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### Technical Shop Mathematics

Manufacturing Engineering Processes

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