Pre-Algebra Essentials For Dummies

Mark Zegarelli

• Publisher: For Dummies
• Year: 2019
• ISBN:
  9781119591023
• Edition: 1
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Pre-Algebra Essentials For Dummies (9781119590866) was previously published as Pre-Algebra Essentials For Dummies (9780470618387). 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.

Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need to a refresher of the core concepts.

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Chapter 1

Arming Yourself with Math Basics

IN THIS CHAPTER

Identifying four important sets of numbers

Reviewing addition, subtraction, multiplication, and division

Examining commutative, associative, and distributive operations

Knowing exponents, roots, and absolute values

Understanding how factors and multiples are related

You already know more about math than you think you know. In this chapter, you review and gain perspective on basic math ideas such as sets of numbers and concepts related to the Big Four operations (adding, subtracting, multiplying, and dividing). I introduce you (or reintroduce you) to properties and operations that will assist with solving problems. Finally, I explain the relationship between factors and multiples, taking you from what you may have missed to what you need to succeed as you move onward and upward in math.

Understanding Sets of Numbers

You can use the number line to deal with four important sets (or groups) of numbers. Each set builds on the one before it:

• Counting numbers (also called natural numbers): The set of numbers beginning 1, 2, 3, 4, … and going on infinitely
• Integers: The set of counting numbers, zero, and negative counting numbers
• Rational numbers: The set of integers and fractions
• Real numbers: The set of rational and irrational numbers

Even if you filled in all the rational numbers, you’d still have points left unlabeled on the number line. These points are the irrational numbers.

An irrational number is a number that’s neither a whole number nor a fraction. In fact, an irrational number can only be approximated as a non-repeating decimal. In other words, no matter how many decimal places you write down, you can always write down more; furthermore, the digits in this decimal never become repetitive or fall into any pattern. (For more on repeating decimals, see Chapter 5.)

The most famous irrational number is

(you find out more about

when I discuss the geometry of circles in Chapter 11):

Together, the rational and irrational numbers make up the real numbers, which comprise every point on the number line.

The Big Four Operations

When most folks think of math, the first thing that comes to mind is four little (or not-so-little) words: addition, subtraction, multiplication, and division. I call these operations the Big Four all through the book.

Adding things up

Addition is the first operation you find out about, and it’s almost everybody’s favorite. Addition is all about bringing things together, which is a positive thing. This operation uses only one sign — the plus sign

.

When you add two numbers together, those two numbers are called addends, and the result is called the sum.

Adding a negative number is the same as subtracting, so

is the same as

.

Take it away: Subtracting

Subtraction is usually the second operation you discover, and ...