Basic College Mathematics: An Applied Approach

724 Pages·2013·59.36 MB·English

by  Richard N. Aufmann

SECTION 5.1    IntroductIon to Percents 205
Take AIM and Succeed!
ExamplE 2 yOu Try IT 2
Write 162% as a fraction. Write 331% as a fraction.
3 3
2 2 1
Solution 16 %516 3 Your solution AIM
3 3 10A0 ufmann Interactive Method
50 1 50 1
5 3 5 5
3 100 300 6
Solution on p. S12
The Aufmann Interactive Method (AIM) is a proven learning system that
S12 CHAPTER 5   
has help  eOdBJ EtChToIVEu Bs anTdo wsr itoe af descitmuadl ore an frtasct iomn asa as petrecern tconcepts and achieve results.
A decimal or a fraction can be written as a percent by multiplying by 100%.
5 n 24 jars n jars
You Try It 4 5 •  Find the cross  Solution 5
7 20 products.  How to 1 Write6 0 .b37o xase as percen1t.5 boxes
5320573n To fTohlelno wsol vteh  e aim, s tep0 .t3h7 r o5u g h0.3 7th3 2e14 0H03% O1 55W5 63T7%3On
"
100573n exafmorp nl.es that are prov ided and then wo 3rk60 th5ro6u3ghn
Move the decimal point
100475n the matched EXAMP LE /" YtwoO plaUces tTo thR 3e6 rY0igh 4t.I TTh6e n5p anirs.
14.3<n write the percent sign. 605n
15 12 60 jars can be packed in 15 boxes.
You Try It 5 5 •  Find the cross  When changing a fraction to a percent, if the fraction can be written as a terminating
20 n products. Then  decimal, the percent is written in decimal form. If the decimal representationA of tuhe fframc- ann
153n520312 solve for n. tion is a repeating decimal, the answer is written with a fraction.
153n5240 take Note Solutions to Chapter 5: “You Try It”
n5240415 tTehrme dineacteims.al form of 38 How to 2 Write 38 as a percent.
n516 0.375 SEC3TIO3N 510.01% 3
8q 3.000 5 3 • 50.375 is a terminating decimal.
Check: 15 12 2 0 3 12 5 24202 4 You 8Try8 It 11 a. 125%58 12530.0151.25
60
20 16 15 3 16 5 240256 5300% 1
40 8 125%51253
240 100
0 537.5% • The answer is written in decimal form.
125 5 1
12 7 5 5 51
You Try It 6 5 100 4 4
123 4n84554nn3377 2r tTehpa0eek 6daeetsc .NIim0noa.1lt 6feo6tCrmHe oAf 16rP aTEc R t5  iH 16v o5wPe e16tro3c 31e0n10%tsWrbite. 16 8 8as.. 55a %%per•c 55 e16n5t.880...1556 33is a0 1r.e0p1eat5ing 0.085
48475n 6q12.0600 100% decimal. 100
6.86<n ExAm234P60lE 3 5 6 581 3 1you•  T8R.y5 5iT 385 581
40 2 2 100 10 2
You Try It 7 1n2 5 41 Write 203.64015 and 2 .3 as p e5rc1e6n3t%s. • 5 Twhiteh 1 aan7 fsrwa3ecrti iosn w.1riWtterni te 0.048 and 3.6 as percents.
2 100
n3151234 Solution Your solution
17
n31548 Unles0s o.th0er1wis5e no5ted, all0 co.n0ten1t on5 this3 pag e 1is ©0 C0en%gage Learning. 5 • Multiply the fractions.
51.5% 200
n54841
c. 0.25%50.2530.0150.0025
n548 2.352.33100% 1
Check: 48 4 1 2 3 4 5 4 8 5230% 0.25%50.253
65440_ch05_203-232.indd 205 100 8/8/12 7:37 AM
12 1 48 3 1 5 48 1 1 25 1
5 3 • 0.255 5
4 100 100 4
You Try It 8
1
5 • Multiply the fractions.
Strategy T o find the number of tablespFooorn se oxf fterrati lsizuepr port, you can find the complete s4o0l0utions to
needed, write and solve a prtohpeo rYtioOn uUsin gT RY IT problems in the ba1ck of th1e tex1t.
You Try It 2 33 %533 3
n to represent the number of tablespoons of 3 3 100
fertilizer. ExAmPlE 4 Me10t0hod1 you TRy iT 4
5 3
Solution Write 19 as a percent. 3 100Write 5 as a percent.
80 16
100 1
3 tablespoons n tablespoons 5 5
5 •  The unit “tableSsoplouotniso”n  300 3 Your solution
4 gallons 10 gallons is in the numer1a9tor. 100% 1Y9o00u% Try It 3 0.04850.0483100%54.8%
3 5
3310543n The unit “gallo8n0s” is in1  80 3.653.63100%5360%
the denominator. 523.75% •  Write the answer in 
30543n
decimal form5. 100%
You Try It 4 3
30445n 16 1
7.55n 500%
5 531.25% • Write in decimal form.
F or 10 gallons of water, 7.5 tablespoons of 16
fertilizer are required. 5 5 100% 500% 1
You Try It 5 5 3 5 583 %
6 6 1 6 3
You Try It 9
Strategy T o find the number of jars that caCnop byreigh pt 2a0c12k CeendgEa gxe LAeamrninPg.l AEll R 5ights ResServEed. CMaTy nIoOt be Ncop ie5d,. s2canned, or duplicated, in whole or in part. Due toy eolecutro nTic Rrigyht s,i Tso m5e third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
in 15 boxes, write and solve a proportion
Write 2 as a perceYnot.u Try It 1 Percent3base5amWoriuten 5t as a percent.
using n to represent the number of jars. 3 6
0.06331505n
Solution Your solution
65440_ifc.indd 2 9.455n 8/22/12 10:01 AM
2 2 100%
5 3
3 3 1
200%
5
3
2
566 % •  Write the answer with a fraction.
3
65440_em_sol_S01-S32.indd 12 8/16/12 9:27 AM
Solutions on p. S12
65440_ch05_203-232.indd 206 8/16/12 9:25 AM
Ask the Authors!
We have taught math for many years. During that time, we have
had students ask us a number of questions about mathematics
and this course. Here you find some of the questions we have
been asked most often, starting with the big one.
Dick Aufmann Joanne Lockwood

Why do I have to take this course? You may have heard that “Math is everywhere.” That
is probably a slight exaggeration, but math does find its way into many disciplines. There are obvious places
like engineering, science, and medicine. There are other disciplines such as business, social science, and
political science where math may be less obvious but still essential. If you are going to be an artist, writer,
or musician, the direct connection to math may be even less obvious. Even so, as art historians who have
studied the Mona Lisa have shown, there is a connection to math. But, suppose you find these reasons not
all that compelling. There is still a reason to learn basic math skills: You will be a better consumer and
be able to make better financial choices for you and your family. For instance, is it better to buy a car or
lease a car? Math can provide an answer.
I find math difficult. Why is that? It is true that some people, even very smart people,
find math difficult. Some of this can be traced to previous math experiences. If your basic skills are lacking,
it is more difficult to understand the math in a new math course. Some of the difficulty can be attributed to
the ideas and concepts in math. They can be quite challenging to learn. Nonetheless, most of us can learn
and understand the ideas in the math courses that are required for graduation. If you want math to be less
difficult, practice. When you have finished practicing, practice some more. Ask an athlete, actor, singer,
dancer, artist, doctor, skateboarder, or (name a profession) what it takes to become successful and the one
common characteristic they all share is that they practiced—a lot.
Why is math important? As we mentioned earlier, math is found in many fields of study. There
are, however, other reasons to take a math course. Primary among these reasons is to become a better
problem solver. Math can help you learn critical thinking skills. It can help you develop a logical plan to solve
a problem. Math can help you see relationships between ideas and to identify patterns. When employers are
asked what they look for in a new employee, being a problem solver is one of the highest ranked criteria.

What do I need to do to pass this course? The most important thing you must do is to
know and understand the requirements outlined by your instructor. These requirements are usually given to
you in a syllabus. Once you know what is required, you can chart a course of action. Set time aside to study
and do homework. If possible, choose your classes so that you have a free hour after your math class. Use
this time to review your lecture notes, rework examples given by the instructor, and begin your homework.
All of us eventually need help, so know where you can get assistance with this class. This means know-
ing your instructor’s office hours, the hours of the math help center, and how to access available online
resources. And finally, do not get behind. Try to do some math EVERY day, even if it is for only 20 minutes.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Basic College
edition
10
Mathematics
An Applied ApproAch
richard n. Aufmann
Palomar College
Joanne S. lockwood
Nashua Community College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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Basic College Mathematics: © 2014, 2009 Brooks/Cole, Cengage Learning
An Applied Approach,
ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
Tenth Edition
may be reproduced, transmitted, stored, or used in any form or by any means,
Richard N. Aufmann, Joanne S. Lockwood
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 v
Contents
chApter
A
AIM for Success AIM-1
This important chapter outlines some study skills that are used by students who
have been successful in this course. Topics include how to stay motivated, making
a commitment to succeed, how to manage your time, and preparing for and
taking tests. There is a complete guide to the textbook and how to use its features
to become a successful student.
chApter
1
Whole Numbers 1
prep teSt 1
Section 1.1 A To identify the order relation between two numbers 2
B To write whole numbers in words and in standard form 3
c To write whole numbers in expanded form 3
d To round a whole number to a given place value 4
Section 1.2 A To add whole numbers 8
B To solve application problems 11
Section 1.3 A To subtract whole numbers without borrowing 16
B To subtract whole numbers with borrowing 17
c To solve application problems 19
checK YoUr proGreSS 24
Section 1.4 A To multiply a number by a single digit 25
B To multiply larger whole numbers 27
c To solve application problems 28
Section 1.5 A To divide by a single digit with no remainder in the quotient 33
B To divide by a single digit with a remainder in the quotient 36
c To divide by larger whole numbers 37
d To solve application problems 39
Section 1.6 A To simplify expressions that contain exponents 47
B To use the Order of Operations Agreement to simplify
expressions 48
Section 1.7 A To factor numbers 53
B To find the prime factorization of a number 5 4
chApter 1 SUMMArY 57
concept 1 reVieW eXerciSeS 61
chApter 1 teSt 63 v
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
65440_fm_i-xxviii.indd 5 8/29/12 7:24 AM
vi contents
chApter
2
Fractions 65
prep teSt 6 5
Section 2.1 A To find the least common multiple (LCM) 66
B To find the greatest common factor (GCF) 6 7
Section 2.2 A To write a fraction that represents part of a whole 70
B To write an improper fraction as a mixed number or a whole number,
and a mixed number as an improper fraction 71
Section 2.3 A To find equivalent fractions by raising to higher terms 74
B To write a fraction in simplest form 75
Section 2.4 A To add fractions with the same denominator 78
B To add fractions with different denominators 78
c To add whole numbers, mixed numbers, and fractions 79
d To solve application problems 81
Section 2.5 A To subtract fractions with the same denominator 87
B To subtract fractions with different denominators 8 7
c To subtract whole numbers, mixed numbers, and fractions 88
d To solve application problems 90
checK YoUr proGreSS 96
Section 2.6 A To multiply fractions 97
B To multiply whole numbers, mixed numbers, and fractions 98
c To solve application problems 99
Section 2.7 A To divide fractions 105
B To divide whole numbers, mixed numbers, and fractions 106
c To solve application problems 107
Section 2.8 A To identify the order relation between two fractions 114
B To use the Order of Operations Agreement to simplify
expressions 115
chApter 2 SUMMArY 120
chApter 2 reVieW eXerciSeS 123
chApter 2 teSt 125
cUMUlAtiVe reVieW eXerciSeS 127
chApter
3
Decimals 129
prep teSt 129
Section 3.1 A To write decimals in standard form and in words 130
B To round a decimal to a given place value 132
c To compare decimals 133
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
65440_fm_i-xxviii.indd 6 8/29/12 7:24 AM