Table Of ContentM E
ATH SSENTIALS
C F , D
ONQUER RACTIONS ECIMALS
P —
AND ERCENTAGES
G R A E T !
ET THE IGHT NSWER VERY IME
S E
ECOND DITION
S S
TEVEN LAVIN
NEW YORK
Copyright ©2000 Learning Express,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
Slavin,Steven.
Math essentials / Steven Slavin.
CIPDATATK
CIP
Printed in the United States ofAmerica
9 8 7 6 5 4 3 2 1
Second Edition
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C
ONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Section I Reviewing the Basics. . . . . . . . . . . . . . . . . . . . 1
Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Review Lesson 1 Addition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Review Lesson 2 Subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Review Lesson 3 Multiplication. . . . . . . . . . . . . . . . . . . . . . . . . 21
Review Lesson 4 Division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Section II Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Lesson 1 Fraction Conversions . . . . . . . . . . . . . . . . . . . 39
Lesson 2 Adding Fractions . . . . . . . . . . . . . . . . . . . . . . 43
Lesson 3 Subtracting Fractions . . . . . . . . . . . . . . . . . . . 49
Lesson 4 Multiplying Fractions . . . . . . . . . . . . . . . . . . . 55
Lesson 5 Dividing Fractions. . . . . . . . . . . . . . . . . . . . . . 61
Lesson 6 Working with Improper Fractions . . . . . . . . . 67
Lesson 7 Working with Mixed Numbers. . . . . . . . . . . . 75
Lesson 8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Section III Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Lesson 9 Adding and Subtracting Decimals . . . . . . . . . 89
Lesson 10 Multiplying Decimals . . . . . . . . . . . . . . . . . . . 95
Lesson 11 Dividing Decimals. . . . . . . . . . . . . . . . . . . . . 101
Lesson 12 Decimals and Fractions as Tenths,
Hundredths, and Thousandths. . . . . . . . . . . 107
Lesson 13 Converting Fractions into Decimals and
Decimals into Fractions. . . . . . . . . . . . . . . . . 117
Lesson 14 Fast Multiplication and Fast Division . . . . . . 123
Lesson 15 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 135
Section IV Percentages . . . . . . . . . . . . . . . . . . . . . . . . . 145
Lesson 16 Converting Decimals into Percents and
Percents into Decimals . . . . . . . . . . . . . . . . . 147
Lesson 17 Converting Fractions into Percents and
Percents into Fractions. . . . . . . . . . . . . . . . . 153
Lesson 18 Finding Percentage Changes . . . . . . . . . . . . 163
Lesson 19 Percentage Distribution . . . . . . . . . . . . . . . . 171
Lesson 20 Finding Percentages of Numbers. . . . . . . . . 179
Lesson 21 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 183
Final Exam . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Additional Resources . . . . . . . . . . . . . . . . . . 211
I
NTRODUCTION
I
f you’re like most other people, you use a
pocket calculator to do your basic arithmetic. The calculator is fast
and accurate as long,of course,as you punch in the right numbers.
So what could be bad about a tool that saves you so much work and gives
you the right answers?
Let me be brutally frank.You know why you bought this book, and
it’s not for the story. By working your way through this book, problem
by problem, you will be amazed by how much your math skills will
improve.But—and this is a really big BUT—I don’t want you to use your
calculator at all.So put it away for the time you spend working through
this book.And who knows—you may never want to use it again.
Your brain has its own built-in calculator, and it, too, can work
quickly and accurately.But you know the saying,“Use it or lose it.”
vii
MATH ESSENTIALS
The book is divided into four sections—a review of basic arithmetic,
and then sections on fractions,decimals,and percentages.Each section is
subdivided into four to eight lessons, which focus on building specific
skills, such as converting fractions into decimals, or finding percentage
changes.You’ll then get to use these skills by solving word problems in the
applications section. There are 21 lessons plus four review lessons, so if
you spend 20 minutes a day working out the problems in each lesson,you
can complete the entire book in about a month.
One thing that distinguishes this book from most other math books is
that virtually every problem is followed by its full solution.I don’t believe
in skipping steps. You, of course, are free to skip as many steps as you
wish,as long as you keep getting the right answers.Indeed,there may well
be more than one way of doing a problem, but there’s only one right
answer.
When you’ve completed this book,you will have picked up some very
useful skills.You can use these skills to figure out the effect of mortgage
rate changes and understand the fluctuations in stock market prices or
how much you’ll save on items on sale at the supermarket. And you’ll
even be able to figure out just how much money you’ll save on a low-
interest auto loan.
Once you’ve mastered fractions, decimals, and percentages, you’ll be
prepared to tackle more advanced math,such as algebra,business math,
and even statistics.At the end of the book, you’ll find my list of recom-
mended books to further the knowledge you gain from this book (see
Additional Resources).
If you’re just brushing up on fractions,decimals,and percentages,you
probably will finish this book in less than 30 days.But if you’re learning
the material for the first time,then please take your time.And whenever
necessary,repeat a lesson,or even an entire section.Just as Rome wasn’t
built in a day, you can’t learn a good year’s worth of math in just a few
weeks.
While I’m doing clichés, I’d like to note that just as a building will
crumble if it doesn’t have a strong foundation, you can’t learn more
advanced mathematical concepts without mastering the basics. And it
doesn’t get any more basic than the concepts covered in this book.So put
away that calculator,and let’s get started.
viii
SECTION I
R
EVIEWING THE
B
ASICS
O
n every page of this book you’re going
to be playing with numbers,so I want you to get used to them
and be able to manipulate them. In this section you’ll review
the basic operations of arithmetic—addition, subtraction, multiplica-
tion,and division.
Your skills may have grown somewhat rusty.Or,as the saying goes,if
you don’t use it,you’ll lose it.This section will quickly get you back up
to speed. Of course different people work at different speeds, so when
you’re sure you have mastered a particular concept, feel free to skip the
rest ofthat lesson and go directly to the next.On the other hand,ifyou’re
just not getting it, then you’ll need to keep working out problems until
you do.
1
REVIEWING THE BASICS
Indeed,the basic way most students learn math is through repetition.
It would be great if you could get everything right the first time. Of
course if you could,then this book and every other math book would be
a lot shorter. Once you get the basics down, there’s no telling how far
you’ll go.So what are we waiting for? Let’s begin.
2
P
RETEST
T
he first thing you’re going to do is take a
short pretest to give you an idea of what you know and what you
don’t know. This pretest covers only addition, subtraction,
multiplication, and division; all of which are necessary for learning the
other concepts we will be studying later on in this book.Remember,you
must not use a calculator.The solutions—completely worked out so you
can see exactly how to do the problems—follow immediately after the
pretest for you to check your work.
3
REVIEWING THE BASICS
Add each of these columns of numbers.
1. 29 3. 1,025
34 872
16 2,097
44 1,981
37 655
23 2,870
56 + 3,478
+ 21
4. 19,063
2. 402 12,907
199 10,184
276 7,602
850 14,860
727 23,968
233 17,187
+ 196 + 10,493
Do each of these subtraction problems.
5. 74 7. 2,436
– 29 – 1,447
6. 335 8. 94,032
– 286 – 76,196
Do each of these multiplication problems.
9. 49 11. 2,849
× 96 × 7,491
10. 309 12. 56,382
× 783 × 96,980
4
