Elementary technical mathematics

1. BASIC CONCEPTS. Unit1A Review of Operations with Whole Numbers. 1.1 Review of Basic Operations. 1.2 Order of Operations. 1.3 Area and Volume. 1.4 Formulas. 1.5 Prime Factorization Divisibility. Unit 1A: Review. Unit 1B Review of Operations with Fractions. 1.6 Introduction to Fractions. 1.7 Addition and Subtraction of Fractions. 1.8 Multiplication and Division of Fractions. 1.9 The U.S. System of Weights and Measures. Unit 1B: Review. Unit 1C Review of Operations with Decimal Fractions and Percent. 1.10 Addition and Subtraction of Decimal Fractions. 1.11 Rounding Numbers. 1.12 Multiplication and Division of Decimal Fractions. 1.13 Percent. 1.14 Part, Base, and Rate. 1.15 Powers and Roots. 1.16 Application Involving Percent: Business and Personal Finance. Unit 1C: Review. Chapter 1: Group Activities. Chapter 1: Summary. Chapter 1: Review. Chapter 1: Test.2. SIGNED NUMBERS AND POWERS OF 10. 2.1 Addition of Signed Numbers. 2.2 Subtraction of Signed Numbers. 2.3 Multiplication and Division of Signed Numbers. 2.4 Signed Fractions. 2.5 Powers of 10. 2.6 Scientific Notation. 2.7 Engineering Notation. Chapter 2: Group Activities. Chapter 2: Summary. Chapter 2: Review. Chapter 2: Test. Chapter 1-2: Cumulative Review.3. THE METRIC SYSTEM. 3.1 Introduction to the Metric System. 3.2 Length. 3.3 Mass and Weight. 3.4 Volume and Area. 3.5 Time, Current, and Other Units. 3.6 Temperature. 3.7 Metric and U.S. Conversion. Chapter 3: Group Activities. Chapter 3: Summary. Chapter 3: Review. Chapter 3: Test.4. MEASUREMENT. 4.1 Approximate Numbers and Accuracy. 4.2 Precision and Greatest Possible Error. 4.3 The Vernier Caliper. 4.4 The Micrometer Caliper. 4.5 Addition and Subtraction of Measurements. 4.6 Multiplication and Division of Measurements. 4.7 Relative Error and Percent of Error. 4.8 Color Code of Electrical Resistors. 4.9 Reading Scales. Chapter 4: Group Activities. Chapter 4: Summary. Chapter 4: Review. Chapter 4: Test. Chapter 1-4: Cumulative Review.5. POLYNOMIALS: AN INTRODUCTION TO ALGEBRA. 5.1 Fundamental Operations. 5.2 Simplifying Algebraic Expressions. 5.3 Addition and Subtraction of Polynomials. 5.4 Multiplication of Monomials. 5.5 Multiplication of Polynomials. 5.6 Division by a Monomial. 5.7 Division by a Polynomial. Chapter 5: Group Activities. Chapter 5: Summary. Chapter 5: Review. Chapter 5: Test.6. EQUATIONS AND FORMULAS. 6.1 Equations. 6.2 Equations with Variables in Both Members. 6.3 Equations with Parentheses. 6.4 Equations with Fractions. 6.5 Translating Words into Algebraic Symbols. 6.6 Applications Involving Equations. 6.7 Formulas. 6.8 Substituting Data into Formulas. 6.9 Reciprocal Formulas Using a Calculator. Chapter 6: Group Activities. Chapter 6: Summary. Chapter 6: Review. Chapter 6: Test. Chapters 1-6: Cumulative Review.7. RATIO AND PROPORTION. 7.1 Ratio. 7.2 Proportion. 7.3 Direct Variation. 7.4 Inverse Variation. Chapter 7: Group Activities. Chapter 7: Summary. Chapter 7: Review. Chapter 7: Test.8. GRAPHING LINEAR EQUATIONS. 8.1 Linear Equations with Two Variables. 8.2 Graphing Linear Equations. 8.3 The Slope of a Line. 8.4 The Equation of a Line. Chapter 8: Group Activities. Chapter 8: Summary. Chapter 8: Review. Chapter 8: Test. Chapters 1-8: Cumulative Review.9. SYSTEMS OF LINEAR EQUATIONS. 9.1 Solving Pairs of Linear Equations by Graphing. 9.2 Solving Pairs of Linear Equations by Addition. 9.3 Solving Pairs of Linear Equations by Substitution. 9.4 Applications Involving Pairs of Linear Equations. Chapter 9: Group Activities. Chapter 9: Summary. Chapter 9: Review. Chapter 9: Test.10. FACTORING ALGEBRAIC EXPRESSIONS. 10.1 Finding Monomial Factors. 10.2 Finding the Product of Two Binomials Mentally. 10.3 Finding Binomial Factors. 10.4 Special Products. 10.5 Finding Factors of Special Products. 10.6 Factoring General Trinomials. Chapter 10: Group Activities. Chapter 10: Summary. Chapter 10: Review. Chapter 10: Test. Chapters 1-10: Cumulative Review.11. QUADRATIC EQUATIONS. 11.1 Solving Quadratic Equations by Factoring. 11.2 The Quadratic Formula. 11.3 Applications Involving Quadratic Equations. 11.4 Graphs of Quadratic Equations. 11.5 Imaginary Numbers. Chapter 11: Group Activities. Chapter 11: Summary. Chapter 11: Review. Chapter 11: Test.12. GEOMETRY. 12.1 Angles and Polygons. 12.2 Quadrilaterals. 12.3 Triangles. 12.4 Similar Polygons. 12.5 Circles. 12.6 Radian Measure. 12.7 Prisms. 12.8 Cylinders. 12.9 Pyramids and Cones. 12.10 Spheres. Chapter 12: Group Activities. Chapter 12: Summary. Chapter 12: Review. Chapter 12: Test. Chapters 1-12: Cumulative Review.13. RIGHT TRIANGLE TRIGONOMETRY. 13.1 Trigonometric Ratios. 13.2 Using Trigonometric Ratios to Find Angles. 13.3 Using Trigonometric Ratios to Find Sides. 13.4 Solving Right Triangles. 13.5 Applications Involving Trigonometric Ratios. Chapter 13: Group Activities. Chapter 13: Summary. Chapter 13: Review. Chapter 13: Test.14. TRIGONOMETRY WITH ANY ANGLE. 14.1 Sine and Cosine Graphs. 14.2 Period and Phase Shift. 14.3 Solving Oblique Triangles: Law of Sines. 14.4 Law of Sines: The Ambiguous Case. 14.5 Solving Oblique Triangles: Law of Cosines. Chapter 14: Group Activities. Chapter 14: Summary. Chapter 14: Review. Chapter 14: Test. Chapters 1-14: Cumulative Review.15. BASIC STATISTICS. 15.1 Bar Graphs. 15.2 Circle Graphs. 15.3 Line Graphs. 15.4 Other Graphs. 15.5 Mean Measurement. 15.6 Other Average Measurements and Percentiles. 15.7 Range and Standard Deviation. 15.8 Grouped Data. 15.9 Standard Deviation for Grouped Data. 15.10 Statistical Process Control. 15.11 Other Graphs for Statistical Data. 15.12 Normal Distribution. 15.13 Probability. 15.14 Independent Events. Chapter 15: Group Activities. Chapter 15: Summary. Chapter 15: Review. Chapter 15: Test.16. BINARY AND HEXADECIMAL NUMBERS. 16.1 Introduction to Binary Numbers. 16.2 Addition of Binary Numbers. 16.3 Subtraction of Binary Numbers. 16.4 Multiplication of Binary Numbers. 16.5 Conversion from Decimal to Binary System. 16.6 Conversion from Binary to Decimal System. 16.7 Hexadecimal System. 16.8 Addition and Subtraction of Hexadecimal Numbers. 16.9 Binary to Hexadecimal Conversion. 16.10 Hexadecimal Code for Colors. Chapter 16: Group Activities. Chapter 16: Summary. Chapter 16: Review. Chapter 16: Test. Chapters 1-16: Cumulative Review.Appendix A: Tables. Table 1: Formulas from Geometry. Table 2: Electrical Symbols.Appendix B: Exponential Equations.Appendix C: Simple InequalitiesAppendix D: Instructor's Answer Key to All Exercises. Contents 5 List of Application 11 Preface 15 Ch 1: Basic Concepts 21 1.1: Review of Basic Operations 22 1.2: Order of Operations 31 1.3: Area and Volume 34 1.4: Formulas 39 1.5: Prime Factorization 42 1.6: introduction to Fractions 46 1.7: Addition and Subtraction of Fractions 51 1.8: Multiplication and Division of Fractions 63 1.9: The U.S. System of Weights and Measures 71 1.10: Addition and Subtraction of Decimal Fractions 75 1.11: Rounding numbers 84 1.12: Multiplication and Division of Decimal Fractions 87 1.13: Percent 94 1.14: Rate, Base, and Part 99 1.15: Powers and Roots 107 1.16: Applications Involving Percent: Business and Personal Finance 110 Chapter 1: Group Activities 117 Chapter 1: Summary 117 Chapter 1: Review 120 Chapter 1: Test 122 Ch 2: Signed Numbers and Powers of 10 125 2.1: Addition of Signed Numbers 126 2.2: Subtraction of Signed Numbers 130 2.3: Multiplication and Division of Signed Numbers 132 2.4: Signed Fractions 135 2.5: Powers of 10 139 2.6: Scientific Notation 143 2.7: Engineering Notation 148 Chapter 2: Group Activities 151 Chapter 2: Summary 151 Chapter 2: Review 152 Chapter 2: Test 153 Chapters 1-2: Cumulative Review 154 Ch 3: The Metric System 155 3.1: Introduction to the Metric System 156 3.2: Length 159 3.3: Mass and Weight 162 3.4: Volume and Area 164 3.5: Time, Current, and Other Units 167 3.6: Temperature 170 3.7: Metric and U.S. Conversion 172 Chapter 3: Group Activities 176 Chapter 3: Summary 177 Chapter 3: Review 177 Chapter 3: Test 178 Ch 4: Measurement 179 4.1: Approximate Numbers and Accuracy 180 4.2: Precision and Greatest Possible Error 183 4.3: The Vernier Caliper 187 4.4: The Micrometer Caliper 194 4.5: Addition and Subtraction of Measurements 202 4.6: Multiplication and Division of Measurements 206 4.7: Relative Error and Percent of Error 209 4.8: Color Code of Electrical Resistors 213 4.9: Reading Scales 217 Chapter 4: Group Activities 225 Chapter 4: Summary 226 Chapter 4: Review 227 Chapter 4: Test 228 Chapters 1–4: Cumulative Review 229 Ch 5: Polynomials: an Introduction to Algebra 231 5.1: Fundamental Operations 232 5.2: Simplifying Algebraic Expressions 234 5.3: Addition and Subtraction of Polynomials 238 5.4: Multiplication of Monomials 241 5.5: Multiplication of Polynomials 244 5.6: Division by a Monomial 246 5.7: Division by a Polynomial 248 Chapter 5: Group Activities 250 Chapter 5: Summary 250 Chapter 5: Review 252 Chapter 5: Test 252 Ch 6: Equations and Formulas 253 6.1: Equations 254 6.2: Equations with Variables in Both Members 258 6.3: Equations with Parentheses 260 6.4: Equations with Fractions 263 6.5: Translating Words into Algebraic Symbols 267 6.6: Applications Involving Equations 268 6.7: Formulas 273 6.8: Substituting Data into Formulas 276 6.9: Reciprocal Formulas Using a Calculator 279 Chapter 6: Group Activities 282 Chapter 6: Summary 282 Chapter 6: Review 283 Chapter 6: Test 284 Chapters 1–6: Cumulative Review 284 Ch 7: Ratio and Proportion 287 7.1: Ratio 288 7.2: Proportion 292 7.3: Direct Variation 299 7.4: Inverse Variation 305 Chapter 7: Group Activities 309 Chapter 7: Summary 309 Chapter 7: Review 309 Chapter 7: Test 310 Ch 8: Graphing Linear Equations 311 8.1: Linear Equations with Two Variables 312 8.2: Graphing Linear Equations 317 8.3: The Slope of a Line 324 8.4: The Equation of a Line 330 Chapter 8: Group Activities 335 Chapter 8: Summary 335 Chapter 8: Review 337 Chapter 8: Test 338 Chapters 1–8: Cumulative Review 338 Ch 9: Systems of Linear Equations 341 9.1: Solving Pairs of Linear Equations by Graphing 342 9.2: Solving Pairs of Linear Equations by Addition 348 9.3: Solving Pairs of Linear Equations by Substitution 353 9.4: Applications Involving Pairs of Linear Equations 354 Chapter 9: Group Activities 360 Chapter 9: Summary 360 Chapter 9: Review 361 Chapter 9: Test 362 Ch 10: Factoring Algebraic Expressions 363 10.1: Finding Monomial Factors 364 10.2: Finding the Product of Two Binomials Mentally 365 10.3: Finding Binomial Factors 368 10.4: Special Products 370 10.5: Finding Factors of Special Products 372 10.6: Factoring General Trinomials 374 Chapter 10: Group Activities 377 Chapter 10: Summary 377 Chapter 10: Review 378 Chapter 10: Test 378 Chapters 1–10: Cumulative Review 378 Ch 11: Quadratic Equations 381 11.1: Solving Quadratic Equations by Factoring 382 11.2: The Quadratic Formula 385 11.3: Applications Involving Quadratic Equations 387 11.4: Graphs of Quadratic Equations 391 11.5: Imaginary Numbers 395 Chapter 11: Group Activities 399 Chapter 11: Summary 399 Chapter 11: Review 400 Chapter 11: Test 400 Ch 12: Geometry 401 12.1: Angles and Polygons 402 12.2: Quadrilaterals 409 12.3: Triangles 413 12.4: Similar Polygons 422 12.5: Circles 426 12.6: Radian Measure 434 12.7: Prisms 439 12.8: Cylinders 444 12.9: Pyramids and Cones 450 12.10: Spheres 457 Chapter 12: Group Activities 459 Chapter 12: Summary 460 Chapter 12: Review 463 Chapter 12: Test 465 Chapters 1–12: Cumulative Review 466 Ch 13: Right Triangle Trigonometry 469 13.1: Trigonometric Ratios 470 13.2: Using Trigonometric Ratios to Find Angles 474 13.3: Using Trigonometric Ratios to Find Sides 477 13.4: Solving Right Triangles 478 13.5: Applications Involving Trigonometric Ratios 480 Chapter 13: Group Activities 488 Chapter 13: Summary 488 Chapter 13: Review 489 Chapter 13: Test 490 Ch 14: Trigonometry with Any Angle 493 14.1: Sine and Cosine Graphs 494 14.2: Period and Phase Shift 500 14.3: Solving Oblique Triangles: Law of Sines 504 14.4: Law of Sines: The Ambiguous Case 507 14.5: Solving Oblique Triangles: Law of Cosines 513 Chapter 14: Group Activities 518 Chapter 14: Summary 519 Chapter 14: Review 520 Chapter 14: Test 520 Chapters 1–14: Cumulative Review 521 Ch 15: Basic Statistics 523 15.1: Bar Graphs 524 15.2: Circle Graphs 527 15.3: Line Graphs 530 15.4: Other Graphs 533 15.5: Mean Measurement 534 15.6: Other Average Measurements and Percentiles 536 15.7: Range and Standard Deviation 539 15.8: Grouped Data 541 15.9: Standard Deviation for Grouped Data 548 15.10: Statistical Process Control 550 15.11: Other Graphs for Statistical Data 554 15.12: Normal Distribution 557 15.13: Probability 560 15.14: Independent Events 562 Chapter 15: Group Activities 563 Chapter 15: Summary 564 Chapter 15: Review 565 Chapter 15: Test 566 Ch 16: Binary and Hexadecimal Numbers 569 16.1: Introduction to Binary Numbers 570 16.2: Addition of Binary Numbers 572 16.3: Subtraction of Binary Numbers 573 16.4: Multiplication of Binary Numbers 574 16.5: Conversion from Decimal to Binary System 575 16.6: Conversion from Binary to Decimal System 577 16.7: Hexadecimal System 578 16.8: Addition and Subtraction of Hexadecimal Numbers 580 16.9: Binary to Hexadecimal Conversion 583 16.10: Hexadecimal Code for Colors 584 Chapter 16: Group Activities 585 Chapter 16: Summary 586 Chapter 16: Review 587 Chapter 16: Test 587 Chapters 1–16: Cumulative Review 588 Appendix A: Tables 589 Table 1: Formulas from Geometry 589 Table 2: Electrical Symbols 591 Appendix B: Exponential Equations 593 Appendix C: Simple Inequalities 599 Appendix D: Answers to Odd-Numbered Exercises and All Chapter Review and Cumulative Review Exercises 605 Index 633 WCN: 02-200-203 Helps students with minimal math background prepare for technical, trade, allied health, or Tech Prep programs. This book focuses on fundamental concepts in basic arithmetic including the metric system and measurement, algebra, geometry, trigonometry, and statistics.