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Master Math: Basic Math and Pre-Algebra

Book Description

Get ready to master basic arithmetic subjects, principles, and formulas! Master Math: Basic Math and Pre-Algebra is a comprehensive reference guide that explains and clarifies mathematic principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced, Master Math: Basic Math and Pre-Algebra explains the principles and operations of arithmetic, provides step-by-step procedures and solutions, and presents examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up on their basic math skills, Master Math: Basic Math and Pre-Algebra will help you master everything from fractions and decimals to roots and radicals.

Table of Contents

  1. Copyright
  2. Acknowledgments
  3. About the Author
  4. Introduction
  5. 1. Numbers and Their Operations
    1. 1.1. Digits and the Base Ten System
    2. 1.2. Whole Numbers
    3. 1.3. Addition of Whole Numbers
      1. A Detailed Explanation of Addition
      2. A Detailed Description of the Standard Addition Technique
    4. 1.4. Subtraction of Whole Numbers
      1. A Detailed Explanation of Subtraction
      2. A Detailed Description of the Standard Subtraction Technique
    5. 1.5. Multiplication of Whole Numbers
      1. An Explanation of Multiplication
      2. A Detailed Description of the Standard Multiplication Technique
    6. 1.6. Division of Whole Numbers
      1. A Description of the Long Division Technique
    7. 1.7. Divisibility, Remainders, Factors, and Multiples
    8. 1.8. Integers
    9. 1.9. Even and Odd Integers
    10. 1.10. Zero
    11. 1.11. Addition and Subtraction of Negative and Positive Integers
    12. 1.12. Multiplication and Division of Negative and Positive Integers
    13. 1.13. The Real Number Line
    14. 1.14. Absolute Value
    15. 1.15. Prime Numbers
    16. 1.16. Rational vs. Irrational Numbers
    17. 1.17. Complex Numbers
    18. 1.18. Rounding, Truncating, and Estimating Numbers
    19. 1.19. Inequalities, >, <, ≥, ≤
    20. 1.20. Factorial
  6. 2. Fractions
    1. 2.1. Definitions
    2. 2.2. Multiplying Fractions
    3. 2.3. Adding and Subtracting Fractions with Common Denominators
    4. 2.4. Adding and Subtracting Fractions with Different Denominators
    5. 2.5. Dividing Fractions
    6. 2.6. Reducing Fractions
    7. 2.7. Complex Fractions, Mixed Numbers, and Improper Fractions
      1. Method 1
      2. Method 2
    8. 2.8. Adding and Subtracting Mixed Numbers
    9. 2.9. Comparing Fractions: Which is Larger or Smaller?
  7. 3. Decimals
    1. 3.1. Definitions
    2. 3.2. Adding and Subtracting Decimals
    3. 3.3. Multiplying Decimals
    4. 3.4. Dividing Decimals
    5. 3.5. Rounding Decimals
    6. 3.6. Comparing the Size of Decimals
    7. 3.7. Decimals and Money
  8. 4. Percentages
    1. 4.1. Definitions
    2. 4.2. Figuring Out the Percents of Numbers
    3. 4.3. Adding, Subtracting, Multiplying, and Dividing Percents
    4. 4.4. Percent Increase and Decrease (Percent Change)
    5. 4.5. Simple and Compound Interest
  9. 5. Converting Percentages, Fractions, and Decimals
    1. 5.1. Converting Fractions to Percents
    2. 5.2. Converting Percents to Fractions
    3. 5.3. Converting Fractions to Decimals
    4. 5.4. Converting Decimals to Fractions
    5. 5.5. Converting Percents to Decimals
    6. 5.6. Converting Decimals to Percents
  10. 6. Ratios, Proportions, and Variation
    1. 6.1. Definitions
    2. 6.2. Comparing Ratios to Fractions and Percents
    3. 6.3. Variation and Proportion
  11. 7. Powers and Exponents
    1. 7.1. Definition of the Exponent or Power
    2. 7.2. Negative Exponents and Bases
    3. 7.3. Multiplying Exponential Expressions with the Same Base
    4. 7.4. Multiplying Exponential Expressions with Different Bases
    5. 7.5. Dividing Exponential Expressions with the Same Base
    6. 7.6. Dividing Exponential Expressions with Different Bases
    7. 7.7. Raising Exponential Expressions to a Power
    8. 7.8. Distributing Exponents into Parentheses
    9. 7.9. Addition of Exponential Expressions
    10. 7.10. Subtraction of Exponential Expressions
    11. 7.11. Exponential Expressions Involving Fractions
  12. 8. Logarithms
    1. 8.1. Definition of the Logarithm
    2. 8.2. Common (Base Ten) and Natural Logarithm
    3. 8.3. Solving Equations with Logarithms or Exponents
    4. 8.4. Exponential Form and Logarithmic Form
    5. 8.5. Laws of Logarithms: Addition, Subtraction, Multiplication, Division, Power, and Radical
    6. 8.6. Examples: The Richter Scale, pH, and Radiometric Dating
  13. 9. Roots and Radicals
    1. 9.1. Definitions
    2. 9.2. The Square Root
    3. 9.3. Estimating Square Roots
    4. 9.4. The Cubed Root
    5. 9.5. The Fourth and Fifth Roots
    6. 9.6. Simplifying Radicals by Factoring
    7. 9.7. Multiplying Radicals
    8. 9.8. Dividing Radicals
    9. 9.9. Radicals Involving Fractions
    10. 9.10. Rationalizing the Denominator
    11. 9.11. Addition of Radicals
    12. 9.12. Subtraction of Radicals
  14. 10. Important Statistical Quantities
    1. 10.1. Average (Arithmetic Mean)
    2. 10.2. Median
    3. 10.3. Mode
    4. 10.4. Probability
    5. 10.5. Standard Deviation, Variance, Histograms, and Distributions
      1. Standard Deviation and Variance
      2. The Histogram, Binomial Distribution, Gaussian Distribution, and Poisson Distribution