## Mathematics for Machine TechnologyOccupations like those of machinists, tool and die makers, pattern makers, drafters, and designers require a fundamental knowledge of general math as well as of more advanced topics like oblique trigonometry, compound angles, and numerical control. This updated edition of Mathematics for Machine Technology promotes an understanding of all the mathematical concepts necessary for success in the machine trades and manufacturing fields. The author effectively combines math concepts with the relevant machine applications so that readers fully understand the value of what they are learning. Industry-specific examples, realistic illustrations, and actual applications further enhance the theory-to-application connection. |

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### Contents

Common Fractions Decimal Fractions and Percentage UNIT 1 Introduction to Common Fractions and Mixed Numbers | 1 |

Addition of Common Fractions and Mixed Numbers | 6 |

Subtraction of Common Fractions and Mixed Numbers | 11 |

Multiplication of Common Fractions and Mixed Numbers | 15 |

Division of Common Fractions and Mixed Numbers | 19 |

Combined Operations of Common Fractions and Mixed Numbers | 22 |

Fractions and Mixed Numbers | 27 |

Introduction to Decimal Fractions | 35 |

Fundamentals of Plane Geometry | 251 |

ProtractorsSimple Semicircular and Vernier | 264 |

Types of Angles and Angular Geometric Principles | 270 |

Introduction to Triangles | 277 |

Geometric Principles for Triangles and Other Common Polygons | 283 |

Introduction to Circles | 293 |

Ares and Angles of Circles Tangent Circles | 302 |

Fundamental Geometric Constructions | 313 |

Rounding Decimal Fractions and Equivalent Decimal and Common Fractions | 36 |

Addition and Subtraction of Decimal Fractions | 41 |

Multiplication of Decimal Fractions | 45 |

Division of Decimal Fractions | 47 |

Powers | 51 |

Roots | 57 |

Table of Decimal Equivalents and Combined Operations of Decimal Fractions | 62 |

Decimals | 68 |

373 | 71 |

introduction to Percents | 73 |

Basic Calculations of Percentages Percents and Rates | 76 |

Percent Practical Applications | 82 |

Achievement ReviewSection One | 87 |

Customary English and Metric | 95 |

Degree of Precision Greatest Possible Error Absolute Error and Relative Error | 102 |

Tolerance Clearance and Interference | 107 |

Customary and Metric Steel Rules | 115 |

Customary Vernier Calipers and Height Gages | 121 |

Customary Micrometers | 129 |

Customary and Metric Gage Blocks | 135 |

Fundamentals of Algebra | 136 |

Achievement ReviewSection Two | 139 |

Symbolism and Algebraic Expressions | 145 |

Signed Numbers | 152 |

Algebraic Operations of Addition Subtraction and Multiplication | 165 |

Algebraic Operations of Division Powers and Roots | 172 |

Introduction to Equations | 184 |

Solution of Equations by the Subtraction Addition and Division Principles of Equality | 191 |

Solution of Equations by the Multiplication Root and Power Principles of Equality | 200 |

Solution of Equations Consisting of Combined Operations and Rearrangement of Formulas | 207 |

Ratio and Proportion | 215 |

Direct and Inverse Proportions | 225 |

Applications of Formulas to Cutting Speed Revolutions Per Minute and Cutting Time | 229 |

Applications of Formulas to Spur Gears | 239 |

Achievement ReviewSection Three | 246 |

Achievement ReviewSection Four | 320 |

Areas and Volumes | 329 |

Areas of Triangles | 336 |

Areas of Circles Sectors and Segments | 340 |

Volumes of Prisms and Cylinders | 346 |

Volumes of Pyramids and Cones | 354 |

Volumes of Spheres and Composite Solid Figures | 361 |

Achievement ReviewSection Five | 366 |

Introduction to Trigonometric Functions | 373 |

Analysis of Trigonometric Functions | 382 |

Basic Calculations of Angles and Sides of Right Triangles | 387 |

Simple Practical Machine Applications | 395 |

Complex Practical Machine Applications | 402 |

The Cartesian Coordinate System | 412 |

Law of Sines and Law of Cosines | 416 |

Achievement ReviewSection Six | 426 |

Compound Angles | 431 |

Computing Angles of Rotation and Tilt Using Given Lengths | 434 |

Computing Angles of Rotation and Tilt Using Given Angles | 438 |

Computing Angles of Rotation and Tilt | 445 |

Computing Angles Made by the Intersection of Two Angular Surfaces | 452 |

Computing Compound Angles on Cutting and Forming Tools | 458 |

Achievement ReviewSection Seven | 465 |

Computer Numerical Control CNC | 467 |

Control Systems Absolute Positioning Incremental Positioning | 470 |

Binary Numeration System | 478 |

Achievement ReviewSection Eight | 483 |

A United States Customary and Metric Units of Measure | 485 |

B Principles of Plane Geometry | 486 |

Formulas for Areas A of Plane Figures | 488 |

Formulas for Volumes of Solid Figures | 489 |

E Trigonometry | 490 |

Answers to OddNumbered Applications | 493 |

521 | |

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### Common terms and phrases

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