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Introductory Technical Mathematics

ISBN: 9781418015435 | 1418015431
Edition: 5th
Format: Paperback
Publisher: Cengage Learning
Pub. Date: 6/9/2006

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SummaryTable of Contents
Technical Mathematics, 5E provides current and practical vocational/technical applications of mathematical concepts for today?s sophisticated trade and technical work environments. Each unit provides a unique learning experience by featuring practical math concepts alongside step-by-step examples and problems drawn from various occupations that illustrate on-the-job applications of math. Enhancements to the Fifth Edition include a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a sec... MORE
Prefacexvii
SECTION I Fundamentals of General Mathematics
1(196)
Unit 1 Whole Numbers
2(31)
... MORE
Place Value
2(1)
Expanding Whole Numbers
3(1)
Estimating (Approximating)
4(1)
Addition of Whole Numbers
5(2)
Subtraction of Whole Numbers
7(1)
Problem Solving---Word Problem Practical Applications
8(1)
Adding and Subtracting Whole Numbers in Practical Applications
9(2)
Multiplication of Whole Numbers
11(4)
Division of Whole Numbers
15(3)
Multiplying and Dividing Whole Numbers in Practical Applications
18(2)
Combined Operations of Whole Numbers
20(2)
Combined Operations of Whole Numbers in Practical Applications
22(7)
Unit Exercise and Problem Review
25(4)
Computing with a Calculator: Whole Numbers
29(4)
Unit 2 Common Fractions
33(48)
Definitions
33(1)
Fractional Parts
34(1)
A Fraction as an Indicated Division
35(1)
Equivalent Fractions
35(1)
Expressing Fractions in Lowest Terms
36(1)
Expressing Mixed Numbers as Improper Fractions
36(1)
Expressing Improper Fractions as Mixed Numbers
37(1)
Division of Whole Numbers: Quotients as Mixed Numbers
38(1)
Use of Common Fractions in Practical Applications
38(2)
Addition of Common Fractions
40(5)
Subtraction of Common Fractions
45(3)
Adding and Subtracting Common Fractions in Practical Applications
48(4)
Multiplication of Common Fractions
52(4)
Multiplying Common Fractions in Practical Applications
56(3)
Division of Common Fractions
59(3)
Dividing Common Fractions in Practical Applications
62(3)
Combined Operations with Common Fractions
65(2)
Combined Operations of Common Fractions in Practical Applications
67(7)
Unit Exercise and Problem Review
69(5)
Computing with a Calculator: Fractions and Mixed Numbers
74(7)
Unit 3 Decimal Fractions
81(50)
Meaning of Fractional Parts
82(1)
Reading Decimal Fractions
82(1)
Simplified Method of Reading Decimal Fractions
83(1)
Writing Decimal Fractions
83(1)
Rounding Decimal Fractions
84(1)
Expressing Common Fractions as Decimal Fractions
84(1)
Expressing Decimal Fractions as Common Fractions
85(1)
Expressing Decimal Fractions in Practical Applications
86(2)
Adding Decimal Fractions
88(1)
Subtracting Decimal Fractions
88(1)
Adding and Subtracting Decimal Fractions in Practical Applications
89(3)
Multiplying Decimal Fractions
92(3)
Multiplying Decimal Fractions in Practical Applications
95(2)
Dividing Decimal Fractions
97(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 Measure796(2)
Appendix B Formulas for Areas (A) of Plane Figures798(1)
Appendix C Formulas for Volumes and Areas of Solid Figures799(1)
Appendix D Answers to Odd-Numbered Exercises800(45)
Index845

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