1001 MATH PROBLEMS

240 Pages·2005·0.9 MB·English

1001 MATH
PROBLEMS
2ND EDITION

N E W Y O R K

1001 MATH
PROBLEMS
2ND EDITION

®

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 of Congress 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 of America

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

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

Contents

v

A

re you frightened of mathematics? 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 of an alien spaceship.I decided I’d better do something quick,so I went to a friend of mine,
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 of prob-
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.”

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!

vii

And it did finally! I’m proud to say I no longer
have to pay someone to do my 1040 form for the IRS,
and I don’t squirm and make excuses when, at lunch
with friends, I’m called on to figure the tip in my head.
I even balance my checkbook now!
Learn by doing. It’s an old lesson, tried and true.
And it’s the tool this book is designed to give you.
Of course, this method works for people who
don’t have math anxiety, too. Maybe you have simply
forgotten a lot of what you learned about math because
you haven’t had to use it much. Or maybe you’re a stu-
dent tackling arithmetic, algebra, and geometry for the
first time, and you just need more practice than your
textbook gives you. Perhaps you’re getting ready for an
exam, and you just want to make sure your math skills
are up to the task. Whatever your situation, you can
benefit from the method of this book. That old maxim
really is true: Practice makes perfect.

� An Overview of This Book

1001 Math Problems is divided into sections,each focus-
ing on one kind of math:

Section 1: Miscellaneous Math (page 1)
Section 2: Fractions (page 25)
Section 3: Decimals (page 47)
Section 4: Percentages (page 71)
Section 5: Algebra (page 95)
Section 6: Geometry (page 123)

Each section is subdivided into short sets of about
16 problems each,so as to make the whole project seem
less overwhelming.You will begin with one or two sets
of fairly simple nonword problems; later sets focus on
word problems dealing with real-world situations.

In each section, you will find a few pre-algebra
problems mixed in—problems that ask you to deal with
variables (letters that stand for unknown numbers,such
as x or y), exponents (those little numbers hanging
above the other numbers, like 24), and the like. These
problems are a warm-up for Section 5,Algebra. If they
are too hard for you at first, just skip them. If you can
answer them, you will be ahead of the game when you
get to Section 5.
The most important learning tool in this book is
not the problems, but the answers. At the back of the
book, each answer is fully explained.After you finish a
set, go to the back of the book and see how many ques-
tions you got right. But don’t stop there: look at the
explanations for all the questions,both the ones you got
right and the ones you got wrong.You will be learning
by doing, and learning from your mistakes—the best
way to learn any subject.

� How to Use This Book

Whether you are working alone or helping someone
else brush up on their math, this book can help you
improve math skills.

Working On Your Own
If you are working alone to brush up on the basics, you
may want to use this book in combination with a basic
text or with Practical Math Success in 20 Minutes a Day.
It will be helpful to read a summary of the different
kinds of fractions and how to convert fractions into
another form,before tackling fraction problems.If you
are fairly sure of your basic math skills, however, you
can use this book by itself.
No matter how you decide to use the book, you
will find it most helpful if you do not use a calculator,

–HOW TO USE THIS BOOK–

viii

so as to prevent (or cure) “calculitis”—too much
reliance on a calculator.

Tutoring Others
This book will work very well in combination with
almost any basic math text. You will probably find it
most helpful to give the student a brief lesson in the
particular operation they will be learning—whole
numbers, fractions, decimals, percentages, algebra, or
geometry—and then have him or her spend the
remainder of the class or session actually doing prob-
lems. You will want to impress upon him or her the
importance of learning by doing,and caution not to use
a calculator so as to gain a better understanding of the
operation in question.

� Additional Resources

If you want more than just problems to work out—if
you would like explanations of the kinds of math you

find in this book—you may want to try one of the fol-
lowing books.

■ Practical Math Success in 20 Minutes a Day by
Judith Robinovitz (LearningExpress)

■ Algebra the Easy Way, 3rd ed. by Douglas
Downing (Barron’s)

■ All the Math You’ll Ever Need by Steve Slavin
(Wiley)

■ Essential Math/Basic Math for Everyday Use by
Edward Williams and Robert A. Atkins
(Barron’s)

■ Everyday Math for Dummies by Charles Seiter
(IDG)

■ Math the Easy Way, 3rd ed. by Anthony Prindle
and Katie Prindle (Barron’s)

■ Math Essentials by Steve Slavin
(LearningExpress)

■ Math Smart: Essential Math for These Numeric
Times (Princeton Review)

■ Mathematics Made Simple by Abraham Sper-
ling and Monroe Stuart (Doubleday)

–HOW TO USE THIS BOOK–

ix

T

he following section consists of 10 sets of miscellaneous math,including basic arithmetic ques-
tions and word problems with whole numbers.You will also see problems involving pre-algebra
concepts such as negative numbers, exponents, and square roots (getting you ready for the
algebra in Section 5).This section will provide a warm-up session before you move on to more difficult kinds
of problems.

S E C T I O N

Miscellaneous
Math
1

1

� Set 1 (Answers begin on page 157.)

1. 7 + 3 =
a. 4
b. 8
c. 9
d. 10

2. 9 − 2 =
a. 7
b. 8
c. 6
d. 5

3. 8 ÷ 2 =
a. 6
b. 4
c. 5
d. 7

4. 3 × 3 =
a. 6
b. 7
c. 8
d. 9

5. 54 − 17 =
a. 37
b. 39
c. 41
d. 43

6. 62 + 7 =
a. 64
b. 68
c. 69
d. 70

7. 25 + 16 =
a. 37
b. 41
c. 45
d. 51

8. 23 + 22 =
a. 45
b. 55
c. 61
d. 62

9. 39 − 18 =
a. 7
b. 11
c. 16
d. 21

10. 36,785 − 188 =
a. 35,697
b. 36,497
c. 36,597
d. 37,007

11. 72 + 98 − 17 =
a. 143
b. 153
c. 163
d. 170

12. 376 − 360 + 337 =
a. 663
b. 553
c. 453
d. 353

–MISCELLANEOUS MATH–

2

13. 444 + 332 − 216 =
a. 312
b. 450
c. 560
d. 612

14. 2,710 + 4,370 − 400 =
a. 6,780
b. 6,680
c. 6,580
d. 6,480

15. 7,777 − 3,443 + 1,173 =
a. 5,507
b. 5,407
c. 5,307
d. 5,207

16. | 7 | =
a. –7
b. 0.7
c. 7
d. 17

–MISCELLANEOUS MATH–

3

� Set 2 (Answers begin on page 158.)

17. (25 + 17)(64 − 49) =
a. 57
b. 63
c. 570
d. 630

18. 42 ÷ 6 =
a. 8
b. 7
c. 6
d. 5

19. 292 × 50 =
a. 14,600
b. 14,500
c. 10,500
d. 1,450

20. 500 × 65 =
a. 30,500
b. 32,500
c. 35,000
d. 35,500

21. 2,273 × 4 =
a. 9,092
b. 8,982
c. 8,892
d. 8,882

22. What is the value of 43,254 ÷ 8, rounded to the
nearest whole number?
a. 5,000
b. 5,400
c. 5,406
d. 5,407

23. | –9 | =
a. –9
b. –8
c. 0
d. 9

24. 703 × 365 =
a. 67,595
b. 255,695
c. 256,595
d. 263,595

25. 2,850 ÷ 190 =
a. 15
b. 16
c. 105
d. 150

26. 62,035 ÷ 5 =
a. 1,247
b. 12,470
c. 12,407
d. 13,610

27. Estimate the value of 6,302 ÷ 63.
a. 1
b. 10
c. 100
d. 1,000

28. 4,563 × 45 =
a. 205,335
b. 206,665
c. 207,305
d. 206,335

–MISCELLANEOUS MATH–

4

29. 12(84 – 5) – (3 ÷ 54) =
a. 786
b. 796
c. 841
d. 54,000

30. (2 + 4) × 8 =
a. 84
b. 64
c. 48
d. 32

31. (14 × 7) + 12 =
a. 98
b. 266
c. 110
d. 100

32. (667 × 2) + 133 =
a. 1,467
b. 1,307
c. 1,267
d. 1,117

–MISCELLANEOUS MATH–

5