Master Math: Basic Math and Pre-Algebra (Master Math Series)

Introduction 1

Chapter 1 Numbers and Their Operations 5

1.1. Digits and the base ten system 6 1.2. Whole numbers 7 1.3. Addition of whole numbers 7 1.4. Subtraction of whole numbers 15 1.5. Multiplication of whole numbers 22 1.6. Division of whole numbers 35 1.7. Divisibility, remainders, factors and multiples 43 1.8. Integers 45 1.9. Even and odd integers 46 1.10. Zero 47 1.11. Addition and subtraction of negative and positive integers 48 1.12. Multiplication and division of negative and positive integers 51 1.13. The real number line 52 1.14. Absolute value 53 1.15. Prime numbers 54 1.16. Rational vs. irrational numbers 54 1.17. Complex numbers 55 1.18. Rounding, truncating and estimating numbers 59 1.19. Inequalities, >, <, Y, Ue 62 1.20. Factorial 66

Chapter 2 Fractions 67

2.1. Definitions 67 2.2. Multiplying fractions 68 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 87

3.1. Definitions 87 3.2. Adding and subtracting decimals 90 3.3. Multiplying decimals 93 3.4. Dividing decimals 95 3.5. Rounding decimals 97 3.6. Comparing the size of decimals 98 3.7. Decimals and money 99

Chapter 4 Percentages 101

4.1. Definitions 101 4.2. Figuring out the percents of numbers 102 4.3. Adding, subtracting, multiplying and dividing percents 105 4.4. Percent increase and decrease (percent change) 107 4.5. Simple and compound interest 109

Chapter 5 Converting Percentages, Fractions and Decimals 111

5.1. Converting fractions to percents 111 5.2. Converting percents to fractions 112 5.3. Converting fractions to decimals 113 5.4. Converting decimals to fractions 113 5.5. Converting percents to decimals 115 5.6. Converting decimals to percents 117

Chapter 6 Ratios, Proportions and Variation 118

6.1. Definitions 118 6.2. Comparing ratios to fractions and percents 120 6.3. Variation and proportion 121

Chapter 7 Powers and Exponents 123

7.1. Definition of the exponent or power 123

7.2. Negative exponents 124 7.3. Multiplying exponents with the same base 125 7.4. Multiplying exponents with different bases 126 7.5. Dividing exponents with the same base 126 7.6. Dividing exponents with different bases 128 7.7. Raising a power of a base to a power 128 7.8. Distributing exponents into parenthesis 129 7.9. Addition of exponents 130 7.10. Subtraction of exponents 131 7.11. Exponents involving fractions 131

Chapter 8 Logarithms 133

8.1. Definition of the logarithm 133 8.2. Common (base ten) and natural logarithm 135 8.3. Solving equations with logarithms or exponents 136 8.4. Exponential form and logarithmic form 138 8.5. Laws of logarithms; addition, subtraction, multiplication, division, power and radical 139 8.6. Examples: the Richter scale, pH and radiometric dating 140

Chapter 9 Roots and Radicals 145

9.1. Definitions 146 9.2. The square root 147 9.3. Estimating square roots 149 9.4. The cubed root 152 9.5. The fourth and fifth roots 153 9.6. Simplifying radicals by factoring 154 9.7. Multiplying radicals 155 9.8. Dividing radicals 155 9.9. Radicals involving fractions 156 9.10. Rationalizing the denominator 156 9.11. Addition of radicals 157 9.12. Subtraction of radicals 158

Chapter 10 Important Statistical Quantities 159

10.1. Average (arithmetic mean) 159 10.2. Median 161 10.3. Mode 163 10.4. Probability 164 10.5. Standard deviation, variance, histograms and distributions 164

Index 170

Appendix 173


Truly understand basic math with this book!   November 5, 2007
Happy Camper
4 out of 4 found this review helpful

The mathematical concepts are explained in terms of what they truly mean. What is multiplication? Students are usually taught some formula, as I was, and told to memorize it. But we are not generally taught what a mathematical operation really is. It is clear throughout this book, and her other Master Math books, that she is trying to explain what is really happening when you are performing a mathematical operation, such as multiplication or division. Fractions, decimals, exponents, etc., are also explained for what they are and what they mean. The beginning of the book has the most basic explanations of numbers, types of numbers, negative numbers, using the number line to visualize negative numbers, and addition and subtraction of negative numbers. It also covers basic addition, subtraction, multiplication and division. Because of calculators, the younger generations do not really understand the basic mathematical operations as well as fractions, decimals, ratios, etc. - Ross explains them. The beginning of the book is a great tool for introducing kids to math. Like most books, Ross presents clearly and succinctly `how to do arithmetic', and for some people this is enough, but I like her explanations of what is really going on. This book also presents the topics logically in a way that builds in difficulty. This book is good for students struggling with basic math because you can quickly look up math topics in the index or table of contents. It is also great for parents who want to tutor their kids. Highly recommended!


Great Reference Math Book   January 25, 2001
11 out of 18 found this review helpful

I like this book. It explains each math concept. It is a good reference tool for math.


Master Math and Pre-Algebra   January 19, 2008
A. Hamilton Richardson
I am please with the condition of the book and the promptness of mailing for me to receive. Thank you very much and keep up the excellent job.


A big help   February 10, 2003
Marilyn Dalrymple (Lancaster, CA United States)
11 out of 11 found this review helpful

I have always avoided math whenever possible, but now I have to pass a college level math course in order to complete a degree. This book has helped me review the basics and slowly work my way into more advanced math.

The only reason I gave it a "4" is because I find I sometimes need to refer elsewhere for further information. That is my weakness, though. Not the books.

I would recommend this book to anyone who has to review basic math skills, and/or move on to higher math.