Barron's Math 360: A Complete Study Guide to Pre-Algebra with Online Practice

Caryl Lorandini

• Publisher: Barrons Educational Services
• Year: 2021
• ISBN:
  9781506281414
• Topic: Aides à l'étude
• Subtopic: Guides d'étude

Barron's Math 360: Pre-Algebra is your complete go-to guide for everything pre-algebra This comprehensive guide is an essential resource for:

• Intermediate and high school courses
• Homeschooling
• Virtual Learning
• Learning pods

Inside you'll find:

• Comprehensive Content Review: Begin your study with the basic building blocks of pre-algebra and build as you go. Topics include, fractions, expressions, equations, graphing word problems, and much more.
• Effective Organization: Topic organization and simple lesson formats break down the subject matter into manageable learning modules that help guide a successful study plan customized to your needs.
• Clear Examples and Illustrations: Easy-to-follow explanations, hundreds of helpful illustrations, and numerous step-by-step examples make this book ideal for self-study and rapid learning.
• Practice Exercises: Each chapter ends with practice exercises designed to reinforce and extend key skills and concepts. These checkup exercises, along with the answers and solutions, will help you assess your understanding and monitor your progress.
• Access to Online Practice: Take your learning online for 50 practice questions designed to test your knowledge with automated scoring to show you how far you have come.

1

PROPERTIES AND ORDER OF OPERATIONS

WHAT YOU WILL LEARN

•Some basic terms and assumptions of numbers and sets

•The difference between rational and irrational numbers

•Properties of real numbers

•Order of operations

SECTIONS IN THIS CHAPTER

•Numbers and Sets

•Properties of Real Numbers

•Order of Operations

1.1 Numbers and Sets

In our daily lives we use numbers to count, compare, order, measure, and solve problems. Numbers are the concept of the amount or quantity in a collection. The numbers we use the most and are most familiar with are whole numbers, but let’s look at some different sets of numbers.

DEFINITIONS

Counting numbersAll whole numbers greater than zero; also called natural numbers: {1, 2, 3, 4, …}.

Whole numbersThe set of counting numbers plus zero: {0, 1, 2, 3, …}.

IntegersThe set of numbers consisting of the counting numbers {1, 2, 3, 4, …}, their opposites {–1, –2, –3, –4, …}, and zero.

Rational numbersAny number that can be expressed as a ratio in the form

where a and b are integers and b ≠ 0. Rational numbers include all counting, whole, and integer numbers. They also include all fractions and decimal numbers, which terminate or have a repeating string of digits.

Decimal numberA fractional number written using base-ten notation; a mixed decimal number has a whole number part as well (e.g., 0.32 is a decimal number and 3.5 is a mixed decimal number).

FractionA number that represents part of a whole, part of a set, or a quotient in the form

, which can be read as a divided by b.

Irrational numberA real number that cannot be represented as an exact ratio of two integers; the decimal form of the number never terminates and never has a repeating string of digits (e.g., π,

,

, 0.010010001…).

Real numbersThe set of numbers that includes all rational and irrational numbers.

THINGS TO THINK A...