Basic Math & Pre-Algebra Super Review

The Editors of REA

• Publisher: Research & Education Association
• Year: 2013
• Print ISBN:
  9780738611198
• eBook ISBN:
  9780738684031
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Need help with Basic Math and Pre-Algebra? Want a quick review or refresher for class? This is the book for you! REA's Basic Math and Pre-Algebra Super Review gives you everything you need to know!This Super Review can be used as a supplement to your high school or college textbook, or as a handy guide for anyone who needs a fast review of the subject.• Comprehensive, yet concise coverage – review covers the material that is typically taught in a beginning-level math and pre-algebra course. Each topic is presented in a clear and easy-to-understand format that makes learning easier.• Packed with practice – each review lesson is packed with practice questions and answers for each topic. Practice what you've learned and build your basic math and pre-algebra skills, so you'll be ready for any problem you encounter on your next quiz or test.• Detailed answers – our practice problems come with step-by-step detailed solutions to help you understand the material and sharpen your skills.Whether you need a quick refresher on the subject, or are prepping for your next exam, we think you'll agree that REA's Super Review provides all you need to know!

CHAPTER 1

---

Integers and Real Numbers

---

1.1 Real Numbers and the Number Line

Most of the numbers used in algebra belong to a set called the real numbers or reals. This set can be represented graphically by the real number line.

Given the number line below, we arbitrarily fix a point and label it with the number 0. In a similar manner, we can label any point on the line with one of the real numbers, depending on its position relative to 0. Numbers to the right of zero are positive, while those to the left are negative. Value increases from left to right, so that if a is to the right of b, it is said to be greater than b.

If we now divide the number line into equal segments, we can label the points on this line with real numbers. For example, the point 2 lengths to the left of zero is − 2, while the point 3 lengths to the right of zero is + 3 (the + sign is usually assumed, so + 3 is written simply as 3). The number line now looks like this:

These boundary points represent the subset of the reals known as the integers. The set of integers is made up of both the positive and negative whole numbers: {… − 4, − 3, − 2, − 1, 0, 1, 2, 3, 4, …}. Some subsets of integers are:

Natural Numbers or Positive Numbers—the set of integers starting with 1 and increasing: N = {1, 2, 3, 4, …}.

Whole Numbers—the set of integers starting with 0 and increasing: W = {0, 1, 2, 3, …}.

Negative Numbers—the set of integers starting with −1 and decreasing: Z = { − 1, − 2, − 3, …}.

Prime Numbers—the set of positive integers greater than 1 that are divisible only by 1 and themselves: {2, 3, 5, 7, 11, …}.

Even Integers—the set of integers divisible by 2: {…, − 4, − 2, 0, 2, 4, 6, …}.

Odd Integers—the set of integers not divisible by 2: {…, −3, −1, 1, 3, 5, 7, …}.

Problem Solving Examples:

Graph the following numbers on a number line: −2, 0, 3.

Step 1 is to draw a number line and label it using numbers near the points you are graphing. All points to the left of zero are negative and are always represented by the number with a negative sign (−). All points to the right of zero are positive and may or may not be represented by a positive sign (+).

Step 2 is to graph the points on the number line. Points on a number line are graphed using closed circles.

On the number line below, find and graph the point that is 4 whole numbers to the right of −3.

Step 1 is...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• REA’s Basic Math & Pre-Algebra Super Review®
• Available Super Review® Titles
• About Research & Education Association
• Acknowledgments
• Contents
• Chapter 1 Integers and Real Numbers
• Chapter 2 Fractions
• Chapter 3 Decimals
• Chapter 4 Ratio and Proportions
• Chapter 5 Percents
• Chapter 6 Exponents and Roots
• Chapter 7 Introduction to Algebra
• Chapter 8 Solving Algebraic Equations
• Chapter 9 Inequalities
• Chapter 10 Word Problems
• Chapter 11 Graphing and Coordinate Geometry
• Chapter 12 Geometry
• Back Cover