Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) E-Book

Mark Zegarelli

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2022

Seitenzahl: 648

Beschreibung

Absolutely everything you need to get ready for Algebra Scared of square roots? Suspicious of powers of ten? You're not alone. Plenty of school-age students and adult learners don't care for math. But, with the right guide, you can make math basics "click" for you too! In Basic Math & Pre-Algebra All-in-One For Dummies, you'll find everything you need to be successful in your next math class and tackle basic math tasks in the real world. Whether you're trying to get a handle on pre-algebra before moving to the next grade or looking to get more comfortable with everyday math--such as tipping calculations or balancing your checkbook--this book walks you through every step--in plain English, and with clear explanations--to help you build a firm foundation in math. You'll also get: * Practice quizzes at the end of each chapter to test your comprehension and understanding * A bonus online quiz for each chapter, with answer choices presented in multiple choice format * A ton of explanations, examples, and practice problems that prepare you to tackle more advanced algebraic concepts From the different categories of numbers to mathematical operations, fractions, percentages, roots and powers, and a short intro to algebraic expressions and equations, Basic Math & Pre-Algebra All-in-One For Dummies is an essential companion for anyone who wants to get a handle on the foundational math concepts that are the building blocks for Algebra and beyond.

Leseprobe

Basic Math & Pre-Algebra All-in-One For Dummies®

Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com

Copyright © 2022 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Control Number: 2022932610

ISBN 978-1-119-86708-1 (pbk); ISBN 978-1-119-86748-7 (ebk); ISBN 978-1-119-86726-5 (ebk)

Basic Math & Pre-Algebra All-in-One For Dummies®

To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Basic Math & Pre-Algebra All-in-One For Dummies Cheat Sheet” in the Search box.

Table of Contents

Cover

Title Page

Copyright

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Unit 1: Getting Started with Basic Math & Pre-Algebra

Chapter 1: Playing the Numbers Game

Inventing Numbers

Understanding Number Sequences

Four Important Sets of Numbers

Chapter 2: The Big Four Operations

The Big Four Operations

Applying the Big Four Operations to Larger Numbers

Unit 2: The Big Four Operations: Addition, Subtraction, Multiplication, and Division

Chapter 3: Counting on Success: Numbers and Digits

Knowing Your Place Value

Close Enough for Rock ‘n’ Roll: Rounding and Estimating

Practice Questions Answers and Explanations

Whaddya Know? Chapter 3 Quiz

Answers to Chapter 3 Quiz

Chapter 4: Staying Positive with Negative Numbers

Understanding Where Negative Numbers Come From

Sign-Switching: Understanding Negation and Absolute Value

Addition and Subtraction with Negative Numbers

Knowing Signs of the Times (and Division) for Negative Numbers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 4 Quiz

Answers to Chapter 4 Quiz

Chapter 5: Putting the Big Four Operations to Work

Switching Things Up with Inverse Operations and the Commutative Property

Getting with the In-Group: Parentheses and the Associative Property

Understanding Inequalities

Moving Beyond the Big Four: Exponents and Square Roots

Practice Questions Answers and Explanations

Whaddya Know? Chapter 5 Quiz

Answers to Chapter 5 Quiz

Unit 3: Getting a Handle on Whole Numbers

Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS

The Three E’s of Math: Equations, Expressions, and Evaluation

Introducing Order of Operations (PEMDAS)

Handling Powers Responsibly

Bringing It All Together: The Order of Operations

Practice Questions Answers and Explanations

Whaddya Know? Chapter 6 Quiz

Answers to Chapter 6 Quiz

Chapter 7: Turning Words into Numbers: Basic Math Word Problems

Dispelling Two Myths about Word Problems

Solving Basic Word Problems

Solving More-Complex Word Problems

Practice Questions Answers and Explanations

Whaddya Know? Chapter 7 Quiz

Answers to Chapter 7 Quiz

Chapter 8: Divisibility and Prime Numbers

Knowing the Divisibility Tricks

Identifying Prime and Composite Numbers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 8 Quiz

Answers to Chapter 8 Quiz

Chapter 9: Divided Attention: Factors and Multiples

Knowing Six Ways to Say the Same Thing

Understanding Factors and Multiples

Finding Fabulous Factors

Generating a Number’s Factors

Decomposing a Number into Its Prime Factors

Finding the Greatest Common Factor

Generating the Multiples of a Number

Finding the Least Common Multiple

Practice Questions Answers and Explanations

Whaddya Know? Chapter 9 Quiz

Answers to Chapter 9 Quiz

Unit 4: Fractions

Chapter 10: Understanding Fractions

Slicing a Cake into Fractions

Knowing the Fraction Facts of Life

Increasing and Reducing Terms of Fractions

Converting between Improper Fractions and Mixed Numbers

Comparing Fractions with Cross-Multiplication

Working with Ratios and Proportions

Practice Questions Answers and Explanations

Whaddya Know? Chapter 10 Quiz

Answers to Chapter 10 Quiz

Chapter 11: Fractions and the Big Four Operations

Multiplying and Dividing Fractions

Adding and Subtracting Fractions with the Same Denominator

Adding and Subtracting Fractions with Different Denominators

Practice Questions Answers and Explanations

Whaddya Know? Chapter 11 Quiz

Answers to Chapter 11 Quiz

Chapter 12: Mixing Things Up with Mixed Numbers

Multiplying and Dividing Mixed Numbers

Adding Mixed Numbers

Subtracting Mixed Numbers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 12 Quiz

Answers to Chapter 12 Quiz

Unit 5: Decimals and Percents

Chapter 13: Getting to the Point with Decimals

Understanding Basic Decimal Stuff

Performing the Big Four Operations with Decimals

Converting between Decimals and Fractions

Simple Decimal-Fraction Conversions

Practice Questions Answers and Explanations

Whaddya Know? Chapter 13 Quiz

Answers to Chapter 13 Quiz

Chapter 14: Playing the Percentages

Making Sense of Percentages

Dealing with Percentages Greater than 100%

Converting to and from Percentages, Decimals, and Fractions

Converting Percentages to Decimals

Changing Decimals to Percentages

Switching from Percentages to Fractions

Converting Fractions to Percentages

Solving Percentage Problems

Putting All the Percent Problems Together

Solving Percent Problems with Equations

Practice Questions Answers and Explanations

Whaddya Know? Chapter 14 Quiz

Answers to Chapter 14 Quiz

Chapter 15: Word Problems with Fractions, Decimals, and Percentages

Adding and Subtracting Parts of the Whole in Word Problems

Problems about Multiplying Fractions

Multiplying Decimals and Percentages in Word Problems

Handling Percent Increases and Decreases in Word Problems

Practice Questions Answers and Explanations

Whaddya Know? Chapter 15 Quiz

Answers to Chapter 15 Quiz

Unit 6: Reaching the Summit: Advanced Pre-Algebra Topics

Chapter 16: Powers and Roots

Memorizing Powers and Roots

Changing the Base

Exponents of 0 and Negative Numbers

Fractional Exponents

Practice Questions Answers and Explanations

Whaddya Know? Chapter 16 Quiz

Answers to Chapter 16 Quiz

Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation

First Things First: Using Powers of Ten as Exponents

Exponential Arithmetic: Multiplying and Dividing Powers of Ten

Working with Scientific Notation

Dividing with Scientific Notation

Practice Questions Answers and Explanations

Whaddya Know? Chapter 17 Quiz

Answers to Chapter 17 Quiz

Chapter 18: How Much Have You Got? Weights and Measures

Understanding Units

Examining Differences between the English and Metric Systems

Estimating and Converting between the English and Metric Systems

Converting between English and Metric Units

Practice Questions Answers and Explanations

Whaddya Know? Chapter 18 Quiz

Answers to Chapter 18 Quiz

Chapter 19: Getting the Picture with Geometry

Getting on the Plane: Points, Lines, Angles, and Shapes

Getting in Shape: Polygon (and Non-Polygon) Basics

Closed Encounters: Shaping Up Your Understanding of 2-D Shapes

Squaring Off with Quadrilaterals

Making a Triple Play with Triangles

Getting Around with Circle Measurements

Taking a Trip to Another Dimension: Solid Geometry

Building Solid Measurement Skills

Solving Geometry Word Problems

Practice Questions Answers and Explanations

Whaddya Know? Chapter 19 Quiz

Answers to Chapter 19 Quiz

Chapter 20: Figuring Your Chances: Statistics and Probability

Gathering Data Mathematically: Basic Statistics

Looking at Likelihoods: Basic Probability

Practice Questions Answers and Explanations

Whaddya Know? Chapter 20 Quiz

Answers to Chapter 20 Quiz

Chapter 21: Setting Things Up with Basic Set Theory

Understanding Sets

Performing Operations on Sets

Practice Questions Answers and Explanations

Whaddya Know? Chapter 21 Quiz

Answers to Chapter 21 Quiz

Unit 7: The X-Files: Introduction to Algebra

Chapter 22: Working with Algebraic Expressions

Seeing How X Marks the Spot

Expressing Yourself with Algebraic Expressions

Evaluating Algebraic Expressions

Knowing the Terms

Adding and Subtracting Like Terms

Multiplying and Dividing Terms

Simplifying Expressions by Combining Like Terms

Removing Parentheses from an Algebraic Expression

FOILing: Dealing with Two Sets of Parentheses

Practice Questions Answers and Explanations

Whaddya Know? Chapter 22 Quiz

Answers to Chapter 22 Quiz

Chapter 23: Solving Algebraic Equations

Understanding Algebraic Equations

The Balancing Act: Solving for x

Rearranging Equations and Isolating x

Practice Questions Answers and Explanations

Whaddya Know? Chapter 23 Quiz

Answers to Chapter 23 Quiz

Chapter 24: Tackling Algebra Word Problems

Solving Algebra Word Problems in Five Steps

Choosing Your Variable Wisely

Solving More-Complex Algebraic Problems

Practice Questions Answers and Explanations

Whaddya Know? Chapter 24 Quiz

Answers to Chapter 24 Quiz

Chapter 25: Graphing Algebraic Equations

Graphing on the xy-Plane

Understanding Linear Equations

Measuring the Slope of a Line

Graphing Linear Equations Using the Slope and y-intercept

Practice Questions Answers and Explanations

Whaddya Know? Chapter 25 Quiz

Answers to Chapter 25 Quiz

Index

About the Author

Advertisement Page

Connect with Dummies

End User License Agreement

List of Tables

Chapter 3

Table 3-1 45,019 Displayed in a Place-Value Chart

Table 3-2 5,001,000 Displayed Incorrectly without Placeholding Zeros

Table 3-3 3,040,070 Displayed with Two Leading Zeros

Table 3-4 A Place-Value Chart Separated by Commas

Chapter 13

Table 13-1 Breaking Down 4,672 in Terms of Place Value

Table 13-2 Breaking Down the Decimal 4,672.389

Table 13-3 Example of Attaching Leading Zeros

Table 13-4 Example of Attaching Trailing Zeros

Table 13-5 Example of Zeros as Placeholders

Table 13-6 Example of Decimal Points and Place Value of Digits

Table 13-7 Example of Numbers Shifting One Place

Chapter 14

TABLE 14-1 The Three Main Types of Percent Problems

Chapter 17

Table 17-1 Powers of Ten Expressed as Exponents

Chapter 18

Table 18-1 Commonly Used English Units of Measurement

Table 18-2 Five Basic Metric Units

Table 18-3 Ten Metric Prefixes

Table 18-4 Comparing Celsius and Fahrenheit Temperatures

Table 18-5 Conversion Factors for English and Metric Units

Chapter 20

Table 20-1 Sister Elena’s Fifth-Grade Survey

Table 20-2 Favorite Colors in Sister Elena’s Class

Table 20-3 Height and Spelling Test Scores

Chapter 25

Table 25-1 Plotting the Points for the Linear Equation

.

Table 25-2 The Slope and

y

-Intercept of Three Linear Equations

List of Illustrations

Chapter 1

FIGURE 1-1: Square numbers.

FIGURE 1-2: The number 12 laid out in two rectangular patterns.

FIGURE 1-3: Composite numbers, such as 8 and 15, can form rectangles.

FIGURE 1-4: Unlucky 13, a prime example of a number that refuses to fit in a bo...

Chapter 4

FIGURE 4-1: Negative numbers on the number line.

Chapter 10

FIGURE 10-1: Two halves of a cake.

FIGURE 10-2: Cake cut into thirds.

FIGURE 10-3: Cakes cut and shaded into

FIGURE 10-4: Cakes cut and shaded into

Chapter 13

FIGURE 13-1: One-half (0.5) of a dollar bill.

FIGURE 13-2: One-fourth (0.25) of a dollar bill.

FIGURE 13-3: Three-fourths (0.75) of a dollar bill.

FIGURE 13-4: Cakes cut and shaded into (A) 0.75, (B) 0.4, (C) 0.1, and (D) 0.7....

Chapter 19

FIGURE 19-1: Unnamed shapes.

FIGURE 19-2: Types of triangles.

FIGURE 19-3: Common quadrilaterals.

FIGURE 19-4: A pentagon, a hexagon, and an octagon.

FIGURE 19-5: Various irregular polygons.

FIGURE 19-6: The area and perimeter of a square using the length of a side (

s

)

.

FIGURE 19-7: The area and perimeter of a rectangle using the length (

l

) and wid...

FIGURE 19-8: The area of a rhombus or parallelogram using the base (

b

) and heig...

FIGURE 19-9: The area of a trapezoid using the length of the two bases (

b

1

and

FIGURE 19-10: The area of a triangle using the base (

b

) and height (

h

)

.

FIGURE 19-11: Using the Pythagorean Theorem to find the hypotenuse (

c

) of a rig...

FIGURE 19-12: The area and circumference of a circle using the radius (

r

).

FIGURE 19-13: A typical cube.

FIGURE 19-14: Common polyhedrons.

FIGURE 19-15: The five regular solids.

FIGURE 19-16: Spheres, cylinders, and cones.

FIGURE 19-17: The volume of a cube using the length of a side (

s

).

FIGURE 19-18: The volume of a box using the length (

l

), width (

w

), and height (

FIGURE 19-19: The volume of a prism or cylinder using the area of the base (

A

b

)...

FIGURE 19-20: The volume of a pyramid or cone using the area of the base (

A

b

) a...

FIGURE 19-21: The volume of a sphere using the radius (

r

).

FIGURE 19-22: Two sons get nonrectangular portions of a rectangular field.

FIGURE 19-23: A labeled sketch shows the important information in a word proble...

FIGURE 19-24: Update the labels in your sketch as you work through the problem.

Chapter 23

FIGURE 23-1: Showing how an equation is similar to a balance scale.

Chapter 25

FIGURE 25-1: The

xy

-plane.

FIGURE 25-2: Plotting four points on the

xy

-plane:

,

,

, and

.

FIGURE 25-3: Graphing the equation

.

FIGURE 25-4: The graph of

on the

xy

-plane.

FIGURE 25-5: The graph of

on the

xy

-plane for three positive values of

m

.

FIGURE 25-6: The graph of

on the

xy

-plane for three negative values of

m

.

FIGURE 25-7: The graph of

on the

xy

-plane for three positive values of

b

.

FIGURE 25-8: The graph of

on the

xy

-plane for three negative values of

b

.

FIGURE 25-9: Four linear equations graphed on the

xy

-plane.

FIGURE 25-10: Graphing slopes of 1, 0, and –1.

FIGURE 25-11: Graphing positive and negative slopes.

Guide

Cover

Title Page

Copyright

Table of Contents

Begin Reading

Index

About the Author

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Unit 1

Getting Started with Basic Math & Pre-Algebra

In This Unit …

Chapter 1: Playing the Numbers Game

Inventing Numbers

Understanding Number Sequences

Four Important Sets of Numbers

Chapter 2: The Big Four Operations

The Big Four Operations

Applying the Big Four Operations to Larger Numbers

Unit 2

The Big Four Operations: Addition, Subtraction, Multiplication, and Division

In This Unit …

Chapter 3: Counting on Success: Numbers and Digits

Knowing Your Place Value

Close Enough for Rock ‘n’ Roll: Rounding and Estimating

Practice Questions Answers and Explanations

Whaddya Know? Chapter 3 Quiz

Answers to Chapter 3 Quiz

Chapter 4: Staying Positive with Negative Numbers

Understanding Where Negative Numbers Come From

Sign-Switching: Understanding Negation and Absolute Value

Addition and Subtraction with Negative Numbers

Knowing Signs of the Times (and Division) for Negative Numbers

Practice Questions Answers and Explanations

Whaddya Know? Chapter 4 Quiz

Answers to Chapter 4 Quiz