit 16 The Cartesian Coordinate System and Graphs of Linear Equations

373

(12)

Description of the Cartesian (Rectangular) Coordinate System

373

(1)

Graphing a Linear Equation

374

(3)

Slope of a Linear Equation

377

(1)

Slope Intercept Equation of a Straight Line

378

(1)

Point-Slope Equation of a Straight Line

378

(1)

Determining an Equation, Given Two Points

379

(1)

Describing a Straight Line

380

(5)

Unit Exercise and Problem Review

383

(2)

Unit 17 Systems of Equations

385

(18)

Graphical Method of Solving Systems of Equations

385

(2)

Substitution Method of Solving Systems of Equations

387

(1)

Addition or Subtraction Method of Solving Systems of Equations

388

(4)

Types of Systems of Equations

392

(1)

Determinants

393

(1)

Cramer's Rule

394

(1)

Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications

395

(8)

Unit Exercise and Problem Review

401

(2)

Unit 18 Quadratic Equations

403

(20)

General or Standard Form of Quadratic Equations

403

(1)

Incomplete Quadratic Equations (ax2 = c)

404

(4)

Complete Quadratic Equations

408

(3)

Practical Applications of Complete Quadratic Equations, Equations Given

411

(6)

Word Problems Involving Complete Quadratic Equations, Equations Not Given

417

(6)

Unit Exercise and Problem Review

421

(2)

SECTION IV Fundamentals of Plane Geometry

423

(118)

Unit 19 Introduction to Plane Geometry

424

(6)

Plane Geometry

424

(1)

Axioms and Postulates

425

(3)

Points and Lines

428

(2)

Unit Exercise and Problem Review

429

(1)

Unit 20 Angular Measure

430

(18)

Units of Angular Measure

430

(1)

Units of Angular Measure in Degrees, Minutes, and Seconds

431

(1)

Expressing Degrees, Minutes, and Seconds as Decimal Degrees

432

(1)

Expressing Decimal Degrees as Degrees, Minutes, and Seconds

432

(3)

Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds

435

(6)

Simple Semicircular Protractor

441

(4)

Complements and Supplements of Scale Readings

445

(3)

Unit Exercise and Problem Review

445

(3)

Unit 21 Angular Geometric Principles

448

(13)

Naming Angles

448

(1)

Types of Angles

448

(1)

Angles Formed by a Transversal

449

(2)

Theorems and Corollaries

451

(10)

Unit Exercise and Problem Review

458

(3)

Unit 22 Triangles

461

(16)

Types of Triangles

462

(2)

Angles of a Triangle

464

(4)

Isoseeles and Equilateral Triangles

468

(1)

Isosceles Triangle Practical Applications

468

(1)

Equilateral Triangle Practical Applications

469

(1)

The Pythagorean Theorem

470

(1)

Pythagorean Theorem Practical Applications

470

(7)

Unit Exercise and Problem Review

473

(4)

Unit 23 Congruent and Similar Figures

477

(14)

Congruent Figures

477

(2)

Similar Figures

479

(3)

Practical Applications of Similar Triangles

482

(9)

Unit Exercise and Problem Review

488

(3)

Unit 24 Polygons

491

(14)

Types of Polygons

491

(2)

Types of Quadrilaterals

493

(2)

Polygon Interior and Exterior Angles

495

(1)

Practical Applications of Polygon Interior and Exterior Angles

495

(5)

Practical Applications of Trapezoid Median

500

(5)

Unit Exercise and Problem Review

502

(3)

Unit 25 Circles

505

(36)

Definitions

505

(2)

Circumference Formula

507

(1)

Are Length Formula

508

(2)

Radian Measure

510

(2)

Circle Postulates

512

(1)

Chords, Arcs, and Central Angles

513

(2)

Practical Applications of Circle Chord Bisector

515

(3)

Circle Tangents and Chord Segments

518

(1)

Practical Applications of Circle Tangent

518

(1)

Practical Applications of Tangents from a Common Point

519

(3)

Angles Formed Inside and on a Circle

522

(1)

Practical Applications of Inscribed Angles

523

(1)

Practical Applications of Tangent and Chord

524

(2)

Angles Outside a Circle

526

(2)

Internally and Externally Tangent Circles

528

(1)

Practical Applications of Internally Tangent Circles

529

(1)

Practical Applications of Externally Tangent Circles

530

(11)

Unit Exercise and Problem Review

534

(7)

SECTION V Geometric Figures: Areas and Volumes

541

(76)

Unit 26 Areas of Common Polygons

542

(22)

Areas of Rectangles

542

(4)

Areas of Parallelograms

546

(4)

Areas of Trapezoids

550

(3)

Areas of Triangles Given the Base and Height

553

(2)

Areas of Triangles Given Three Sides

555

(9)

Unit Exercise and Problem Review

559

(5)

Unit 27 Areas of Circles, Sectors, Segments, and Ellipses

564

(14)

Areas of Circles

564

(1)

Ratio of Two Circles

565

(3)

Areas of Sectors

568

(2)

Areas of Segments

570

(2)

Areas of Ellipses

572

(6)

Unit Exercise and Problem Review

574

(4)

Unit 28 Prisms and Cylinders: Volumes, Surface Areas, and Weights

578

(13)

Prisms

578

(1)

Volumes of Prisms

578

(4)

Cylinders

582

(1)

Volumes of Cylinders

582

(2)

Computing Heights and Bases of Prisms and Cylinders

584

(2)

Lateral Areas and Surface Areas of Right Prisms and Cylinders

586

(5)

Unit Exercise and Problem Review

589

(2)

Unit 29 Pyramids and Cones: Volumes, Surface Areas, and Weights

591

(16)

Pyramids

591

(1)

Cones

592

(1)

Volumes of Regular Pyramids and Right Circular Cones

592

(2)

Computing Heights and Bases of Regular Pyramids and Right Circular Cones

594

(1)

Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones

595

(3)

Frustums of Pyramids and Cones

598

(1)

Volumes of Frustums of Regular Pyramids and Right Circular Cones

599

(2)

Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones

601

(6)

Unit Exercise and Problem Review

605

(2)

Unit 30 Spheres and Composite Figures: Volumes, Surface Areas, and Weights

607

(10)

Spheres

607

(1)

Surface Area of a Sphere

608

(1)

Volume of a Sphere

608

(2)

Volumes and Surface Areas of Composite Solid Figures

610

(7)

Unit Exercise and Problem Review

615

(2)

SECTION VI Basic Statistics

617

(70)

Unit 31 Graphs: Bar, Circle, and Line

618

(39)

Types and Structure of Graphs

618

(1)

Reading Bar Graphs

619

(5)

Drawing Bar Graphs

624

(2)

Drawing Bar Graphs with a Spreadsheet

626

(5)

Circle Graphs

631

(4)

Drawing Circle Graphs with a Spreadsheet

635

(2)

Line Graphs

637

(1)

Reading Line Graphs

638

(2)

Reading Combined-Data Line Graphs

640

(4)

Drawing Line Graphs

644

(1)

Drawing Broken-Line Graphs

644

(2)

Drawing Broken-Line Graphs with a Spreadsheet

646

(2)

Drawing Straight-Line Graphs

648

(1)

Drawing Curved-Line Graphs

649

(8)

Unit Exercise and Problem Review

653

(4)

Unit 32 Statistics

657

(30)

Probability

657

(2)

Independent Events

659

(2)

Mean Measurement

661

(2)

Other Average Measurements

663

(1)

Quartiles and Percentiles

664

(3)

Grouped Data

667

(5)

Variance and Standard Deviation

672

(5)

Statistical Process Control: X-Bar Charts

677

(4)

Statistical Process Control: R-Charts

681

(6)

Unit Exercise and Problem Review

685

(2)

SECTION VII Fundamentals of Trigonometry

687

(109)

Unit 33 Introduction to Trigonometric Functions

688

(11)

Ratio of Right Triangle Sides

688

(1)

Identifying Right Triangle Sides by Name

689

(1)

Trigonometric Functions: Ratio Method

690

(2)

Customary and Metric Units of Angular Measure

692

(1)

Determining Functions of Given Angles and Determining Angles of Given Functions

692

(7)

Unit Exercise and Problem Review

696

(3)

Unit 34 Trigonometric Functions with Right Triangles

699

(12)

Variation of Functions

699

(2)

Functions of Complementary Angles

701

(2)

Determining an Unknown Angle When Two Sides of a Right Triangle Are Known

703

(2)

Determining an Unknown Angle When an Acute Angle an One Side of a Right Triangle Are Known

705

(6)

Unit Exercise and Problem Review

709

(2)

Unit 35 Practical Applications with Right Triangles

711

(28)

Solving Problems Stated in Word Form

711

(5)

Solving Problems Given in Picture Form that Require Auxiliary Lines

716

(9)

Solving Complex Problems that Require Auxiliary Lines

725

(14)

Unit Exercise and Problem Review

734

(5)

Unit 36 Functions of Any Angle, Oblique Triangles

739

(35)

Cartesian (Rectangular) Coordinate System

739

(1)

Determining Functions of Angles in Any Quadrant

740

(3)

Alternating Current Applications

743

(3)

Determining Functions of Angles Greater Than 360°

746

(1)

Instantaneous Voltage Related to Time Application

747

(1)

Solving Oblique Triangles

748

(1)

Law of Sines

748

(1)

Solving Problems Given Two Angles and a Side. Using the Law of Sines

749

(2)

Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines

751

(4)

Law of Cosines (Given Two Sides and the Included Angle)

755

(1)

Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines

755

(3)

Law of Cosines (Given Three Sides)

758

(1)

Solving Problems Given Three Sides, Using the Law of Cosines

759

(3)

Practical Applications of Oblique Triangles

762

(12)

Unit Exercise and Problem Review

769

(5)

Unit 37 Vectors

774

(22)

Scalar and Vector Quantities

774

(1)

Description and Naming Vectors

774

(1)

Vector Ordered Pair Notation

775

(1)

Vector Length and Angle Notation

776

(1)

Adding Vectors

776

(2)

Graphic Addition of Vectors

778

(4)

Addition of Vectors Using Trigonometry

782

(6)

General (Component Vector) Procedure for Vectors Using Trigonometry

788

(8)

Unit Exercise and Problem Review

793

(3)

Appendix A United States Customary and Metric Units of Measure

796

(2)

Appendix B Formulas for Areas (A) of Plane Figures

798

(1)

Appendix C Formulas for Volumes and Areas of Solid Figures

799

(1)

Appendix D Answers to Odd-Numbered Exercises

800

(45)

Index

845

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Introductory Technical Mathematics

Summary

Table of Contents

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