Math You Can Really Use - Every Day

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MATH
YOU CAN REALLY USE—
EVERY DAY
David Alan Herzog
Copyright © 2007 by Wiley Publishing, Inc., Hoboken, New Jersey. All rights reserved.
Published by Wiley Publishing, Inc., Hoboken, New Jersey
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Library of Congress Cataloging-in-Publication Data:
Herzog, David Alan.
Math you can really use : every day / David A. Herzog.
p. cm.
Includes index.
ISBN-13: 978-0-470-05402-4 (pbk.)
ISBN-10: 0-470-05402-6 (pbk.)
1. Mathematics—Popular works. I. Title.
QA93.H4 2007
510—dc22
2007005095
Printed in the United States of America
10987654321
Book production by Wiley Publishing, Inc., Composition Services
Wiley Bicentennial Logo: Richard J. Pacifico
This book is dedicated to the memory of my sister, Lois
Herzog Cullen, who was taken from us much too soon.
It is also dedicated to Francesco, Sebastian, and Gino
Nicholas Bubba, Hailee Foster, Rocio, Myles, Kira, and
Reese Herzog, Jakob and Alex Cherry, Marcelo, all their
parents, Uncle Ian, and Grandma Birdie.
Acknowledgments
I find it only fitting that I should acknowledge the two Wiley acquisi-
tions editors who have kept me in projects over the past several years,
Greg Tubach and Roxane Cerda. Also deserving of mention is
Suzanne Snyder, who with this volume has project edited four of my
books in a row, and has not only put up with my sometimes weird
sense of humor without changing my quips, but has from time to time
thrown in or suggested a wry subheading or two. Then there’s
Christina Stambaugh with whom I have had no direct contact, but who
has been a critical part of this whole operation—in that she was instru-
mental in setting up this book’s production schedule and (along with
Wiley’s designers) in creating an interior design for this book. Finally,
I must acknowledge my wife Karen, who has refrained from nagging
me to “get a real job.”
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
1
Close Enough . . . . . . . . . . . . . . . . . . . . . . . . . . .1
It’s the Big Ones That Count . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Rounding Up or Down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
2
A Number of Realms of Numbers . . . . . . . . . . . .5
The Realm McCoys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Once, Twice, Three Shoot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
When I Was in My Prime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
3
Arithmetic of Whole Numbers . . . . . . . . . . . . . .11
Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
Hey, Hey, Take It Away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Standard Column Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Renaming in Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
A House Divided . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
4
Common Fractions . . . . . . . . . . . . . . . . . . . . . .37
What Is a Fraction? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Equivalent Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
Adding and Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . .41
Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
Reciprocals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Fractions Greater than One . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Adding Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Subtracting Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
Changing Mixed Numbers to Fractions . . . . . . . . . . . . . . . . . . . .53
Multiplying and Dividing Mixed Numbers . . . . . . . . . . . . . . . . . .54
5
Decimal Fractions . . . . . . . . . . . . . . . . . . . . . . .56
Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
Extending Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
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