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Debra Anne Ross [Debra Anne Ross] - Master Math: Basic Math and Pre-Algebra

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Debra Anne Ross [Debra Anne Ross] Master Math: Basic Math and Pre-Algebra

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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.

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Chapter . Introduction

Basic Math and Pre-Algebra is the first book in the Master Math series. The series also includes Algebra, Pre-Calculus, Geometry, Trigonometry, 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 fundamental 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 learning algebra and pre-calculus. Basic Math and Pre-Algebra is invaluable for students of all ages, 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 book contains a complete table of contents and a comprehensive index, so 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 languagethe universal language. A person struggling with mathematics should approach it in the same fashion or 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. Dont give up.

Chapter 1. Numbers and Their Operations
  • Digits and the Base Ten System

  • Whole Numbers

  • Addition of Whole Numbers

  • Subtraction of Whole Numbers

  • Multiplication of Whole Numbers

  • Division of Whole Numbers

  • Divisibility, Remainders, Factors, and Multiples

  • Integers

  • Even and Odd Integers

  • Zero

  • Addition and Subtraction of Negative and Positive Integers

  • Multiplication and Division of Negative and Positive Integers

  • The Real Number Line

  • Absolute Value

  • Prime Numbers

  • Rational vs. Irrational Numbers

  • Complex Numbers

  • Rounding, Truncating, and Estimating Numbers

  • Inequalities, >, <, ,

  • Factorial

Digits and the Base Ten System

The system of numbers used for counting is based on groups of ten and is called the base ten system.

Numbers are made up of digits that each correspond to a value. For example, the number 5,639,248 or five million, six hundred thirty-nine thousand, two hundred forty-eight represents:

  • 5 millions, 6 hundred thousands, 3 ten thousands, 9 thousands, 2 hundreds, 4 tens, and 8 ones

This number can also be written:

  • 5,000,000 + 600,000 + 30,000 + 9,000 + 200 + 40 + 8

The ones digit indicates the number of ones, (1).

The tens digit indicates the number of tens, (10).

The hundreds digit indicates the number of hundreds, (100).

The thousands digit indicates the number of thousands, (1,000).

The ten thousands digit indicates the number of tens of thousands, (10,000).

The hundred thousands digit indicates the number of hundreds of thousands, (100,000).

The millions digit indicates the number of millions, (1,000,000).

Whole Numbers

Whole numbers include zero and the counting numbers greater than zero.

Negative numbers and numbers in the form of fractions, decimals, percents, or exponents are not whole numbers.

Whole numbers are depicted on the number line and include zero and numbers to the right of zero.

  • Whole numbers can be written in the form of a set Whole Numbers 0 1 2 - photo 1

Whole numbers can be written in the form of a set.

  • Whole Numbers = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, )

Addition of Whole Numbers

This section includes definitions, a detailed explanation of addition, and a detailed description of the standard addition technique.

The symbol for addition is +.

Addition is written 6 + 2.

The numbers to be added are called addends .

The answer obtained in addition is called the sum .

The symbol for what the sum is equal to is the equal sign =.

Note: The symbol for not equal is .

For any number n, the following is true: n + 0 = n (Note that letters are often used to represent numbers.)

A Detailed Explanation of Addition

Consider the following examples:

  • 5 + 3 = 8

  • 34 + 76 = 110

  • 439 + 278 = 717

  • 5 + 3 + 2 = 10

  • 33 + 28 + 56 = 117

  • 456 + 235 + 649 = 1,340

To add numbers that have two or more digits, it is easier to write the numbers in a column format with ones, tens, hundreds, etc., aligned, then add each column.

Example: Add 5 + 3.

  • Master Math Basic Math and Pre-Algebra - image 2

Example: Add 4 + 6.

  • Master Math Basic Math and Pre-Algebra - image 3

Example: Add 7 + 0.

  • Master Math Basic Math and Pre-Algebra - image 4

Example: Add 7 + 8.

  • Master Math Basic Math and Pre-Algebra - image 5

Note that 15 ones is equivalent to 1 ten and 5 ones.

Example: Add 21 + 32.

  • This equation can be rewritten as Example Add 34 76 - photo 6

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