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Fundamentals of Mathematics by Denny Burzynski, Wade Ellis, et al

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Fundamentals of Mathematics is a work text that will help the student develop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives:

  • to provide the student with an understandable and usable source of information,
  • to provide the student with the maximum opportunity to see that arithmetic concepts and techniques are logically based,
  • to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material, courses, and nonclassroom situations, and
  • to give the student the ability to correctly interpret arithmetically obtained results.

The authors have tried to meet these objectives by presenting material dynamically, much the way an instructor might present the material visually in a classroom. Intuition and understanding are some of the keys to creative thinking; the material presented in this text will help the student realize that mathematics is a creative subject.

This text can be used in standard lecture or self-paced classes.

License: Creative Commons Attribution. This license is considered to be some to be the most open license since it is the least restrictive. It allows reuse, remixing, and distribution (including commercial), only requiring attribution. The content can be remixed into content of other license, but on the other hand it allows the remix to be put under a more restrictive license.
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  • Chapter 1 Addition and Subtraction of Whole Numbers
    • 1.1 Objectives
    • 1.2 Whole Numbers
    • 1.3 Reading and Writing Whole Numbers
    • 1.4 Rounding Whole Numbers
    • 1.5 Addition of Whole Numbers
    • 1.6 Subtraction of Whole Numbers
    • 1.7 Properties of Addition
    • 1.8 Summary of Key Concepts
    • 1.9 Exercise Supplement
    • 1.10 Proficiency Exam
  • Chapter 2 Multiplication and Division of Whole Numbers
    • 2.1 Objectives
    • 2.2 Multiplication of Whole Numbers
    • 2.3 Concepts of Division of Whole Numbers
    • 2.4 Division of Whole Numbers
    • 2.5 Some Interesting Facts about Division
    • 2.6 Properties of Multiplication
    • 2.7 Summary of Key Concepts
    • 2.8 Exercise Supplement
    • 2.9 Proficiency Exam
  • Chapter 3 Exponents, Roots, and Factorization of Whole Numbers
    • 3.1 Objectives
    • 3.2 Exponents and Roots
    • 3.3 Grouping Symbols and the Order of Operations
    • 3.4 Prime Factorization of Natural Numbers
    • 3.5 The Greatest Common Factor
    • 3.6 The Least Common Multiple
    • 3.7 Summary of Key Concepts
    • 3.8 Exercise Supplement
    • 3.9 Proficiency Exam
  • Chapter 4 Introduction to Fractions and Multiplication and Division of Fractions
    • 4.1 Objectives
    • 4.2 Fractions of Whole Numbers
    • 4.3 Proper Fractions, Improper Fractions, and Mixed Numbers
    • 4.4 Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms
    • 4.5 Multiplication of Fractions
    • 4.6 Division of Fractions
    • 4.7 Applications Involving Fractions
    • 4.8 Summary of Key Concepts
    • 4.9 Exercise Supplement
    • 4.10 Proficiency Exam
  • Chapter 5 Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions
    • 5.1 Objectives
    • 5.2 Addition and Subtraction of Fractions with Like Denominators
    • 5.3 Addition and Subtraction of Fractions with Unlike Denominators
    • 5.4 Addition and Subtraction of Mixed Numbers
    • 5.5 Comparing Fractions
    • 5.6 Complex Fractions
    • 5.7 Combinations of Operations with Fractions
    • 5.8 Summary of Key Concepts
    • 5.9 Exercise Supplement
    • 5.10 Proficiency Exam
  • Chapter 6 Decimals
    • 6.1 Objectives
    • 6.2 Reading and Writing Decimals
    • 6.3 Converting a Decimal to a Fraction
    • 6.4 Rounding Decimals
    • 6.5 Addition and Subtraction of Decimals
    • 6.6 Multiplication of Decimals
    • 6.7 Division of Decimals
    • 6.8 Nonterminating Divisions
    • 6.9 Converting a Fraction to a Decimal
    • 6.10 Combinations of Operations with Decimals and Fractions
    • 6.11 Summary of Key Concepts
    • 6.12 Exercise Supplement
    • 6.13 Proficiency Exam
  • Chapter 7 Ratios and Rates
    • 7.1 Objectives
    • 7.2 Ratios and Rates
    • 7.3 Proportions
    • 7.4 Applications of Proportions
    • 7.5 Percent
    • 7.6 Fractions of One Percent
    • 7.7 Applications of Percents
    • 7.8 Summary of Key Concepts
    • 7.9 Exercise Supplement
    • 7.10 Proficiency Exam
  • Chapter 8 Techniques of Estimation
    • 8.1 Objectives
    • 8.2 Estimation by Rounding
    • 8.3 Estimation by Clustering
    • 8.4 Mental Arithmetic-Using the Distributive Property
    • 8.5 Estimation by Rounding Fractions
    • 8.6 Summary of Key Concepts
    • 8.7 Exercise Supplement
    • 8.8 Proficiency Exam
  • Chapter 9 Measurement and Geometry
    • 9.1 Objectives
    • 9.2 Measurement and the United States System
    • 9.3 The Metric System of Measurement
    • 9.4 Simplification of Denominate Numbers
    • 9.5 Perimeter and Circumference of Geometric Figures
    • 9.6 Area and Volume of Geometric Figures and Objects
    • 9.7 Summary of Key Concepts
    • 9.8 Exercise Supplement
    • 9.9 Proficiency Exam
  • Chapter 10 Signed Numbers
    • 10.1 Objectives
    • 10.2 Variables, Constants, and Real Numbers
    • 10.3 Signed Numbers
    • 10.4 Absolute Value
    • 10.5 Addition of Signed Numbers
    • 10.6 Subtraction of Signed Numbers
    • 10.7 Multiplication and Division of Signed Numbers
    • 10.8 Summary of Key Concepts
    • 10.9 Exercise Supplement
    • 10.10 Proficiency Exam
  •  11 Algebraic Expressions and Equations
    • 11.1 Objectives
    • 11.2 Algebraic Expressions
    • 11.3 Combining Like Terms Using Addition and Subtraction
    • 11.4 Solving Equations of the Form x+a=b and x-a=b
    • 11.5 Solving Equations of the Form ax=b and x/a=b
    • 11.6 Applications I: Translating Words to Mathematical Symbols
    • 11.7 Applications II: Solving Problems
    • 11.8 Summary of Key Concepts
    • 11.9 Exercise Supplement
    • 11.10 Proficiency Exam
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