Quick Arithmetic: A Self-Teaching Guide

By Robert A. Carman and Marilyn J. Carman

Master math at your own pace!

Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school?

Quick Arithmetic, Third Edition is the quickest and easiest way to teach yourself the basic math skills you need to advance on the job or in school. Using cartoons and a clear writing style, this practical guide provides a fresh start for learning or reviewing how to work with whole numbers, fractions, decimals, and percentages. The book's proven self-teaching approach allows you to work at your own pace and learn only the material you need. Previews and objectives at the beginning of each section help you determine your particular needs, while self-tests, practice problems, and a final exam let you measure your progress and reinforce what you've learned.

For anyone who has ever felt intimidated by a page of numbers, Quick Arithmetic, Third Edition has the answers!

• Language: English
• Publisher: Turner Publishing Company
• Release date: Mar 14, 2002
• ISBN: 9780471151340

Book preview

Quick Arithmetic

A Self-Teaching Guide

Wiley Self-Teaching Guides teach practical skills from accounting to astronomy, management to mathematics. Look for them at your local bookstore.

Other Wiley Self-Teaching Guides:

Science

Astronomy, Fifth Edition, by Dinah L. Moche

Basic Physics, Second Edition, by Karl F. Kuhn

Biology, by Steven D. Garber

Chemistry: Concepts and Problems, Second Edition, by Clifford C. Houk and Richard Post

Geology, by Barbara Murck

Math

All the Math You’ll Ever Need, Revised Edition, by Steve Slavin

Geometry and Trigonometry for Calculus, by Peter H. Selby

Practical Algebra, Second Edition, by Peter H. Selby and Steve Slavin

Quick Algebra Review, Second Edition, by Peter H. Selby and Steve Slavin

Quick Business Math, by Steve Slavin

Quick Calculus, Second Edition, by Daniel Kleppner and Norman Ramsey

Statistics, Fourth Edition, by Donald Koosis

Quick Arithmetic

A Self-Teaching Guide

Third Edition

Robert A. Carman

Santa Barbara Community College

Santa Barbara, California

Marilyn J. Carman

Santa Barbara City Schools

Santa Barbara, California

John Wiley & Sons, Inc.

New York • Chichester • Weinheim • Brisbane • Singapore • Toronto

Disclaimer:

Some images in the original version of this book are not available for inclusion in the eBook.

Copyright © 1984 by John Wiley & Sons, Inc. All rights reserved

Copyright © 2001 by Robert A. Carman and Marilyn J. Carman

Published by John Wiley & Sons, Inc.

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, [phone], Fax [phone]. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, [phone], fax [phone], email: [e-mail].

This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought.

This title is also available in print as ISBN 0-471-38494-1.

For Ed Graper

Of making books

there is no end. . . .

This one’s for you,

our guide, philosopher,

and friend.

Contents

Preface

How to Use This Book

1Whole Numbers

Preview 1

Reading and Writing Numbers

Adding Whole Numbers

Subtracting Whole Numbers

Multiplying Whole Numbers

Dividing Whole Numbers

Factors and Factoring

Exponents and Square Roots

Chapter 1 Self-Test

2Fractions

Preview 2

Renaming Fractions

Multiplying Fractions

Dividing Fractions

Adding and Subtracting Fractions

Solving Word Problems

Chapter 2 Self-Test

3Decimals

Preview 3

Decimal Numbers

Adding and Subtracting Decimal Numbers

Multiplying and Dividing Decimal Numbers

Decimal Fractions

Chapter 3 Self-Test

4Percent

Preview 4

Numbers and Percent

Percent Problems

Applications of Percent

Chapter 4 Self-Test

Final Exam

Appendix

Answers: Boxes and Problem Sets

Answers: Chapter Self-Tests

Answers: Final Exam

Index

Preface

Many very bright and competent people enrolled in colleges, universities, and community colleges are frustrated. They are eager, ambitious, and quite capable of succeeding in their careers or moving to a better job. They want to learn but find themselves handicapped because they do not have the basic mathematics skills needed to continue. They need help with these essential skills. If that describes where you are, this book is for you.

This book is designed to help you review or relearn basic arithmetic skills. It is more like a private tutor than a lecturer; you participate in the process rather than simply reading, listening, or sleeping through it.

The book is organized in a format that respects your unique needs and interests and teaches you accordingly:

•You can use it for self-study, for study with a tutor or helper, or as a text in a formal course.

•Each chapter begins with a preview and a sample test to help you see your particular needs.

•You have the option of designing your own course, skipping familiar material to save time or working through all of it if you need it.

•Many practice problems and self-tests are included, including drill problems, practical applications, more difficult brain boosters, and problems where a calculator should be used. Each chapter ends with an optional self-test.

•Answers to all problems are in the back of the book.

•Unlike previous mathematics textbooks you may have used, this book is careful to explain every operation. Sometimes we even explain our explanations.

This book has been used by hundreds of thousands of students and they tell us it is helpful, interesting, and even fun to work through. We hope you agree with them.

It is a pleasure for us to acknowledge our debts to the many people who have contributed to the development of this book and to this third edition. Jeffrey Golick and the staff at John Wiley & Sons, Inc., have been most supportive and patient throughout the lengthy process of producing a book. We were fortunate to have W. Royce Adams, formerly the director of the Reading Center at Santa Barbara Community College, read preliminary versions of the book and provide valuable assistance in improving its readability.

Finally, we wish to extend special thanks to our kindest critics and most enthusiastic helpers: our children—Pat, Laurie, Maire, and Eric—our other works in collaboration.

—RAC

—MJC

How to Use This Book

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Many people go through life afraid of mathematics and upset by numbers. They bumble along miscounting their change, bouncing checks, and eventually trying to avoid college courses or jobs that require even simple math. Most such people need to return and make a fresh start. Few get the chance. This book presents fresh-start math. It is designed so that you can:

•Start at the beginning or wherever you need to start

•Work on only what you need to know

•Move as fast or as slowly as you wish

•Skip material you already understand

•Do as many practice problems as you need

•Take self-tests to measure your progress

In other words, if you find mathematics difficult and want a fresh start, this book is designed for you.

This is no ordinary book. You cannot easily browse in it. You don’t read it; you work your way through it. Ideas are arranged step-by-step in short portions or frames. Each frame contains information, careful explanations, examples, and questions to test your understanding. Frames are numbered on the left.

 7 Read the material in each frame carefully, follow the examples, and answer the questions that lead to the next frame. Correct answers move you quickly through the book. Incorrect answers lead you to frames providing further information. You move through the book frame by frame, sometimes forward, sometimes backward.

Each major section of the book starts with a preview that will help you determine those parts on which you need to work.

Notice the following symbols designed to help you:

Important terms are noted in the margin where they are first used or defined.

Students are led step-by-step through examples and explanations:

•Step 1 Many worked examples are given . . .

•Step 2 ... with explanations for each step . . .

•Step 3 ... and immediate feedback in the text and in and

Most students hesitate to ask questions. They would rather risk failure than look foolish by asking dumb questions. To relieve this worry, we ask and answer these FAQs (frequently asked questions) in the cartoons. Learning the FAQs produces smart students.

---

Special Topics

As you move through the book, special topics appear within lines like this. Check them out.

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In 1846, the Reverend H. W. Adams described what happened when the 10-year-old math whiz Truman Safford was asked to multiply, in his head, the number 365,365,365,365,365,365 by itself. He flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking, and then, seeming to be in agony, in not more than one minute, he said 133,491,850,208,566,925,016,658,299,941,583,225.* In this book we will show you a way to do arithmetic that is not so strenuous, quite a bit slower, and not nearly so much fun to watch.

Now, turn to page 1 and let’s begin.

*James R. Newman, The World of Mathematics (New York: Simon and Schuster, 1956), p. 466.

    1 Whole Numbers

PREVIEW 1

If you are certain you can work all of these problems correctly, turn to page 81 for a self-test. If you want help with any of these objectives or if you cannot work one of the preview problems, turn to the page indicated. Super-students (those who want to be certain they learn all of this), turn to frame 1 and begin work there.

ANSWERS TO

PREVIEW 1 PROBLEMS

1. (a) 21, 163

(b) 26,879

(c) 1,804,776

(d) 1,350,048

(e) 63 with remainder 51

(f) 81 with remainder 6

(g) 67

(h) 0

(i) 16

2. (a) 2² ⋅ 3³ ⋅ 5 ⋅ 7

(b) 2³ ⋅ 3 ⋅ 7 ⋅ 11

3. (a) 8

(b) 1764

4. (a) 13

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1 Reading and Writing Numbers

 1 Once upon a time, most people used numbers to tell time, count things, and keep track of their lunch money. But we are living in an age of calculators and computers, and math skills are important in everything we do. Using a calculator requires a good understanding of basic math skills and concepts. For most educated adults, working with numbers is as important a part of their job as being able to read and write.

In this chapter we will take a how-to-do-it look at the basic operations of mathematics: addition, subtraction, multiplication, and division.

What is a number? It is a way of thinking, an idea, that enables us to compare very different sets of objects. It is the idea behind the act of counting. The number three is the idea that describes any collection of three objects: 3 people, 3 trees, 3 colors, 3 dreams. We recognize that these collections all have the quality of threeness even though they may differ in every other way.

Is 10 a digit? Think about it. Then turn to 3 to continue.

 2 Hi. What are you doing here? Lost? Window shopping? Just passing through? Nowhere in this book are you directed to frame 2 (Notice that little 2 to the left above? That’s a frame number.) Remember, in this book you move from frame to frame as directed, but not necessarily in 1-2-3 order. Follow directions and you’ll never get lost.

Now return to 1 and keep working.

 3 No, 10 is not a digit. It is a numeral formed from the two digits 1 and 0.

Remember:

•A number is an idea related to counting.

•A numeral is a symbol used to represent a number.

•A digit is one of the ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) we use to form numerals.

How many letters are in this set?

Count them. Write your answer, and then turn to frame 4.

 4 We counted 23, and of course we write it in the ordinary, everyday manner. Leave the Roman, Chinese, and other numeral systems to Romans, Chinese, and people who enjoy the history of mathematics.

The basis of our system of numeration is grouping into sets of ten or multiples of ten.

46 = 40 + 6