The Cartoon Guide to Algebra

241 Pages·2018·17.88 MB·English

by  Larry Gonick

THE CARTOON GUIDE TO
SY 1-ARRY GON llK
Al-~
THE CARTOON HISTORY OF THE UNIVERSE, VOl.UMES 1-7
THE CARTOON HISTORY OF THE UNIVERSE, VOl.UMES 9-1'3
THE CARTOON HISTORY OF TH™E U' NIVERSE, VOl.UMES 14-19
nu; CARTOON MISTORY OF M017(;RN WORl.17, PART 1
TM(; CARTOON MISTORY OF TM(; M017(;RN WORl.17, PART 2.
THE CARTOON HISTORY OF THE UNITED STATES
TM(; CARTOOON 6U117(; TO CAI.CUI.US
THE CARTOON GUIDE TO CHEMISTRY (WITH CRAIG CRIDDl.E)
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THE CARTOON GUIDE TO GENETICS (WITH MARK WHEEi.iS)
THE CARTOON GUIDE TO (NON)lOMMUNICATION
THE CARTOON GUIDE TO PHYSICS (WITH ART HUFFMAN)
THE CARTOON GUIDE TO sex (WITH CHRISTINE DEVAUl.T)
THE CARTOON GUIDE TO STATISTICS (WITH WOOl.l.lOTT SMITH)
TM(; ATTACK OF TM(; SMART Pl(;S
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THE CARTOON GUIDE TO
LARRY GONICK
~
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An !mprmt of HarpcrCollinsP11b/1shcn
THE CARTOON GUIDE TO ALGEBRA. Copyright <O 2015 by Lany Gonic:k. All rights reserved under International and
Pan-American Copyright Conventions. By payment of the required fees, you have been granted the nonexclusive,
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FIRST EDITION
ISBN 978-0-06-220269-7
EPub Edition January 2015 ISBN 9780062403223
15 16 17 18 19 OV/RRD 10 9 B 7 6 5 4 3 2 1
CONTENTS
CHAPTER 0 .......................................................................................... 1
WMAT IS Al.b,SRA ASOlJT?
CHAPTER 1 ....................................................................................................... c;
™'
NUMS'R I.IN'
tMAPT'R 2 .....................................................................................................1 ' 3
ADDITION AND SUSTRAtTION
tMAPT'R '3 ................................................................................................... 2'3
MUl.TIPl.ltATION AND DIVISION
tMAPT'R 4 .................................................................................................... 3c;
'XPR,~IONS AND VARIASl.'S
tMAPT'R c; .................................................................................................... c;9
SAl.ANtlNb AtT
tMAPT'R 6 ..................................................................................................... 71
R~l. WOR(l.)D PROSl.~S
tMAPT'R 7 .................................................................................................... 93
MOR' TMAN ON' UNKNOWN
tMAPT'R 9 .................................................................................................... 9c;
DRAWINb '®ATIONS
tMAPT'R 9 ................................................................................................... 11-;
POW'R Pl.AY
tMAPT'R 10. ................................................................................................ 12'3
RATIONAi. 'XPR,SSIONS
tMAPT'R 11 .................................................................................................. 1'3 c;
RAT'S
tMAPT'R 12 ................................................................................................. 1c;c;
ASOlJT AV,RAb'
tMAPT'R 1'3 ..................................................................................................1 69
~UAR'S
tMAPT'R 14 .................................................................................................. 191
~UAR' ROOTS
tMAPT'R 1c; ................................................................................................. 19'3
SOl.VINb QUADRATlt '®ATIONS
tMAPT'R 16 ................................................................................................. 217
WMAT'S N'XT?
SOl.UTIONS TO S~l.m'D PROS!.~$ ..................................................... 224
IND'X ...........................................................................................................2 -~0
v
TMb CMAl.l.bN6"b IN Al.6"b8RA I~ TO KbbP IT FUN WMll.b KbbPIN6" IT RbAl.
THE CHAI.I.ENGE 8b1N6" TMAT RbAl.ITY l~N'T Al.WAY~ FUN. TMb AUTMOR I~
INDb8TbD TO ANDRbW 6-RIM~TAD, DAVID MUMFORD, MbATMbR DAI.I.A~. AND
MARC OWbN ROTM FOR TMblR Mbl.PFUI. COMMbNT~ AND CONVbR~ATION~
IN TMI~ Rb6"ARD. ~PbCIAI. TMANK~ TO MARC FOR ~U6"6-b~TIN6" TMb
"SASYl.ONIAN 6-RAPMIC TRbATMbNT OF COMPl.bTIN6" TMb ~UARb.
The Multiplication Table
2 ? 4 r; 6 7 9 9 10 11 12
2 4 6 9 10 12 14 16 19 20 22 24
? 6 9 12 1? 19 21 24 27 ?O ?? ?6
4 9 12 16 20 24 29 ?2 ?6 40 44 49
r; 10 1? 20 2? ?O ?? 40 4? ?O r;r; 60
6 12 19 24 ?O ?6 42 49 r;4 60 66 72
7 14 21 29 ?? 42 49 ?6 6? 10 77 94
9 16 24 ?2 40 49 ?6 64 72 90 99 96
9 19 27 ?6 4r; ?4 6? 72 91 90 99 109
10 20 ?O 40 r;o 60 10 90 90 100 110 120
11 22 ?? 44 r;r; 66 77 99 99 110 121 1?2
12 24 ?6 49 60 72 94 96 109 120 1?2 144
vi
Chapter 0
What Is Algebra About?
S(;FOR(; AL.6'(;8RA, W(; L.(;ARN MOW
TO t:OM81N(; NUM8(;R$ 8Y ADDINb,
$U8TRAt:TIN6', MUL.TIPL.YINb, AND
DIVIDINb AUORDINb TO fl.I(; RUI.(;$
OF ARITMM(;Tft. TO bO ON IN TM1$
SOOK, YOU MU$T KNOW ARITMM(;Tlt:!
Pl(;t:(; OF
t:AK(; ...
IF ARITMM~ll 1$ ABOUT
l0M81NIN6' NUM8,R$,
TM'N WMAT 1$ Al.6',8RA
ABOUT? TO AN$W'R
TM1$ QU,$TION, 8~1N
WITM $OM' ORDINARY
ARITMM~ll PR08l.,M$ ...
AND R~RIT' TMO$' PR08L.~$ MORIZONTAL.l.Y, AL.ON(;. A l.IN':
<W
~IB ~ ~~ ~~¥~
c{? g
~IB?l ~ lI~ ~ ~1f ~
®® 7l
~ ~~9r~
g
IN TM1$ FORM, AN ARITMM~ll PR08l.'M 1$ AN bQUATION, A $TAT~'NT TMAT ON'
QUANTITY bQUA~S ANOTM,R, 8UT WITM A TWl$T: ON' $ID' OF™' 'QUATION, ™'
ANSWbR, 1$ UNKNOWN, AT l.~$T UNTIL. W' WORK OUT TM' lAL.lUL.ATION.
'QUATION, BOTM
$ID,$ KNOWN
ARITMM~ll PR08L.~:
AN 'QUATION WITM
ON' $ID' UNKNOWN
2
Al.bG8RA AL~ INVOLVG$ GQUATION$, 8UT WITM TM1$ ONG LITTLG DIFFGRGNCG: TMG UNKNOWN
AN$WGR-TMG "WMAT?"-CAN 8G ANYW~UiR,. RATMGR TMAN $1TTING ALONG ON ONG $1DG, TMG
UNKNOWN CAN 8G $TUCK IN TMG MID$T OF TMG GQUATION, OFTGN IN MORG TMAN ONG PLACG.
MGRG 1$ AN ALGG8RA PR08LGM:
TMG PR08LGM IN WORD$:
IF YOU DOU8LG A NUM8GR
AND $U8TRACT ~. TMG
RG$ULT 1$ 11. WMAT 1$
TMG NUM8GR?
YOU'RG
IN ALGG8RA, WG TRGAT
JUGGLING ...
TMAT TMING CALLGD
WMAT?
"WMAT?" M JU$T
ANOTMGR NUM8GR, TO
8G MANDLGD IN TMG
$AMG WAY A$ YOU
WOULD TRGAT 1 OR 2
OR 6. (8UT IN$TGAD OF
"WMAT?," WG'LL U$UALLY
WRITG x OR y OR
~MG OTMGR LITTGR.)
WG'LL $Gb MOW TO MAKG AND U$G MANY COM81NATION$ OF LITTGR$ AND NIJM8GR$,
COM81NATION$ KNOWN A$ AL."SRAll 'XPR,$$10N$. LIKG MIJMAN GXPRG$$10N$, ALGG8RAIC
GXPRG$$10N$ CAN 8G $1MPLG OR GXCGGDINGLY COMPLGX.
A $1MPLG A MORG
GXPRG$$10N COMPLICATGD
GXPRG$$10N