Basic Math and Pre-Algebra E-Book

Mark Zegarelli

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 350

Beschreibung

1001 Basic Math & Pre- Algebra Practice Problems For Dummies Practice makes perfect--and helps deepen your understanding of basic math and pre-algebra by solving problems 1001 Basic Math & Pre-Algebra Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Basic Math & Pre-Algebra For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in your math course. You begin with some basic arithmetic practice, move on to fractions, decimals, and percents, tackle story problems, and finish up with basic algebra. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find: * One year free subscription to all 1001 practice problems * On-the-go access any way you want it--from your computer, smart phone, or tablet * Multiple choice questions on all you math course topics * Personalized reports that track your progress and help show you where you need to study the most * Customized practice sets for self-directed study * Practice problems categorized as easy, medium, or hard The practice problems in 1001 Basic Math & Pre-Algebra Practice Problems For Dummies give you a chance to practice and reinforce the skills you learn in class and help you refine your understanding of basic math & pre-algebra. Note to readers: 1,001 Basic Math & Pre-Algebra Practice Problems For Dummies, which only includes problems to solve, is a great companion to Basic Math & Pre-Algebra I For Dummies, which offers complete instruction on all topics in a typical Basic Math & Pre-Algebra course.

Leseprobe

Published byJohn Wiley & Sons, Inc.111 River St.Hoboken, NJ 07030-5774www.wiley.com

Copyright © 2013 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Control Number: 2013932103

ISBN 978-1-118-44656-0 (pbk); ISBN 978-1-118-44645-4 (ebk); ISBN 978-1-118-44653-9 (ebk); ISBN 978-1-118-44654-6 (ebk)

Manufactured in the United States of America

10 9 8 7 6 5 4 3 2 1

About the Author

Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, Calculus II For Dummies, and five other books on math, logic, and test preparation. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.

Mark lives in San Francisco, California, and Long Branch, New Jersey.

Dedication

This is for Suleiman.

Author’s Acknowledgments

This is my eighth For Dummies book and, as always, the experience of writing it has been productive and fun. Thanks so much to editors Tim Gallan, Christy Pingleton, Lindsay Lefevere, Shira Fass, and Suzanne Langebartels for setting me right as needed.

And thanks to the folks at Borderlands Café on Valencia Street in San Francisco for the friendly, peaceful, and caffeine-accessible environment that virtually any writer (this one, for example) would find conducive to putting actual words on paper.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Vertical Websites

Senior Project Editor: Tim Gallan

Executive Editor: Lindsay Sandman Lefevere

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Cover Photos: © Sandra van der Steen/iStockphoto.com

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Proofreaders: Jacqui Brownstein, Dwight Ramsey

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Publishing and Editorial for Consumer Dummies

Kathleen Nebenhaus, Vice President and Executive Publisher

David Palmer, Associate Publisher

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1,001 Basic Math & Pre-Algebra Practice Problems For Dummies®

Visit www.dummies.com/cheatsheet/1001basicmath&pre-algebra to view this book's cheat sheet.

Table of Contents

Introduction

What You’ll Find

How This Workbook Is Organized

Part I: Questions

Part II: Answers

Beyond the Book

What you’ll find online

How to register

Where to Go for Additional Help

Part I: The Questions

Chapter 1: The Big Four Operations

The Problems You’ll Work On

What to Watch Out For

Chapter 2: Less than Zero: Working with Negative Numbers

The Problems You’ll Work On

What to Watch Out For

Chapter 3: You’ve Got the Power: Powers and Roots

The Problems You’ll Work On

What to Watch Out For

Chapter 4: Following Orders: Order of Operations

The Problems You’ll Work On

What to Watch Out For

Chapter 5: Big Four Word Problems

The Problems You’ll Work On

What to Watch Out For

Chapter 6: Divided We Stand

The Problems You’ll Work On

What to Watch Out For

Chapter 7: Factors and Multiples

The Problems You’ll Work On

What to Watch Out For

Chapter 8: Word Problems about Factors and Multiples

The Problems You’ll Work On

What to Watch Out For

Chapter 9: Fractions

The Problems You’ll Work On

What to Watch Out For

Chapter 10: Decimals

The Problems You’ll Work On

What to Watch Out For

Chapter 11: Percents

The Problems You’ll Work On

What to Watch Out For

Chapter 12: Ratios and Proportions

The Problems You’ll Work On

What to Watch Out For

Chapter 13: Word Problems for Fractions, Decimals, and Percents

The Problems You’ll Work On

What to Watch Out For

Chapter 14: Scientific Notation

The Problems You’ll Work On

What to Watch Out For

Chapter 15: Weights and Measures

The Problems You’ll Work On

What to Watch Out For

Chapter 16: Geometry

The Problems You’ll Work On

What to Watch Out For

Chapter 17: Graphing

The Problems You’ll Work On

What to Watch Out For

Chapter 18: Statistics and Probability

The Problems You’ll Work On

What to Watch Out For

Chapter 19: Set Theory

The Problems You’ll Work On

What to Watch Out For

Chapter 20: Algebraic Expressions

The Problems You’ll Work On

What to Watch Out For

Chapter 21: Solving Algebraic Equations

The Problems You’ll Work On

What to Watch Out For

Chapter 22: Solving Algebra Word Problems

The Problems You’ll Work On

What to Watch Out For

Part II: The Answers

Chapter 23: Answers

Answers 1 - 100

Answers 101 - 200

Answers 201 - 300

Answers 301 - 400

Answers 401 - 500

Answers 501 - 600

Answers 601 - 700

Answers 701 - 800

Answers 801 - 900

Answers 901 - 1001

Cheat Sheet

End User License Agreement

Introduction

Are you kidding . . . 1,001 math problems, really?

That’s right, a thousand questions plus one to grow on, here in your hot little hands. I’ve arranged them in order, starting with beginning arithmetic and ending with basic algebra. Topics include everything from the Big Four operations (adding, subtracting, multiplying, and dividing), through negative numbers and fractions, on to geometry and probability, and finally algebra — plus lots more!

Every chapter provides tips for solving the problems in that chapter. And, of course, the back of the book includes detailed explanations of the answers to every question.

It’s all here, so get to work!

What You’ll Find

This book includes 1,001 basic math and pre-algebra problems, divided into 22 chapters. Each chapter contains problems focusing on a single math topic, such as negative numbers, fractions, or geometry.

Within each chapter, topics are broken into subtopics so that you can work on a specific type of math skill until you feel confident with it. Generally speaking, each section starts with easy problems, moves on to medium ones, and then finishes with hard problems.

You can jump right in anywhere you like and solve these problems in any order. You can also take on one chapter or section at a time, working from easy to medium to hard problems. Or, if you like, you can begin with Question #1 and move right through to Question #1,001.

Additionally, each chapter begins with a list of tips for answering the questions in that chapter.

Every question in Part I is answered in Part II, with a full explanation that walks you through how to understand, set up, and solve the problem.

How This Workbook Is Organized

This workbook includes 1,001 questions in Part I and answers to all of these questions in Part II.

Part I: Questions

Here are the topics covered by the 1,001 questions in this book:

Basic arithmetic: In Chapters 1 through 5, you find dozens of basic arithmetic problems. Chapter 1 begins with rounding numbers and then moves on to basic calculating with addition, subtraction, multiplication, and division. Then, in Chapter 2, you tackle negative numbers, and in Chapter 3, you move on to working with powers and square roots. Chapter 4 gives you plenty of practice in solving arithmetic problems using the order of operations. You may remember this using the mnemonic PEMDAS — Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Finally, in Chapter 5, you put all of this information together to answer arithmetic word problems, from easy to challenging.

Divisibility, factors, and multiples: Chapters 6, 7, and 8 cover a set of topics related to divisibility. In Chapter 6, you discover a variety of divisibility tricks, which allow you to find out whether a number is divisible by another without actually doing the division. You also work with division with remainders and understand the distinction between prime and composite numbers.

Chapter 7 focuses on factors and multiples. You discover how to generate all the factors and prime factors of a number and calculate the greatest common factor (GCF) for a set of two or more numbers. Additionally, you generate a partial list of the multiples, and calculate the least common multiple (LCM) of two or more numbers.

Chapter 8 wraps up the section with word problems that sharpen and extend your skills working with factors, multiples, remainders, and prime numbers.

Fractions, decimals, percents, and ratios: Chapters 9 through 13 focus on four distinct ways to represent parts of a whole — fractions, decimals, percents, and ratios. In Chapter 9, you work with fractions, including increasing the terms of fractions and reducing them to lowest terms. You change improper fractions to mixed numbers, and vice versa. You add, subtract, multiply, and divide fractions, including mixed numbers. You also simplify complex fractions.

In Chapter 10, you convert fractions to decimals, and vice versa. You add, subtract, multiply, and divide decimals. You also find out how to work with repeating decimals. Chapter 11 focuses on percents. You convert fractions and multiples to percents, and vice versa. You discover a few tricks for calculating simple percents. You also work on more difficult percent problems by creating word equations, which can then be translated into equations and solved.

Chapter 12 presents a variety of problems, including word problems, that use ratios and proportions. And in Chapter 13, you tackle even more word problems where you apply your skills working with fractions, decimals, and percents.

Scientific notation, weights and measures, geometry, graphs, statistics and probability, and sets: In Chapters 14 through 19, you take a great stride forward working with a wide variety of intermediate basic math skills. In Chapter 14, the topic is scientific notation, which is used to represent very large and very small numbers. Chapter 15 introduces you to weights and measures, focusing on the English and metric systems, and conversions between the two. Chapter 16 gives you a huge number of geometry problems of every description, including both plane and solid geometry. In Chapter 17, you work with a variety of graphs, including bar graphs, pie charts, line graphs, pictographs, and the xy-graph that is used so much in algebra and later math.

Chapter 18 gives you an introduction to basic statistics, including the mean, median, and mode. It also provides problems in probability and gives you an introduction to counting both independent and dependent events. Chapter 19 gives you some problems in basic set theory, including finding the union, intersection, relative complement, and complement. Additionally, you use Venn diagrams to solve word problems.

Algebraic expressions and equations: To finish up, Chapters 20, 21, and 22 give you a taste of the work you’ll be doing in your first algebra class. Chapter 20 shows you the basics of working with algebraic expressions, including evaluating, simplifying, and factoring. In Chapter 21, you solve basic algebraic equations. And in Chapter 22, you put these skills to use, solving a set of word problems with basic algebra.

Part II: Answers

In this part, you find answers to all 1,001 questions that appear in Part I. Each answer contains a complete step-by-step explanation of how to solve the problem from beginning to end.

Beyond the Book

This book gives you plenty of math to work on and prepares you for algebra. But maybe you want to track your progress as you tackle the problems, or maybe you’re having trouble with certain types of problems and wish they were all presented in one place where you could methodically make your way through them. You’re in luck. Your book purchase comes with a free one-year subscription to all 1,001 practice problems online. You get on-the-go access any way you want it — from your computer, smartphone, or tablet. Track your progress and view personalized reports that show where you need to study the most. And then do it. Study what, where, when, and how you want.

What you’ll find online

The online practice that comes free with this book offers you the same 1,001 questions and answers that are available here, presented in a multiple-choice format. The beauty of the online problems is that you can customize your online practice to focus on the topic areas that give you the most trouble. So if you need help converting fractions to decimals or have trouble grasping pre-algebra, then select these problem types online and start practicing. Or, if you’re short on time but want to get a mixed bag of a limited number of problems, you can specify the quantity of problems you want to practice. Whether you practice a few hundred problems in one sitting or a couple dozen, and whether you focus on a few types of problems or practice every type, the online program keeps track of the questions you get right and wrong so that you can monitor your progress and spend time studying exactly what you need.

You can access this online tool using a PIN code, as described in the next section. Keep in mind that you can create only one login with your PIN. Once the PIN is used, it’s no longer valid and is nontransferable. So you can’t share your PIN with other users after you’ve established your login credentials.

How to register

To gain access to additional tests and practice online, all you have to do is register. Just follow these simple steps:

1. Find your PIN access code:

• Print-book users: If you purchased a print copy of this book, turn to the inside front cover of the book to find your access code.

• E-book users: If you purchased this book as an e-book, you can get your access code by registering your e-book at www.dummies.com/go/getaccess. Go to this website, find your book and click it, and answer the security questions to verify your purchase. You'll receive an email with your access code.

2. Go to Dummies.com and click Activate Now.

3. Find your product (SAT For Dummies) and then follow the on-screen prompts to activate your PIN.

Now you’re ready to go! You can come back to the program as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time. For Technical Support, please visit http://wiley.custhelp.com or call Wiley at 1-800-762-2974 (U.S.), [phone] (international).

Your registration is good for one year from the day you activate your PIN. After that time frame has passed, you can renew your registration for a fee. The website gives you all the important details about how to do so.

Where to Go for Additional Help

Every chapter in this book opens with tips for solving the problems in that chapter. And, of course, if you get stuck on any question, you can flip to the answer section and try to work through the solution provided. However, if you feel that you need a bit more basic math information than this book provides, I highly recommend my earlier book Basic Math & Pre-Algebra For Dummies. This book gives you a ton of useful information for solving every type of problem included here.

Additionally, you can also check out my Basic Math & Pre-Algebra Workbook For Dummies. It contains a nice mix of short explanations for how to do various types of problems, followed by practice. And, for a quick take on the most important basic math concepts, have a look at Basic Math & Pre-Algebra Essentials For Dummies. Yep, I wrote that one, too — how’s that for shameless plugs?

Part I

The Questions

Visit www.dummies.com for great Dummies content online

In this part . . .

One thousand and one math problems. That’s one problem for every night in the Arabian Nights stories. That’s almost ten problems for every floor in the Empire State Building. In short, that’s a lot of problems — plenty of practice to help you attain the math skills you need to do well in your current math class. Here’s an overview of the types of questions provided:

Basic arithmetic, including absolute value, negative numbers, powers, and square roots (Chapters 1 through 5)

Divisibility, factors, and multiples (Chapters 6 through 8)

Fractions, decimals, percents, and ratios (Chapters 9 through 13)

Scientific notation, measures, geometry, graphs, statistics, probability, and sets (Chapters 14 through 19)

Algebraic expressions and equations (Chapters 20 through 22)

Chapter 3

You’ve Got the Power: Powers and Roots

Powers provide a shorthand notation for multiplication using a base number and an exponent. Roots — also called radicals — reverse the process of powers. In this chapter, you practice taking powers and roots of positive integers as well as fractions and negative integers.

The Problems You’ll Work On

This chapter deals with the following types of problems:

Using powers to multiply a number by itself

Applying exponents to negative numbers and fractions

Understanding square roots

Knowing how to evaluate negative exponents and fractional exponents

What to Watch Out For

Following are some tips for working with powers and roots:

When you find the power of a number, multiply the base by itself as many times as indicated by the exponent. For example, .

When the base is a negative number, use the standard rules of multiplication for negative numbers (see Chapter 2). For example, .

When the base is a fraction, use the standard rules of multiplication for fractions (see Chapter 9). For example, .

To find the square root of a square number, find the number that, when multiplied by itself, results in the number you started with. For example, , because .

To simplify the square root of a number that’s not a square number, if possible, factor out a square number and then evaluate it. For example, .

Evaluate an exponent of as the square root of the base. For example, .

Evaluate an exponent of –1 as the reciprocal of the base. For example, .

To evaluate an exponent of a negative number, make the exponent positive and evaluate its reciprocal. For example, .

Multiplying a Number by Itself

58–72

58. Evaluate each of the following.

i.

ii.

iii.

iv.

v.

59.

60.

61.

62.

63.

64.

65. Evaluate each of the following.

i.

ii.

iii.

iv.

v.

66.

67.

68.

69. Evaluate each of the following.

i.

ii.

iii.

iv.

v.

70.

71.

72.

Finding Square Roots

73–79

73. Simplify each of the following as a whole number by finding the square root.

i.

ii.

iii.

iv.

v.

74. Simplify each of the following as a whole number by finding the square root and then multiplying.

i.

ii.

iii.

iv.

v.

75.

76.

77.

78.

79.

Negative and Fractional Exponents

80–90

80. Express each of the following as a square root and then simplify as a positive whole number.

i.

ii.

iii.

iv.

v.

81.

82.

83.

84.

85. Simplify each of the following as a fraction.

i.

ii.

iii.

iv.

v.

86.

87.

88.

89.

90.

Chapter 5

Big Four Word Problems

Word problems provide an opportunity for you to apply your math skills to real-world situations. In this chapter, all the problems can be solved using the Big Four operations (adding, subtracting, multiplying, and dividing).

The Problems You’ll Work On

The problems in this chapter fall into three basic categories, based on their difficulty:

Basic word problems where you need to perform a single operation

Intermediate word problems where you need to use two different operations

Tricky word problems that require several different operations and more difficult calculations

What to Watch Out For

Here are a few tips for getting the right answer to word problems:

Read each problem carefully to make sure you understand what it’s asking.

Use scratch paper to gather and organize information from the problem.

Think about which Big Four operation (adding, subtracting, multiplying, or dividing) will be most helpful for solving the problem.

Perform calculations carefully to avoid mistakes.

Ask yourself whether the answer you got makes sense.

Check your work to make sure you’re right.

Basic Word Problems

145–154

145. A horror movie triple-feature included Zombies Are Forever, which was 80 minutes long, An American Werewolf in Bermuda, which ran for 95 minutes, and Late Night Snack of the Vampire, which was 115 minutes from start to finish. What was the total length of the three movies?

146. At a height of 2,717 feet, the tallest building in the world is the Burj Khalifa in Dubai. It’s 1,263 feet taller than the Empire State Building in New York City. What is the height of the Empire State Building?

147. Janey’s six children are making colored eggs for Easter. She bought a total of five dozen eggs for all of the children to use. Assuming each child gets the same number of eggs, how many eggs does each child receive?

148. Arturo worked a 40-hour week at $12 per hour. He then received a raise of $1 per hour and worked a 30-hour week. How much more money did he receive for the first week of work than the second?

149. A restaurant has 5 tables that seat 8 people each, 16 tables with room for 6 people each, and 11 tables with room for 4 people each. What is the total capacity of all the tables at the restaurant?

150. The word pint originally comes from the word pound because a pint of water weighs 1 pound. If a gallon contains 8 pints, how many pounds does 40 gallons of water weigh?

151. Antonia purchased a sweater normally priced at $86, including tax. When she brought it to the cash register, she found that it was selling for half off. Additionally, she used a $20 gift card to help pay for the purchase. How much money did she have to spend to buy the sweater?

152. A large notebook costs $1.50 more than a small notebook. Karan bought two large notebooks and four small notebooks, while Almonte bought five large notebooks and one small notebook. How much more did Almonte spend than Karan?

153. A company invests $7,000,000 in the development of a product. Once the product is on the market, each sale returns $35 on the investment. If the product sells at a steady rate of 25,000 per month, how long will it take for the company to break even on its initial investment?

154. Jessica wants to buy 40 pens. A pack of 8 pens costs $7, but a pack of 10 pens costs $8. How much does she save by buying packs of 10 pens instead of packs of 8 pens?

Intermediate Word Problems

155–171

155. Jim bought four boxes of cereal on sale. One box weighed 10 ounces and the remaining boxes weighed 16 ounces each. How many ounces of cereal did he buy altogether?

156. Mina took a long walk on the beach each day of her eight-day vacation. On half of the days, she walked 3 miles and on the other half she walked 5 miles. How many miles did she walk altogether?

157. A three-day bike-a-thon requires riders to travel 100 miles on the first day and 20 miles fewer on the second day. If the total trip is 250 miles, how many miles do they travel on the third day?

158. If six T-shirts sell for $42, what is the cost of nine T-shirts at the same rate?

159. Kenny did 25 pushups. His older brother, Sal, did twice as many pushups as Kenny. Then, their oldest sister, Natalie, did 10 more pushups than Sal. How many pushups did the three children do altogether?

160. A candy bar usually sells at two for 90 cents. This week, it is specially packaged at three for $1.05. How much can you save on a single candy bar by buying a package of three rather than two?

161. Simon noticed a pair of square numbers that add up to 130. He then noticed that when you subtract one of these square numbers from the other, the result is 32. What is the smaller of these two square numbers?

162. If Donna took 20 minutes to read 60 pages of a 288-page graphic novel, how long did she take to read the whole novel, assuming that she read it all at the same rate?

163. Kendra sold 50 boxes of cookies in 20 days. Her older sister, Alicia, sold twice as many boxes in half as many days. If the two girls continued at the same sales rates, how many total boxes would both girls have sold if they had both sold cookies for 40 days?

164. A group of 70 third graders has exactly three girls for every four boys. When the teacher asks the children to pair up for an exercise, six boy-girl pairs are formed, and the rest of the children pair up with another child of the same sex. How many more boy-boy pairs are there than girl-girl pairs?

165. Together, a book and a newspaper cost $11.00. The book costs $10.00 more than the newspaper. How many newspapers could you buy for the same price as the book?

166. Yianni just purchased a house priced at $385,000 with a mortgage from the bank. His monthly mortgage payment to cover the principal and interest will be $1,800 per month for 30 years. When he has finished paying off the house, how much over and above the cost of the house will Yianni have paid in interest?

167. The distance from New York to San Diego is approximately 2,700 miles. Because of prevailing winds, when flying east-to-west, the flight usually takes one hour longer than when flying west-to-east. If a plane from San Diego to New York travels at a forward speed of 540 miles per hour, what is the forward speed of a plane traveling from New York to San Diego under the same conditions?

168. Arlo went to an all-night poker game hosted by friends. By 11:00, he was down $65 from where he had started. Between 11:00 and 2:00, he won $120. Then, in the next three hours, he lost another $45. In the final hour of the game, he won $30. How much did Arlo win or lose during the game?

169. Clarissa bought a diamond for $1,000 and then sold it to Andre for $1,100. A month later, Andre needed money, so he sold the diamond back to Clarissa for $900. But a few months later, he had a windfall and bought the diamond back from Clarissa for $1,200. How much profit did Clarissa make as a result of the total transactions?

170. Angela and Basil both work at a cafeteria making sandwiches. At top speed, Angela can make four sandwiches in three minutes and Basil can make three sandwiches in four minutes. Working together, how long will they take to make 200 sandwiches?

171. All 16 children in Ms. Morrow’s preschool have either two or three siblings. Altogether, the children have a total of 41 siblings. How many of the children have three siblings?

Advanced Word Problems

172–180

172. What is the sum of all the numbers from 1 to 100?

173. Louise works in retail and has a $1,200-per-day sales quota. On Monday, she exceeded this quota by $450. On Tuesday, she exceeded it by $650. On Wednesday and Thursday, she made her quota exactly. Friday was a slow day, so Louise sold $250 less than her quota. What were her total sales for the five days?

174. A sign posted over a large swimming pool reminds swimmers that 40 lengths of the pool equals 1 mile. Jordy swam 1 length of the pool at a rate of 3 miles per hour. How long did he take to swim 1 length of the pool?

175. In a group of two people, only one pair can shake hands. But in a group of three people, three different pairings of people can shake hands. How many different pairings of people can shake hands in a group of ten people?

176. Marion found that three red bricks and one white brick weighed a total of 23 pounds. Then she replaced one red brick on the scale with two white bricks, and found that the weight went up to 27 pounds. Assuming all red bricks are equal to each other in weight, and that the same is true of all white bricks, what is the weight of one red brick?

177. Angela counted all the coins in her uncle’s change jar. She counted 891 pennies, 342 nickels, 176 dimes, and 67 quarters. How much money was in the jar?

178. On a long car trip, Joel drove the first two hours on the highway at 70 miles per hour. He took a 15-minute break and then drove another hour at 60 miles per hour. Next, he drove on a winding mountain road for two hours at 35 miles per hour. He took a 45-minute break for dinner and then finished up his trip with three hours of driving at 75 miles per hour. What was Joel’s average speed for the whole trip, including the breaks?

179. A candy bar usually sells at two for 90 cents. This week, it is specially packaged at three for $1.05. Heidi bought so many that she saved $5.40 in comparison with the regular price. How many candy bars did she buy?

180. Suppose you decide to save a dollar on the first day of the month, two additional dollars on the second, four additional dollars the third, and continue doubling the amount you add every day. How many days will it take you to save a combined total of more than $30,000?

Chapter 6

Divided We Stand

Division is the most interesting and complex of the Big Four operations (addition, subtraction, multiplication, and division). When you divide two numbers, you divide the dividend by the divisor, and the result is the quotient. For example:

Dividend

Divisor

Quotient

24

8

3

Integer division — that is, division with whole numbers only — always results in a remainder (which may be 0).

Dividend

Divisor

Quotient

Remainder

26

8

3

r2

The remainder is a whole number from 0 to one less than the number you’re dividing by. For example, when you divide any number by 8, the remainder must be a whole number from 0 to 7, inclusive.

The Problems You’ll Work On

This chapter focuses on the following concepts and skills:

Understanding integer division — that is, division with a remainder

Knowing some quick rules for divisibility

Finding the remainder to a division problem without dividing

Distinguishing prime numbers from composite numbers

What to Watch Out For

Following are some rules and tips to utilize when working division problems:

One integer is divisible