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ARITHMETIC
AND ALGEBRA
. . .AGAIN
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ARITHMETIC
AND ALGEBRA
. . .AGAIN
Second Edition
Brita Immergut
Jean Burr Smith
McGraw-Hill, Inc.
New York Chicago San Francisco Lisbon London
Madrid Mexico City Milan New Delhi San Juan
Seoul Singapore Sydney Toronto
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DOI: 10.1036/007146946X
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PREFACE TO
THE SECOND EDITION
It is now ten years since the publication of Arithmetic and Algebra ...Again. My
coauthor Jean Burr Smith passed away four years ago and so the task of preparing
the second edition of this book has fallen on me. Jean was a wonderful person to
work with. I miss her greatly and I am dedicating the new book to her.
In the new edition, I have included at the beginning a section entitled “Tips for
Parents and Tutors,” because, in addition to its use as a college text in classes, this
book will also be used in the home by students who need help with their math home-
work or those who need tutoring to improve their understanding and knowledge of
arithmetic and algebra and to help prepare them for tests.
In general, examples and problems in the new edition have been updated to
reflect current conditions, such as prices, interest rates, and other items that have
undergone change. The use of calculators has become widespread and, therefore, I
have included calculations with calculators in several chapters. There is also a new
chapter devoted to calculators at the end of the book to show what calculators can
do and what they cannot do.
Part Three: Practical Mathematics has been reorganized and expanded. Chap-
ter 10 on applications contains much new material and there are two new chapters:
13 and 14. Chapter 13 is about probability and odds and also contains a section on
sets. Chapter 14 introduces different types of calculators and shows how to use
them to solve different kinds of problems.
It is my hope that this new edition will satisfy the need of many students, young
and old, to feel more comfortable in their mathematics classes or at their jobs when
called upon to solve problems that require a basic knowledge of arithmetic and
algebra.
Brita Immergut
April 30, 2004
v
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TO THE INSTRUCTOR
This arithmetic and beginning algebra text is written for students and anybody
else whose experience with mathematics has been one of frustration but whose
need for it in the working or the academic world has been constantly increasing.
It is designed to help these nontraditional students gain confidence in their abil-
ity to cope with mathematics and to learn or relearn the basics of arithmetic and
algebra necessary for success in their jobs or in other areas of study. Students who
master this material will be ready to take a more rigorous algebra course or a
college-level math course.
Although the book’s primary audience is the student in a one-semester com-
munity or four-year college developmental course that covers the fundamental
operations of arithmetic and elementary algebra, it can also be used for in-house
courses and for teacher training. Part of the book is also suitable as a review
course for high school students.
The order in which the topics are presented is life-experience oriented. Thus,
integers, decimals, and percents are presented before fractions. This is a more ap-
propriate order of presentation than one designed for elementary school students
since adults can draw on their shopping, banking, and other real-world experi-
ences. In working with nontraditional students, we have found that starting with
material that is new to them, such as integers, is more successful than starting with
material that has been troublesome, such as fractions.
The book covers operations with whole numbers, integers, decimals, fractions,
percents, and the application of these skills in problem solving. Basic operations
in algebra, solutions of first-degree equations, and graphing are included. The last
chapters deal with banking problems, statistics, probability, and calculators.
In general, the problems are geared to the adult’s interests and day-to-day
concerns. We have also included some problems from nineteenth century math
books. Our students find them amusing and far removed from the grade-school
variety they may associate with their earlier difficulties.
Since most adults use calculators at work, we encourage them to use calcula-
tors for problem solving but expect them to approximate their answers first. By
showing students several ways of getting the answer (paper and pencil, calcula-
tor, and estimation), we feel that they will become more comfortable with math
and that their math anxiety will gradually disappear.
Definitions and rules are highlighted throughout the text. At the end of each
chapter is a Summary with Vocabulary and Review Problems, a Check List to
help students determine whether they have mastered all topics in the chapter, and
a Readiness Check to indicate their readiness to go on to new material. Answers
to all the exercises and the Readiness Checks will be found at the end of the book.
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