ISBN-10:
0070482543
ISBN-13:
9780070482548
Pub. Date:
11/01/1985
Publisher:
McGraw-Hill Higher Education
Practical Mathematics / Edition 7

Practical Mathematics / Edition 7

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Product Details

ISBN-13: 9780070482548
Publisher: McGraw-Hill Higher Education
Publication date: 11/01/1985
Pages: 542
Product dimensions: 6.70(w) x 9.57(h) x 1.06(d)

Table of Contents

Preface xvii
PART 1 ARITHMETIC 1(100)
Introduction To Arithmetic
3(9)
Symbols Used in Working with Whole Numbers
4(1)
Numbers
4(1)
Definitions of Terms
5(2)
Sequence of Operations
7(2)
Applying Rules and Procedures
9(3)
Common Fractions
12(17)
Fractions and Calculators
12(1)
Common Fractions---Definitions
12(1)
Mixed Numbers
13(1)
Proper and Improper Fractions
13(1)
Reducing a Common Fraction to Its Lowest Terms
13(1)
Reducing an Improper Fraction
14(1)
Changing a Whole or Mixed Number to an Improper Fraction
14(1)
Changing Two or More Fractions to Fractions with the Same Denominator
15(1)
Finding the Lowest Common Denominator
15(1)
Addition of Fractions
16(2)
Subtraction of Fractions
18(2)
Multiplication of Fractions
20(1)
Cancellation
21(2)
Division of Fractions
23(2)
Complex Fractions
25(4)
Decimal Fractions
29(23)
Introduction to Decimal Fractions
29(1)
Definitions of Decimal Fractions
29(1)
Reading Numbers
30(1)
Changing a Common Fraction to a Decimal Fraction
30(2)
Changing a Decimal Fraction to a Common Fraction
32(2)
Decimal Equivalents
34(2)
Adding Decimals
36(1)
Subtracting Decimals
36(1)
Multiplying Decimals
37(1)
Dividing Decimals
38(1)
Rounding Off Numbers
39(4)
Measuring Instruments
43(1)
The Framing Square
43(1)
The Circumference Rule
44(1)
The Micrometer Caliper
45(1)
Micrometer with Vernier
46(1)
Direct-Reading Micrometers
46(2)
Dual-Reading Micrometers
48(1)
The Voltmeter
48(1)
Summary of Measuring Instruments
49(3)
Percentages
52(11)
Introduction to Percentages
52(1)
Percentages as Fractions
52(4)
Relations Shown by Percentage
56(1)
Averages and Percentage of Error
57(1)
List Prices and Discounts
58(2)
Simple Interest
60(3)
Ratio And Proportion
63(11)
Ratio
63(2)
Proportion
65(1)
Principles of Ratio and Proportion
65(4)
An Application: Density
69(1)
Specific Gravity
69(1)
Standards of Specific Gravity
69(1)
Applications of Specific Gravity
70(1)
Conversion of Units
71(3)
Measurement
74(17)
Introduction to Measurement
74(1)
Introduction to the Metric System
74(1)
SI Prefixes
75(1)
Base Units of Measurement
76(1)
The English System
76(1)
Addition and Subtraction of English System Measures
77(1)
Addition and Subtraction of Metric Measures
77(1)
Multiplication and Division of English System Measures
78(2)
Multiplication and Division of Metric Measures
80(2)
Conversion between the English and Metric Systems
82(4)
Precision
86(1)
Precision and Accuracy of Measurements
86(1)
Significant Figures
87(1)
Rounding Off a Number
88(1)
Maintaining Accuracy while Multiplying or Dividing Measurements
88(3)
Powers And Roots
91(10)
Powers
91(1)
Roots
92(1)
Radical Sign and Index of Root
92(1)
Square Root
93(1)
Use of the Table of Square Roots
93(3)
Determining Square Roots by Calculation
96(2)
Cube and Other Roots
98(3)
PART 2 ALGEBRA 101(180)
Introduction To Algebra
102(10)
Introduction to Algebra
102(1)
Numbers
102(1)
Definite Numbers
102(1)
General Numbers
103(1)
Signs of Operation and Grouping
103(1)
Algebraic Expressions
104(1)
Coefficients
104(1)
Powers and Exponents
104(1)
Terms
104(1)
Translation into Algebraic Expressions
105(3)
Formulas
108(1)
Evaluation of Algebraic Expressions and Formulas
108(4)
Addition And Subtraction Of Signed Numbers
112(11)
Introduction to Signed Numbers
112(1)
The Need for Negative Numbers
112(1)
Representation of Negative and Positive Numbers
113(1)
Definitions of Signed Numbers
113(1)
Addition of Signed Numbers
114(1)
Subtraction of Signed Numbers
115(2)
Addition and Subtraction of Literal Algebraic Expressions
117(1)
Adding and Subtracting Polynomials
118(1)
Test or Proof of Results
119(1)
Signs of Grouping
120(2)
Insertion of Signs of Grouping
122(1)
Simple Equations
123(9)
Introduction to Simple Equations
123(1)
Definition of Simple Equations
123(1)
Axioms for Solving Simple Equations
124(1)
Solution of Simple Equations
125(1)
Checking the Unknown
126(1)
Setting Up Equations
127(5)
Multiplication Of Signed Numbers
132(10)
Introduction to Multiplication of Signed Numbers
132(1)
Multiplication of Signed Numbers
132(1)
Multiplying Several Signed Numbers
133(1)
Exponents
134(1)
Multiplying a Monomial by a Monomial
135(1)
Multiplying a Polynomial by a Monomial
135(1)
Multiplying a Polynomial by a Polynomial
136(4)
Solving Equations Involving Multiplication
140(2)
Division Of Signed Numbers And Factoring
142(20)
Introduction to Division with Signed Numbers
142(1)
The Law of Exponents
142(2)
Dividing One Monomial by Another
144(1)
Checking Division with Signed Numbers and Exponents
145(1)
Dividing a Polynomial by a Monomial
145(1)
Dividing a Polynomial by a Polynomial
146(3)
Factoring
149(1)
Factors of a Monomial
149(1)
Factors of a Polynomial When One Factor Is a Monomial
150(1)
The Square of a Binomial
151(1)
Factors of a Trinomial Square
152(1)
The Product of the Sum of Two Quantities Times the Difference of the Same Two Quantities
153(1)
Factors of the Difference of Two Squares
154(1)
General Method for Factoring
155(2)
Factoring Trinomials with No Common Term
157(1)
The Factor Theorem
158(4)
Algebraic Fractions
162(13)
Introduction to Algebraic Fractions
162(1)
Definitions of Algebraic Fractions
162(1)
Principles Used in Working with Fractions
163(3)
Addition of Fractions
166(1)
The Lowest Common Multiple
166(1)
Addition and Subtraction of Algebraic Fractions
167(2)
Multiplication of Fractions
169(1)
Division of Fractions
170(5)
Advanced Equations
175(10)
Introduction to Advanced Equations
175(1)
Solution of Advanced Equations
175(4)
Equations Solved by Factoring
179(3)
Formulas
182(3)
Equations And Applications
185(19)
Introduction to Equations and Applications
185(1)
Clearing Fractions in Equations
185(5)
Setting Up Equations
190(4)
Equations in Electricity
194(1)
Thermometers
195(2)
Horsepower
197(3)
Levers and Moments
200(4)
Graphical Methods
204(22)
Introduction to Graphs
204(2)
Bar Graphs
206(2)
Pie or Circle Graphs
208(1)
Picture Graphs
209(2)
Mathematical Graphs
211(1)
Graphing Definitions
211(1)
Plotting Points
212(1)
Graphing an Equation
213(1)
Simultaneous Equations
214(1)
The Graph of an Equation of Any Degree
215(3)
Slope of a First-Degree Equation
218(1)
Equations of Lines Parallel to an Axis
219(1)
The Equation of Any Straight Line
220(1)
Graphical Solution of Problems
221(5)
Equations With More Than One Unknown
226(11)
Introduction to Equations with More than One Unknown
226(1)
Equations with Two Unknowns
226(2)
Solutions for Two Equations with Two Unknowns
228(1)
Solution by Addition
228(1)
Solution by Subtraction
229(1)
Solution by Substitution
230(1)
Solution by Comparison
231(2)
Solutions for Three Equations with Three Unknowns
233(4)
Exponents And Logarithms
237(18)
Introduction to Exponents and Logarithms
237(1)
Law of Exponents for Multiplication
237(1)
Law of Exponents for Division
238(1)
Law of Exponents for the Power of a Power
238(1)
Fractional Exponents
239(1)
The Root of a Power
239(1)
Applications of Exponents
239(1)
The Power of a Product
240(1)
Power of a Sum or Difference
240(1)
Quantities Affected by Radicals
240(1)
Fractions under the Radical Sign
241(1)
Scientific Notation
241(1)
Introduction to Logarithms
242(2)
Determining the Mantissa
244(1)
Interpolation of a Mantissa
245(1)
Determining the Characteristic
246(1)
Finding the Antilog of a Number
247(2)
Multiplication with Logarithms
249(1)
Division with Logarithms
249(1)
Raising to a Power with Logarithms
249(1)
Roots with Logarithms
250(1)
Natural Logarithms
251(4)
Quadratic Equations
255(14)
Introduction to Quadratic Equations
255(1)
Definitions of Quadratic Equations
255(1)
Solutions for a Pure Quadratic Equation
256(2)
Solution of an Affected Quadratic Equation by Factoring
258(1)
Completing the Square of a Quadratic Equation
259(1)
Equalizing a Quadratic Equation after Completing the Square
260(1)
Solution of a Quadratic Equation by Completing the Square
260(3)
Development of the Quadratic Formula
263(1)
Solutions Using the Quadratic Formula
264(5)
Variation
269(12)
Introduction to Variation
269(1)
Constants and Variables
269(1)
Direct Variation
270(1)
Inverse Variation
271(1)
The Mathematical Statement of an Inverse Relationship
272(1)
Joint Variation
273(2)
A Practical Example of Variation: Transverse Strength of Beams
275(6)
PART 3 GEOMETRY 281(96)
Introduction To Geometry
282(1)
Introduction to Geometry
282(13)
Fundamental Definitions of Geometry
282(2)
Angles
284(2)
Measuring Angles with a Protractor
286(1)
Laying Out Angles with a Protractor
287(1)
Relations of Lines
287(2)
Polygons and Their Properties
289(1)
Triangles and Their Properties
289(3)
Congruent Triangles
292(1)
Quadrilaterals and Their Properties
293(2)
Polygons
295(9)
Introduction to Polygons
295(1)
Area
295(1)
Area of a Rectangle
295(1)
Area of a Parallelogram
296(1)
Basic Formulas for Area
296(1)
Area of a Triangle
297(2)
Area of a Triangle with Three Sides Given
299(1)
Area of a Trapezoid
300(4)
Triangles
304(18)
Introduction to Triangles
304(1)
The Right Triangle
304(2)
The Square and Its Diagonals
306(3)
Similar Triangles
309(1)
Practical Application: Tapers
310(3)
Practical Application: The Steel Square
313(1)
Practical Application: Rafters and Roofs
313(1)
Isosceles and Equilateral Triangles
314(1)
Properties of the Isosceles Triangle
315(1)
Properties of the Equilateral Triangle
315(1)
Altitude and Area of an Equilateral Triangle
316(1)
Properties of the Regular Hexagon
317(2)
Practical Application: Screws and Screw Threads
319(1)
Pitch and Lead of Screw Threads
319(1)
Kinds of Screw Threads
320(1)
Metric Threads
320(2)
The Circle
322(27)
Introduction to The Circle
322(1)
Definitions of the Circle
322(2)
Properties of the Circle
324(2)
Relations between Diameter, Radius, and Circumference
326(1)
Area of a Circle
326(2)
Historical Note Concerning Pi
328(1)
Area of a Ring (Annulus)
328(4)
Area of a Sector
332(1)
Properties of a Segment
332(2)
Area of a Segment
334(3)
Properties of the Ellipse
337(1)
Uses of the Ellipse
337(1)
Area of an Ellipse
338(1)
Circumference of an Ellipse
338(5)
Regular Polygons and Circles
343(2)
Belts, Pulleys, and Gears
345(2)
The Circular Mil and the Square Mil
347(2)
Geometric Solids
349(28)
Introduction to Geometric Solids
349(1)
Prisms
349(1)
Surface Area of a Prism
349(1)
Volume of a Prism
349(2)
Cylinders
351(1)
Volume and Surface Area of a Cylinder
351(1)
Volume of a Hollow Cylinder
352(1)
The Pyramid
352(1)
Surface Area of a Pyramid
353(1)
Volume of a Pyramid
354(1)
The Cone
354(1)
Volume and Surface Area of a Cone
355(1)
Frustums
355(2)
The Sphere
357(1)
Surface Area of a Sphere
358(1)
Volume of a Sphere
358(1)
Segment and Zone of a Sphere
358(2)
The Torus
360(1)
The Prismatoid
361(2)
The Five Regular Polyhedrons
363(14)
PART 4 TRIGONOMETRY 377(97)
Introduction To Trigonometry
378(9)
Introduction to Trigonometry
378(1)
Angles
378(2)
Quadrants
380(1)
Measurement of Angles
381(1)
Degree Measurement of Angles
381(2)
Radian Measurement of Angles
383(1)
The Relation between the Radian and the Degree
384(3)
Trigonometric Functions
387(11)
The Trigonometric Functions
387(1)
The Six Functions
387(1)
Functions for Any Angle
388(3)
Computation of Trigonometric Functions
391(1)
Trigonometric Functions of 30°
391(1)
Trigonometric Functions of 45°
392(1)
Trigonometric Functions of Other Angles
392(1)
Applications to Right Triangles
393(2)
Determining Trigonometric Functions by Construction and Measurement
395(3)
Trigonometric Tables
398(16)
Introduction to Trigonometric Tables
398(1)
Determining Values of Trigonometric Functions from a Table
398(3)
Finding the Angle Corresponding to a Value of a Trigonometric Function
401(2)
Evaluation of Formulas
403(4)
Trigonometric Functions of Angles Greater than 90°
407(1)
Trigonometric Functions of an Angle in the Second Quadrant
407(2)
Trigonometric Functions of an Angle in the Third Quadrant
409(1)
Trigonometric Functions of an Angle in the Fourth Quadrant
409(1)
Functions of a Negative Angle
410(1)
Summary of the Reduction Formulas
411(1)
Functions of an Angle Greater than 360°
411(3)
Right Triangles
414(19)
Introduction to Right Triangles
414(1)
Properties of the Right Triangle
414(1)
Solving Right-Triangle Problems
415(4)
Verbal Right-Triangle Problems
419(7)
Vectors
426(7)
Graphical Representation Of Trigonometric Functions
433(5)
Introduction to Graphing Trigonometric Functions
433(1)
The Sine Curve
433(1)
The Cosine Curve
434(1)
Curves for the Tangent, Cotangent, Secant, and Cosecant
435(3)
Oblique Triangles
438(36)
Introduction to Oblique Triangles
438(1)
The Law of Sines
439(2)
Mollweide's Equations
441(2)
Construction Tests
443(1)
The Law of Cosines
443(6)
Area of a Triangle
449(4)
Diameter of a Circle Circumscribed about a Triangle
453(1)
Radius of a Circle Inscribed in a Triangle
453(2)
Resultant of Forces
455(1)
Computations of a Resultant
456(2)
The Power Factor
458(1)
Refraction
459(3)
The Sine Bar
462(2)
Areas of Sectors and Segments of a Circle
464(3)
Railroad and Highway Curves
467(3)
Distance and Dip of the Horizon
470(2)
Slope of a Line Making a Given Angle with the Line of Greatest Slope
472(2)
Appendix 474(37)
Table 1 Summary of Formulas
474(4)
Table 2 Useful Equivalents
478(1)
Table 3 Decimal and Fractional Equivalents of Parts of an Inch
479(1)
Table 4 U. S. Standard and Sharp V Threads
480(1)
Table 5 Standard Gages for Wire and Sheet Metals
481(2)
Table 6 Specific Gravities and Densities of Substances
483(1)
Table 7 Strength of Materials
484(1)
Table 8 Square Roots
485(4)
Table 9 Common Logarithms
489(2)
Table 10 Natural Sines
491(2)
Table 11 Natural Cosines
493(2)
Table 12 Natural Tangents
495(2)
Table 13 Regular Polygons and Polyhedrons
497(2)
Table 14 Conversions
499(12)
Answers to Odd-Numbered Exercises 511(26)
Index 537

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