1001 MATH PROBLEMS 2ND EDITION 1 0 0 1 M AT H P R O B L E M S 2ND EDITION ® N E W Y O R K Copyright © 2004 LearningExpress,LLC. All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress,LLC,New York. Library ofCongress Cataloging-in-Publication Data: 1001 math problems.—2nd ed. p. cm. Includes index. ISBN 1-57685-512-0 (pbk.:alk.paper) 1.Mathematics—Problems,exercises,etc. QA43.A12 2004 510' .76—dc22 2003027069 Printed in the United States ofAmerica 9 8 7 6 5 4 3 2 1 Second Edition ISBN 1-57685-512-0 For more information or to place an order,contact LearningExpress at: 55 Broadway 8th Floor New York,NY 10006 Or visit us at: www.learnatest.com Contents INTRODUCTION vii SECTION 1 Miscellaneous Math 1 SECTION 2 Fractions 25 SECTION 3 Decimals 47 SECTION 4 Percentages 71 SECTION 5 Algebra 95 SECTION 6 Geometry 123 ANSWERS 157 v Introduction This book—which can be used alone, in combination with the Lear- ningExpress publication, Practical Math Success in 20 Minutes a Day, or along with another basic math text of your choice—will give you practice in dealing with whole numbers, fractions, decimals, percent- ages, basic algebra, and basic geometry. It is designed for individu- als working on their own, and for teachers or tutors helping students learn the basics. Practice on 1001 math problems should help allevi- ate math anxiety, too! A re you frightened ofmathematics? You’re not alone.By the time I was nine,I had developed a full-blown phobia.In fact,my most horrible moments in grade school took place right before an arithmetic test.My terror—and avoidance—lasted well into adulthood,until the day I landed a job with a social service agency and was given the task of figuring budgets,which involved knowing how to do percentages.I might just as well have been asked to decipher the strange squiggles incised on the nose-cone ofan alien spaceship.I decided I’d better do something quick,so I went to a friend ofmine, a fifth-grade teacher,and asked her to design a short course for me. We met on Sundays for almost a year.She began each tutorial with a short lecture on the type ofprob- lem we would be working with,and then provided me with a yellow legal pad and a photocopied set of problems—and sat doing crossword puzzles while I labored.We worked our way up to geometry that way, and on into algebra. “Mathematics works,”she told me early on.“Don’t ask why.Just do the problems.One day the light will dawn.” vii –HOW TO USE THIS BOOK– And it did finally! I’m proud to say I no longer In each section, you will find a few pre-algebra have to pay someone to do my 1040 form for the IRS, problems mixed in—problems that ask you to deal with and I don’t squirm and make excuses when,at lunch variables(letters that stand for unknown numbers,such with friends,I’m called on to figure the tip in my head. as x or y), exponents (those little numbers hanging I even balance my checkbook now! above the other numbers,like 24),and the like.These Learn by doing.It’s an old lesson,tried and true. problems are a warm-up for Section 5,Algebra.Ifthey And it’s the tool this book is designed to give you. are too hard for you at first,just skip them.Ifyou can Of course, this method works for people who answer them,you will be ahead ofthe game when you don’t have math anxiety,too.Maybe you have simply get to Section 5. forgotten a lot ofwhat you learned about math because The most important learning tool in this book is you haven’t had to use it much.Or maybe you’re a stu- not the problems,but the answers.At the back of the dent tackling arithmetic,algebra,and geometry for the book,each answer is fully explained.After you finish a first time,and you just need more practice than your set,go to the back ofthe book and see how many ques- textbook gives you.Perhaps you’re getting ready for an tions you got right. But don’t stop there: look at the exam,and you just want to make sure your math skills explanations for allthe questions,both the ones you got are up to the task.Whatever your situation, you can right and the ones you got wrong.You will be learning benefit from the method ofthis book.That old maxim by doing,and learning from your mistakes—the best really is true:Practice makes perfect. way to learn anysubject. (cid:2) An Overview of This Book (cid:2) How to Use This Book 1001 Math Problemsis divided into sections,each focus- Whether you are working alone or helping someone ing on one kind ofmath: else brush up on their math, this book can help you improve math skills. Section 1:Miscellaneous Math (page 1) Section 2:Fractions (page 25) Working On Your Own Section 3:Decimals (page 47) Ifyou are working alone to brush up on the basics,you Section 4:Percentages (page 71) may want to use this book in combination with a basic Section 5:Algebra (page 95) text or with Practical Math Success in 20 Minutes a Day. Section 6:Geometry (page 123) It will be helpful to read a summary of the different kinds of fractions and how to convert fractions into Each section is subdivided into short sets ofabout another form,before tackling fraction problems.Ifyou 16 problems each,so as to make the whole project seem are fairly sure of your basic math skills,however,you less overwhelming.You will begin with one or two sets can use this book by itself. offairly simple nonword problems;later sets focus on No matter how you decide to use the book,you word problems dealing with real-world situations. will find it most helpful ifyou do notuse a calculator, viii –HOW TO USE THIS BOOK– so as to prevent (or cure) “calculitis”—too much find in this book—you may want to try one ofthe fol- reliance on a calculator. lowing books. Tutoring Others ■ Practical Math Success in 20 Minutes a Dayby This book will work very well in combination with Judith Robinovitz (LearningExpress) almost any basic math text.You will probably find it ■ Algebra the Easy Way,3rd ed.by Douglas most helpful to give the student a brief lesson in the Downing (Barron’s) particular operation they will be learning—whole ■ All the Math You’ll Ever Needby Steve Slavin numbers,fractions,decimals,percentages,algebra,or (Wiley) geometry—and then have him or her spend the ■ Essential Math/Basic Math for Everyday Useby remainder ofthe class or session actually doing prob- Edward Williams and Robert A.Atkins lems.You will want to impress upon him or her the (Barron’s) importance oflearning by doing,and caution not to use ■ Everyday Math for Dummiesby Charles Seiter a calculator so as to gain a better understanding ofthe (IDG) operation in question. ■ Math the Easy Way,3rd ed.by Anthony Prindle and Katie Prindle (Barron’s) ■ Math Essentialsby Steve Slavin (cid:2) Additional Resources (LearningExpress) ■ Math Smart: Essential Math for These Numeric If you want more than just problems to work out—if Times(Princeton Review) you would like explanations ofthe kinds ofmath you ■ Mathematics Made Simpleby Abraham Sper- ling and Monroe Stuart (Doubleday) ix