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Introduction to Master Math: Basic Math and Pre-Algebra: Basic Math and Pre-Algebra is the first book in the Master Math series. The second, third, and fourth books are entitled Algebra, Pre-Calculus and Geometry, and Calculus.. The Master Math series presents the general principles of mathematics from grade school through college including arithmetic, algebra, geometry, trigonometry, pre-calculus and introductory calculus. Basic Math and Pre-Algebra is a comprehensive arithmetic book that explains the subject matter in a way that makes sense to the reader. It begins with the most basic principles and progresses through more advanced topics to prepare a student for algebra. Basic Math and Pre-Algebra explains the principles and operations of arithmetic, provides step-by-step procedures and solutions, and presents examples and applications. Basic Math and Pre-Algebra is a reference book for grade school and middle school students that explains and clarifies the arithmetic principles they are learning in school. It is also a comprehensive reference source for more advanced students currently learning algebra, pre-calculus and calculus. Basic Math and Pre-Algebra is invaluable for students, parents, tutors and anyone needing a basic arithmetic reference source. The information provided in each book and in the series as a whole is progressive in difficulty and builds on itself, which allows the reader to gain perspective on the connected nature of mathematics. The skills required to understand every topic presented are explained in an earlier chapter or book within the series. Each of the books contains a complete table of contents, a comprehensive index, and the tables of contents of the other books in the series that specific subjects, principles and formulas can be easily found. The books are written in a simple style that facilitates understanding and easy referencing of sought-after principles, definitions and explanations. Basic Math and Pre-Algebra and the Master Math series are not replacements for textbooks but rather reference books providing explanations and perspective. The Master Math series would have been invaluable to me during my entire education from grade school through graduate school. There is no other source that provides the breadth and depth of the Master Math series in a single book or series. Finally, mathematics is a language-the universal language. A person struggling with mathematics should approach it in the same fashion he or she would approach learning any other language. If someone moves to a foreign country, he or she does not expect to know the language automatically. It takes practice and contact with a language in order to master it. After a short time in the foreign country he or she would not say, 'I do not know this language well yet. I must not have an aptitude for it.' Yet many people have this attitude toward mathematics. If time is spent learning and practicing the principles, mathematics will become familiar and understandable. Don't give up.
Debra Ross, the author, February 16, 1999
Note to the reader: There is a misprint in books from the first printing on page138: ln (infinity) = infinity, not zero.
Introduction 1
Chapter 1 Numbers and Their Operations 5
1.1 Digits and the Base Ten System 6
1.2 Whole Numbers 6
1.3 Addition of Whole Numbers 7
1.4 Subtraction of Whole Numbers 14
1.5 Multiplication of Whole Numbers 20
1.6 Division of Whole Numbers 32
1.7 Divisibility, Remainders, Factors, and Multiples 40
1.8 Integers 41
1.9 Even and Odd Integers 42
1.10 Zero 44
1.11 Addition and Subtraction of Negative and Positive Integers 45
1.12 Multiplication and Division of Negative and Positive Integers 47
1.13 The Real Number Line 49
1.14 Absolute Value 49
1.15 Prime Numbers 50
1.16 Rational vs. Irrational Numbers 51
1.17 Complex Numbers 51
1.18 Rounding, Truncating, and Estimating Numbers 55
1.19 Inequalities, >, <, <$$$> 58
1.20 Factorial 63
Chapter 2 Fractions 67
2.1 Definitions 68
2.2 Multiplying Fractions 69
2.3 Adding and Subtracting Fractions with Common Denominators 69
2.4 Adding and Subtracting Fractions with Different Denominators 70
2.5 Dividing Fractions 76
2.6 Reducing Fractions 77
2.7 Complex Fractions, Mixed Numbers, and Improper Fractions 78
2.8 Adding and Subtracting Mixed Numbers 82
2.9 Comparing Fractions: Which Is Larger or Smaller? 83
Chapter 3 Decimals 89
3.1 Definitions 90
3.2 Adding and Subtracting Decimals 92
3.3 Multiplying Decimals 95
3.4 Dividing Decimals 97
3.5 Rounding Decimals 98
3.6 Comparing the Size of Decimals 100
3.7 Decimals and Money 100
Chapter 4 Percentages 105
4.1 Definitions 106
4.2 Figuring Out the Percents of Numbers 107
4.3 Adding, Subtracting, Multiplying, and Dividing Percents 109
4.4 Percent Increase and Decrease (Percent Change) 111
4.5 Simple andCompound Interest 112
Chapter 5 Converting Percentages, Fractions, and Decimals 117
5.1 Converting Fractions to Percents 118
5.2 Converting Percents to Fractions 118
5.3 Converting Fractions to Decimals 119
5.4 Converting Decimals to Fractions 119
5.5 Converting Percents to Decimals 121
5.6 Converting Decimals to Percents 122
Chapter 6 Ratios, Proportions, and Variation 125
6.1 Definitions 126
6.2 Comparing Ratios to Fractions and Percents 127
6.3 Variation and Proportion 128
Chapter 7 Powers and Exponents 131
7.1 Definition of the Exponent or Power 132
7.2 Negative Exponents and Bases 132
7.3 Multiplying Exponential Expressions with the Same Base 133
7.4 Multiplying Exponential Expressions with Different Bases 134
7.5 Dividing Exponential Expressions with the Same Base 135
7.6 Dividing Exponential Expressions with Different Bases 136
7.7 Raising Exponential Expressions to a Power 136
7.8 Distributing Exponents into Parentheses 137
7.9 Addition of Exponential Expressions 138
7.10 Subtraction of Exponential Expressions 138
7.11 Exponential Expressions Involving Fractions 139
Chapter 8 Logarithms 143
8.1 Definition of the Logarithm 144
8.2 Common (Base Ten) and Natural Logarithm 145
8.3 Solving Equations with Logarithms or Exponents 146
8.4 Exponential Form and Logarithmic Form 147
8.5 Laws of Logarithms: Addition, Subtraction, Multiplication, Division, Power, and Radical 149
8.6 Examples: The Richter Scale, pH, and Radiometric Dating 149
Chapter 9 Roots and Radicals 157
9.1 Definitions 158
9.2 The Square Root 158
9.3 Estimating Square Roots 159
9.4 The Cubed Root 163
9.5 The Fourth and Fifth Roots 164
9.6 Simplifying Radicals by Factoring 164
9.7 Multiplying Radicals 165
9.8 Dividing Radicals 165
9.9 Radicals Involving Fractions 166
9.10 Rationalizing the Denominator 166
9.11 Addition of Radicals 167
9.12 Subtraction of Radicals 168
Chapter 10 Important Statistical Quantities 171
10.1 Average (Arithmetic Mean) 172
10.2 Median 174
10.3 Mode 175
10.4 Probability 175
10.5 Standard Deviation, Variance, Histograms, and Distributions 176
Index 181
Anonymous
Posted November 8, 2007
This is the best book on learning basic algebra. It is thorough yet concise. The information is presented very clearly. The author has obviously tried to explain the concepts so that they `make sense¿ to students - and their parents. I use the book to explain algebra to my students. Like the other Master Math books by Ross, the topics flow logically and build in difficulty. What a breath of fresh air after the often confusing text books students are given in school. This book is helpful for students struggling with algebra and the parents who are tutoring them. This book is also extremely useful for older students who did not adequately learn algebra, yet find they need to know it later. Topics can easily be looked up and reviewed or learned. I highy recommend this book!
5 out of 7 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Log-IC
Posted October 10, 2009
Splendid clarity and progression.
A cherry on top of this fine sundae,
maybe a single page of exponential,
radical,and complex properties for
a quick reference,( but that's nitpicking).
3 out of 5 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted November 20, 2007
This is the best book out there on learning trigonometry. I especially appreciate the visually-oriented focus. Each concept is described in all its forms, such as sine. Do you know each of the different ways sine can be described? Like the other Master Math books by Ross, the topics flow logically and are in context with what precedes and follows. It is thorough yet concise, and packed full of everything you, as tutor, or your kids need to know. The real world and fun applications are wonderful! The information is explained clearly and in a way that makes sense, so that a given concept is explained in such a way you understand what is being discussed rather than just memorizing formulas. What a breath of fresh air after the often confusing text books I was and my children are given in school. I really feel I can explain trigonometry to young people using this book! if I were going back to school, and taking math or science, this book would be in my backpack.
3 out of 5 people found this review helpful.
Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.Anonymous
Posted November 21, 2012
i am not sure if i am missing something but on page 14 the book says x times $1.00 per glass will equal 20. then shows this equation
X + ($1.00 per glass)=$20.00
1 out of 1 people found this review helpful.
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Posted February 12, 2012
This book is terrible. There are many books that are better. I found websites more helpful.
1 out of 3 people found this review helpful.
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Overview
Introduction to Master Math: Basic Math and Pre-Algebra: Basic Math and Pre-Algebra is the first book in the Master Math series. The second, third, and fourth books are entitled Algebra, Pre-Calculus and Geometry, and Calculus.. The Master Math series presents the general principles of mathematics from grade school through college including arithmetic, algebra, geometry, trigonometry, pre-calculus and introductory calculus. Basic Math and Pre-Algebra is a ...