Introductory Technical Mathematics

by Peterson, John; Smith, Robert D.

• ISBN13: 9781418015459
• ISBN10: 1418015458
• Edition: 5th
• Format: Hardcover
• Copyright: 2006-06-06
• Publisher: CENGAGE Delmar Learning

Summary

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.

Table of Contents

Preface	xvii
SECTION I Fundamentals of General Mathematics	1	(196)
Whole Numbers	2	(31)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Quadratic Equations	403	(20)
General or Standard Form of Quadratic Equations	403	(1)
Incomplete Quadratic Equations (αx2 = 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)
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)
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)
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)
Triangles	461	(16)
Types of Triangles	462	(2)
Angles of a Triangle	464	(4)
Isosceles 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)
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)
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)
Circles	505	(36)
Definitions	505	(2)
Circumference Formula	507	(1)
Arc 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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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	(7)
Unit Exercise and Problem Review	769	(5)
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