Algebra I Essentials For Dummies

Mary Jane Sterling

• Publisher: For Dummies
• Year: 2019
• ISBN:
  9781119590958
• Edition: 1
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Algebra I Essentials For Dummies (9781119590965) was previously published as Algebra I Essentials For Dummies (9780470618349). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.

With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

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Chapter 1

Setting the Scene for Actions in Algebra

IN THIS CHAPTER

Enumerating the various number systems

Becoming acquainted with “algebra-speak”

Operating on and simplifying expressions

Converting fractions to decimals and decimals to fractions

What exactly is algebra? What is it really used for? In a nutshell, algebra is a systematic study of numbers and their relationships, using specific rules. You use variables (letters representing numbers), and formulas or equations involving those variables, to solve problems. The problems may be practical applications, or they may be puzzles for the pure pleasure of solving them!

In this chapter, I acquaint you with the various number systems. You’ve seen the numbers before, but I give you some specific names used to refer to them properly. I also tell you how I describe the different processes performed in algebra — I want to use the correct language, so I give you the vocabulary. And, finally, I get very specific about fractions and decimals and show you how to move from one type to the other with ease.

Making Numbers Count

Algebra uses different types of numbers, in different circumstances. The types of numbers are important because what they look like and how they behave can set the scene for particular situations or help to solve particular problems. Sometimes it’s really convenient to declare, “I’m only going to look at whole-number answers,” because whole numbers do not include fractions or negatives. You could easily end up with a fraction if you’re working through a problem that involves a number of cars or people. Who wants half a car or, heaven forbid, a third of a person?

I describe the different types of numbers in the following sections.

Facing reality with reals

Real numbers are just what the name implies: real. Real numbers represent real values — no pretend or make-believe. They cover the gamut and can take on any form — fractions or whole numbers, decimal numbers that go on forever and ever without end, positives and negatives.

Going green with naturals

A natural number (also called a counting number) is a number that comes naturally. The natural numbers are the numbers starting with 1 and going up by ones: 1, 2, 3, 4, 5, and so on into infinity.

Wholesome whole numbers

Whole numbers aren’t a whole lot different from natural numbers (see the preceding section). Whole numbers are just all the natural numbers plus a 0: 0, 1, 2, 3, 4, 5, and so on into infinity.

Integrating integers

Integers are positive and negative whole numbers: …

,

,

, 0, 1, 2, 3, … .

Integers are popular in algebra. When you solve a long, complicated problem and come up with an integer, you can be joyous because your answer is probably right. After all, most teachers like answers without fractions.

Behaving with rationals

Rational numbers act rationally because their ...

Table of contents

• Cover
• Table of Contents
• Introduction
• Chapter 1: Setting the Scene for Actions in Algebra
• Chapter 2: Examining Powers and Roots
• Chapter 3: Ordering and Distributing: The Business of Algebra
• Chapter 4: Factoring in the First and Second Degrees
• Chapter 5: Broadening the Factoring Horizon
• Chapter 6: Solving Linear Equations
• Chapter 7: Tackling Second-Degree Quadratic Equations
• Chapter 8: Expanding the Equation Horizon
• Chapter 9: Reconciling Inequalities
• Chapter 10: Absolute-Value Equations and Inequalities
• Chapter 11: Making Algebra Tell a Story
• Chapter 12: Putting Geometry into Story Problems
• Chapter 13: Grappling with Graphing
• Chapter 14: Ten Warning Signs of Algebraic Pitfalls
• Index
• About the Author
• Advertisement Page
• Connect with Dummies
• End User License Agreement