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Technical Shop Mathematics

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Engineering and Technical Mathematics

Technical Shop Mathematics
577 pages

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Mathematics is a universal language that has evolved over thousands of years. It draws on contributions from every civilization and corner of the world—from the ancient worlds of the Middle East, Greece, and Rome, to India, China, Russia, Africa, and pre-Columbian Mayan culture.

Mathematics is used all over the world to solve problems in economics, engineering, manufacturing, construction, electronics, social science and myriad other disciplines. Through mathematics, people can communicate abstract ideas with each other even though they may speak different languages and may come from different cultures.

The language of mathematics consists of many dialects, or subdisciplines. These include arithmetic, algebra, geometry, trigonometry, and statistics, to name a few. This book concentrates on the rudimentary skills needed to study mathematics and solve practical problems encountered in technical fields.

TOC

1 THE LANGUAGE OF MATHEMATICS
Symbols — The Alphabet of
Mathematics 1
Properties of Real Numbers 5
Real Number Set and Subsets 6
The Multiplication Table 9
Operations in Arithmetic 10
Order of Mixed Operations 14

2 SIGNED NUMBER OPERATIONS
Addition and Subtraction on the
Number Line 17
Absolute Value 20
Combining More than Two
Numbers through Addition and
Subtraction 22
Multiplication and Division 24
Combining All Signed Number
Operations 26

3 COMMON FRACTIONS
Common Fractions as Division 27
Converting Improper Fractions and
Mixed Numbers 29
Raising a Common Fraction to
Higher Terms 31
Reducing a Common Fraction to
Lowest Terms 32
Addition and Subtraction of
Common Fractions 37
Addition and Subtraction of Mixed
Numbers 43
Multiplication and Division of
Common Fractions 48
Multiplication and Division of Mixed
Numbers 52
Complex Fractions 55

4 DECIMAL FRACTIONS
Meaning of a Decimal Fraction 57
Converting Common Fractions to
Decimal Fractions 59
Converting Decimal Fractions to
Common Fractions 61
Addition and Subtraction of
Decimal Fractions 63
Multiplication of Decimal
Fractions 65
Division of Decimal Fractions 67
Place Value and Rounding 69
Measurement Arithmetic 73
Decimal Tolerances 76

5 OPERATIONS WITH PERCENTS
Working with Percents 83
Solving Percent Problems 90
Simple Interest 95
List Price and Discounts 96

6 EXPONENTS: POWERS AND ROOTS
Powers of Positive and Negative
Bases 99
Exponent Rules Part 1 101
Exponent Rules Part 2 104
Scientific Notation 108
Logarithms 111

7 MEASUREMENT
Systems of Measurement 115
Measures of Length, Area, and Volume 118
Angle Measure 126
Weight and Mass Measure 131
Measures of Temperature and Heat 132
Measures of Pressure 135
Strain 140

8 ALGEBRAIC EXPRESSIONS
Working with Algebraic Expressions 141
Operations on Expressions — Exponents 146
Operations on Expressions — Radicals 149
Operations on Expressions — Rationalizing the
Denominator 151
Operations on Expressions — Combining Like Terms 152

9 SOLVING EQUATIONS AND INEQUALITIES IN X
Solving Linear Equations in One Variable 155
Solving Inequalities in x 163

10 GRAPHING LINEAR EQUATIONS
The Cartesian Plane 169
Graphing Points of a Line 172
The Slope of a Line 175
Applying Linear Equation Forms to Graphs 180

11 TRANSFORMING AND SOLVING SHOP FORMULAS
Literal Equations 187
Applications of Literal Equations in
Shop Mathematics 190

12 RATIO AND PROPORTION
Statements of Comparison 213
Mixture Proportions 223
Tapers and Other Tooling Calculations
Requiring Proportions 225
Variation 233

13 OPERATIONS ON POLYNOMIALS
Expanding Algebraic
Expressions 243
Factoring Polynomials 248
Binomial Factors of a Trinomial 251
Special Products 256
Algebraic Fractions 259

14 SOLVING QUADRATIC EQUATIONS
Solving Quadratic Equations of Form x 2 = Constant 271
The Quadratic Formula 276

15 LINES, ANGLES, POLYGONS, AND SOLIDS
Points, Lines, and Planes 279
Polygons 286
Polyhedrons and Other Solid Figures 294

16 PERIMETER, AREA, AND VOLUME
Perimeter 297
Area of a Polygon 301
Surface Area and Volume of a Solid 31

17 AXIOMS, POSTULATES, AND THEOREMS
Axioms and Postulates 321
Theorems About Lines and Angles in a Plane 325

18 TRIANGLES
Special Lines in Triangles 341
Similar Triangles 344
Pythagorean Theorem 353
Congruent Triangles 360
The Projection Formula 365
Hero’s Formula 369

19 THE CIRCLE
Definitions 375
Theorems Involving Circles 381

20 TRIGONOMETRY FUNDAMENTALS
Some Key Definitions Used in Trigonometry 401
Solving Sides of Triangles Using Trigonometric Functions 410
Special Triangles and the Unit Circle 427
Graphing the Trigonometric Functions 433

21 OBLIQUE ANGLE TRIGONOMETRY
Solving Oblique Triangles Using
Right Triangles 439
Special Laws of Trigonometry 445

Contributed by Harsh Patel

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