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  • Lecture 01: Beginning Algebra (Math 70)

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    Watch at: 00:00 / 00:00:20[Music]Watch at: 00:20 / 00:40okay a formal good morning to you thisis math 70 elementary algebra spring2003 and this is part of a simulcastWatch at: 00:40 / 01:00broadcast and Debbie is doing the camerawork and that was Santana and what didwe end up with at the end okay we did goa smooth and then we'll close with musicat the end a slide will go back similarto what we started on and that's whenyou're able to get up and move aroundWatch at: 01:00 / 01:20until that time then you're pretty muchasked to stay reasonably quiet and keepin mind there are microphones that arelive comments motion etc does getbroadcast across the world the simulcastis what people can watch with a DSLWatch at: 01:20 / 01:40cable modem and let me explain a littlebit of what has happened now again thisis a math 70 and it's an in-classversion of our elementary algebra courseand I'm dr. curl the intent of thisoriginally was to do a channel 27 sortof slash simulcast Channel 27 is noWatch at: 01:40 / 02:00longer part of our what we might thinkof as a service to the community youplease make sure the door is closed andhave a seatI'll talk with you at the end of thehour now the simulcast is still goingWatch at: 02:00 / 02:20and what we tried to do is to provideopportunities for people who were in thedirect broadcast to be registered forthis class but watch it on simulcastwhich means it would be watched in FH124 the library lab or Sierra Hall 221Watch at: 02:20 / 02:40and that would give you an opportunityto take the course see the same lecturebecause we clearly have a limitation onnumber of students that we can allow inthis room what you are experiencingright now will not be experiencedtomorrowwe will not have this many people in theWatch at: 02:40 / 03:00roomnow in order to use the simulcast in themost efficient way what we have donestarting in about two more hours isthere's a section that's going to beopened and that section are youregistered for the course if you are onWatch at: 03:00 / 03:20the waiting list you sort of gave upthat right by not being here when westarted at ten o'clock today say sorrythe effort at noon today is to open aclass and we're going to try to meetWatch at: 03:20 / 03:40people on the waitlist from 17 sectionsof math 70 they're gonna be 85 people inthis class but you will be watching thelectures off of encoded video in one ofthe computer labs the same lectures I'mdoing what I'm doing today will be partWatch at: 03:40 / 04:00of what you would watch and one of thelabs and so that is an alternative tothe course so I will let a certainnumber of students in here this morningnot very many because I have a verylimited number of students I can takebecause of seating then the first fiveon the waitlist after that I willWatch at: 04:00 / 04:20register if you have an interest indoing it into the new section and youwill watch the same presentations I'mdoing in here there's a possibility Imay be able to go up to ten people onthe waitlist but that is it and thedecision as far as who's going to beallowed in here is made today so as farWatch at: 04:20 / 04:40as the future its today the decision ismade as to whether you're in here orgetting on the waitlist to go into thenew course that will open up today nowthe schedule will be the same for bothin here in that course and that is weWatch at: 04:40 / 05:00will have three midterms those dates arealready set and I will share that withyou momentarilyit is listed on the internet I'll sharethat with you and the testing will bedone on a Friday or a Saturday for thepeople who are going to be participatingin this news section we open todaybecause it's open to 17 differentWatch at: 05:00 / 05:20sections we're trying to take the topfive people in the waitlist from each tobe equitable so that's how I will handlethe waitlist situation so to that extentthe following people would with nodifficulty have the course ceciliaWatch at: 05:20 / 05:40batista Yvette Batista Waldo MaryYolanda Grenada Grenada I'm sorry 1 2 34 5 Lisa Lacoste just on the basis ofthat we were going to take 5 people thefirst 5 now if I have some no-showsWatch at: 05:40 / 06:00today and I do so far I will let somepeople in from there and then I willprobably take another 4 or 5 because wehave chairs in the back and surroundingso it's more than likely that I'll beable to take Jennifer Leal KathleenCollins Kerry Rhodes Jessica and RoddyWatch at: 06:00 / 06:20and Jennifer Miranda I think that lookslike and maybe Elizabeth vigil but goingbeyond there there's some question itlooks like it may work out it dependsbasically on how you respond to what I'mWatch at: 06:20 / 06:40going to tell you about the course noteverybody may decide that they want totake the course so I'll give youinformation today if you are on thesecond page of my waitlist probably notlikely that you're going to be able todo the course the three people in thatthere were three of you not a very goodWatch at: 06:40 / 07:00chance but I'd say I'll be able tohandle probably half of you on the firstpage of that waitlist but some of youwill be taking the course by watchingthe presentations that we do daily inone of the labs now since this issimulcast you could be in a lab watchingthis lecture right now it's a 20 secondWatch at: 07:00 / 07:20delay and you could be in a lab watchingthe presentation it's just you would notbe in a directcontact in a classroom environment Iwant to talk more about that but that'swhere we are in terms of role and I'lldeal with that at one o'clock today myoffice hour today will be 1 to 5Watch at: 07:20 / 07:40that's founders Hall 270 C founders Hall270 C and I'll be there from 1:00 to5:00 today trying to deal withenrollment procedures for some of thesections so I will take some people intothis class at the end of the hour I'llWatch at: 07:40 / 08:00close down before 11 o'clock and I willthen check to see who I'm going to takeinto the class give you add cards andthen we'll go from thereI realize it's difficult to get a math70 we're trying to accommodate that asmuch as we can with this new section andproviding you the opportunities to seeWatch at: 08:00 / 08:20the information in one of the computerlabs so let me show you how you firsthave an opportunity to get informationfrom there this is a picture of the webpage that is my web page for two otherWatch at: 08:20 / 08:40courses let's go to that Debbie this isthe home page for math 130 for math 10both of which have been done on directbroadcast and Internet neither of thoseis being done on the internet thissemester and they are both being done insimulcast now there's a globe in theWatch at: 08:40 / 09:00middle if you were in one of the labsand you bring the cursor in the centerof this globe and click you'll get themath 70 home page I wanted to keep itunavailable except two people at themoment who need to know about it sothat's again I'll give you this URL in amoment but you're just going to move theWatch at: 09:00 / 09:20cursor to the center of the globe inthat area click on it and you'll see amath 70 homepage come up now the URL forthis is going to be next on your listand if you're in the course this is apiece of information youWatch at: 09:20 / 09:40need because it's where the homeworksgonna be listed the schedules listed etcokay Debbie let's cut to there that'sthe URL write it down you'll need itvirtual dot you simit e dot CC dot CAWatch at: 09:40 / 10:00dot u s /j curl that's what you need towrite down and that can be accessed fromhome it can be accessed from the libraryit can be accessed from Sierra Hall anyof the computer labs on campus ok sirWatch at: 10:00 / 10:20can I help youok quickly take care of if you can ifyou got that written down notice theperiods between virtual Yosemite CC CAand u.s. no period after us there is noWatch at: 10:20 / 10:40slash after curl just JC URL with no /athat brings you to the home page clickon the globe now what that will provideyou is a home page in which there willbe a link to the schedule that I intendWatch at: 10:40 / 11:00to cover this semester and here isessentially what you see coming up onthat link schedule sections covered Icall this the video based math 70 it'sfor their information but you will beable to access it also so as we slide orgo off that for just a moment Debbie I'mWatch at: 11:00 / 11:20gonna slide up and this just gives youan idea of what we are doing let's seeif I get a little bit tighter there wego so you'll note week 1 that's January6 we're covering chapter 1 and and week- well we got a drift there and week 2Watch at: 11:20 / 11:40we do a review of finish our review ofchapter 1 and chapter 2 week 3 ischapter 2 review in chapter 3 week 4 isgoing to be chapter 3 review and partfour and our first exam is listed andI'll just scroll over to the side theWatch at: 11:40 / 12:00first exam is listed January 31st so theexam schedule is set out here and whatis indicated for you on a weekly basisis what we're covering when you click onthe week itself if we can go to thedocument cam if you click on the linkwhich is week one there will be a pageWatch at: 12:00 / 12:20that tells you what is being done thatweek and this is going to be an ongoingprocess and the homework assignmentswill be listed in there along with thevideos of what you're sitting in andwatching right now in addition to thatWatch at: 12:20 / 12:40my intent is to do the photographs ofthe board presentations have those up asJPEG files that you can then print havethe board content and the lecturepresentation available to you byafternoon of the day it's been done oneof the goals I have during the semesterWatch at: 12:40 / 13:00is to create a video tutorial sectionwhich means that topics on an individualbasis that have been covered will besuch that you can go ahead like an indexin a book look at the topic for examplethe topic today will be the real numbersystem and you can click on the realWatch at: 13:00 / 13:20number system and see a video clipregarding the presentation on thatparticular topic so this provides 24 by7 opportunity to get help small clips ofa video presentation of the content sothat is to your advantageWatch at: 13:20 / 13:40a VHS tape of each day's lecture I'mgoing to take to the library I need totalk with them today but I'm hoping tohave one VHS tape at the reserve desk sothere's another opportunity to watchwhat we're doing I believe we'rerebroadcasting debbie at 9:00 to 955 inthe evening but that means you have toWatch at: 13:40 / 14:00have DSL or a cable modem in order towatch that broadcast if you do it on a56kay you're going to have congestion andbuffering that will just make it nearlyimpossible to see it effectively whendone well it's going to be like watchingWatch at: 14:00 / 14:20a television program when you watch iton simulcast if you have broadband sothat's what we're trying to do in termsof the course and essentially I'mregistering anybody from the Directbroadcast section into this course butWatch at: 14:20 / 14:40you'll be watching it off of broadbandDSL or on campus but not in this roomthat would be the same as it would havebeen done on channel 27 now is there anyquestion I don't know if that's as clearas I'd like yes sirWatch at: 14:40 / 15:00yes the tuesday/thursday you wouldsimply be able to go otherwise okay goodglitch I forgot to mention when this wasoriginally listed it was listed MondayWednesday Friday it is daily so if youare tied up on Tuesday Thursday then youWatch at: 15:00 / 15:20simply sometime during the day onTuesday Thursday watch the lectures inone of the laps and just let me know whoyou areotherwise I will drop you fornon-attendance if it gets excessive butthere may be a few of you who have thatconflict okay but the point being youstill are able to watch the lectures noWatch at: 15:20 / 15:40that will be in the computer lab andwhat you will do is go to the link Ishowed you that's where you would bringup the home page you get to math 70 andthere will be a link for simulcasted soyou just click on there you'll needmedia player to see the simulcast and Idon't know nor does Debbie know whetherWatch at: 15:40 / 16:00that's working the way we want today butwe should have the bugs ironed outfairly soon so tomorrow just go to oneof the labs I can't get the presentationencoded much better than by about 2 p.m.Watch at: 16:00 / 16:19I've been they won't Monday Wednesdayand Friday one o'clock in my office areaso office hours Monday Wednesday Fridayat 1:00 that's in 270 C founders Halland you have questions or something youWatch at: 16:19 / 16:40can drop by there and that one o'clocktypically goes well beyond two butcertainly a guarantee one to two thereare times that I have conflicts in theafternoon with meetings or somethingafter 2:00 but most the time I plan tobe there to nearly three o'clock so thatshould be an opportunity come in soWatch at: 16:40 / 17:00office hours Monday Wednesday Friday1:00 to 2:00 and as long as I'm there inthe afternoon to 7dc my phone number isfive seven five six one one one nowbecause people are going to be watchingthis today and who are not going to beWatch at: 17:00 / 17:20in class typically if you have questionsabout something you'd like discussed inthe next day so let's say that you'vewatched Tuesday and something wasn'tclear to you and you watched it on thepresentation of the lecture on aWatch at: 17:20 / 17:40computer if you leave voicemail for mebefore 6:30 a.m. in my office then I cango ahead hear that voicemail and I willtry to address that issue in my lecturethat next day so this is a way toprovide some feedback now we do have anWatch at: 17:40 / 18:00interactive nature this noun the doublewe're going to work it on a 20 seconddelay but Debbie do you want to run thatnumber that we have on the top of theboard this is a five seven five sixseven five nine if you're in here thisWatch at: 18:00 / 18:20isn't of any value to you because thisis a number that people would referenceif they were watching this in simulcastand have a question they'd like to haveaddressI don't want to be interruptedmid-sentence in something and that's aproblem you have when there's a20-second delay because you don't noticeWatch at: 18:20 / 18:40where I am in the presentation but theway we had tried to work that when wehad channel 27 going was sort of a Oprahkind of thing you could call in and givea question and then I try to answer itduring the hour it just has not workedas well as I would like mostly peopleare a little bit intimidated by being onWatch at: 18:40 / 19:00television with their questions and sothey wait until the you know thepresentation was done and then the phonewould ring about the time we wentoffline they're off the camera so at anyrate that's another opportunity if youwere watching in one of the simulcast assome of you will any other questions onthe mechanist well the mechanisms thatWatch at: 19:00 / 19:20were going through and presenting thecourse yes yes monday through fightingmeans daily in spite of the fact thatsome of the colleagues seems to be in afour-day week you're in a5 and testswill be on fridays so with that said letWatch at: 19:20 / 19:40me make a little transition here formaterials the question of course whatmaterials do you need what about thesyllabus what are we going to coverprerequisites and so on the first interms of prerequisites and getting intoWatch at: 19:40 / 20:00this course it's assumed that you'vepassed a placement test the assessmenttest we did or you've had math 20 nowthat isn't always as good as it soundsour assessment test is such that you canguess through your teeth sometimes andnot have the background that you shouldWatch at: 20:00 / 20:20because it's been too long ago and youmake it through to the course and thatdoesn't mean you're prepared so ifyou're pre-algebra and your backgroundis such that you didn't feel very goodabout the assessment test but somehowother you passed it it suggests you'reand thin ice if you recently came out ofthe math 20 that's a different issueWatch at: 20:20 / 20:40so you have to give some serious thoughtas to what kind of background you haveI'm going to be doing a survey beforethe hours up that you're going to fillout information for me about yourbackgrounds if this is a multiple effortfor you in taking this course you mightwant to consider math 47 which is beingWatch at: 20:40 / 21:00done for students who've had math 70 didnot do well in it or in like a second orthird effort and at that point youprobably aren't going to do any betterthe second or third time than you didthe first unless you solve some of theproblems that relate to arithmetic youWatch at: 21:00 / 21:20must have a very strong background inarithmetic and pre-algebra this is notthe place to solve your problems inarithmetic we have two courses math 10and math 20 you need to know how to findWatch at: 21:20 / 21:40common denominators using primefactoring you need to know how to do theoperations of adding fractions inpre-algebra and do it with prime numbersif yeah it's totally alien to you thenyou probably don't have the preparationyou need the book that we are using forWatch at: 21:40 / 22:00this semester is one you're familiarwith I suspect if you've been to thebookstore if you register for the coursepart of your preparation the first dayis to be here with the book if you'reregistered and are serious about thecourse if you don't yet have the bookWatch at: 22:00 / 22:20and you are registered for the courseyou're probably indicating the lack ofcommitment let's go to this nowbeginning algebra eighth edition by Lyleand Hornsby this is the book you needand you need it today which given thelines in the bookstore is a little bitintimidating I'm sure but you need to dothat there will be a homework assignmentWatch at: 22:20 / 22:40that you will have today that's duetomorrow that will be covering thesyllabus for the course essentiallystarts out with homework I'll have thiswell there's a form of this online rightnow but this is just a hard copyWatch at: 22:40 / 23:00but let's go to the document andhomework it is assigned daily and youshould schedule one to two hours a daylet me slide that over just a little bitone to two hours a day you're to writethe original problem intermediate stepsand your solution the homework should beWatch at: 23:00 / 23:20presented in a neat and orderly fashionon eight and a half by eleven paper andthen I haven't quite decided how I'mgoing to handle homework and the gradingof homework for this particular class Ineed to think a little bit more aboutthat yet this afternoon but certainlythe homework for today should be done inWatch at: 23:20 / 23:40the way that you'd be turning it in andI will plan whatever else happens tocollect a homework assignment tomorrowtests okay there are at least three itturns out there'll be exactly threeone-hour exams at 100 points each thereis a two-hour comprehensive final worthWatch at: 23:40 / 24:00200 points you will need a Blue Book foreach test okay and the exams are closedbook closed notes and no calculatorsused for the course period nocalculators if you cannot functionWatch at: 24:00 / 24:20without a calculator you need to takeanother course ten or twenty and getyourself to the point where you canfunction without a calculatorthey will not be allowed in exam okaynow the grading okay 90 to 100 for the a80 to 90 for the be 65 to 80 for the CWatch at: 24:20 / 24:4050 to 65 for the D and under 50 will bea failing gradecalculators simply not allowedattendance you have to be here daily ifyou miss classes or are not watching ifWatch at: 24:40 / 25:00you have a schedule that requires thatyou watch the videos you basically needto be able to do that if you are notable to participate in lecture then youshouldn't be in the course it's thatsimplehelp certainly office hours you can dropby for that trying to provide helpWatch at: 25:00 / 25:20online on the computer for you andcertainly it's probably a good idea toget into small study groups and helpeach other it's probably the best thingthat you can do so even if that there istutoring available probably the biggestproblem with - doing quite simply if youWatch at: 25:20 / 25:40depend on it to get through yourhomework that's not what to do meansabout tutoring is you've been in thelecture you spent one to two hourstrying to do things on your ownand then you get help beyond that so interms of class five hours a week 10hours and homework and add to that anytutoring time on top of that so you'retalking a 15 hour a week commitment toWatch at: 25:40 / 26:00this course that's my expectation I'mvery upfront about that anything on topof that then as far as tutoring orspending time in the video tutorials orother help does get added on to that theintent of this course is to provide youWatch at: 26:00 / 26:20the necessary background to go into thenext course which is intermediatealgebra of course this course doessatisfy a graduation requirement anyquestions regarding the prerequisites orexpectations essentially if you'reworking a lot of hours and are taking 15to 18 units you have to make someWatch at: 26:20 / 26:40decision about how much sleep you wantto haveheavy loads go with low very low amountof sleep if you have heavy loads andyou're trying to take this course and afull load other than that then it couldbe of some difficulty yes a blue bookWatch at: 26:40 / 27:00which is in a one book store it's asmall but not the large the smallversion yeahand you'll need one brief test you'llneed a total of four of them apieceokay any other questions on topics thatI haven't covered from the syllabus thatyou'd have an interest in discussingWatch at: 27:00 / 27:20okay just a little bit about Who I amI'm a full-time faculty member here atthe college I've been here for a numberof years and it's getting the pointwhere decades it's probably the betterway of referencing it I've been doingthe television broadcasts in math 10 ourintro to math and math 130 for thoseWatch at: 27:20 / 27:40have been the two areas I've been veryinvolved in recently this is the firsttime I've done math 70 in a very longtime I used to do it in the morning at 7a.m. and we've been doing the stat classthen so this is a new effort a newopportunity to try to provide part ofwhat we perceive and have done with theWatch at: 27:40 / 28:00distance learning and I'm hoping that itworks out very well one of my formerstudents Corrine who is out at the Javawagon shared this with me this pointlet's go to the document cam this was inShu over the weekend and she had takenalgebra from me in an early morningWatch at: 28:00 / 28:20class has served in the faculty here isadjunct faculty in English but nothinglike a good mystery is the first part ofthat then the second part of the slidetotally engrossed and then the questionwhat's the title of the mysteryWatch at: 28:20 / 28:40algebra and I thought that was a neatway of sort of addressing what thiscourse is aboutbecause algebra in some ways is workingwith the unknown we talk about solvingproblems and whether you've had 10 is aWatch at: 28:40 / 29:00background or twenty years of backgroundboth courses cover dimensional analysisit's a very important part a problemsolving dimensional analysis you'retrying to find out something that youdon't know how long is it going to takeWatch at: 29:00 / 29:20to get to Los Angeles if you're drivingat a particular speed how much are yougoing to pay for something how long isit going to take to read the book that'sdue at the end of the semester those aremysteries we typically in solving wordproblems in algebra use a letter of thealphabet to represent what we don't knowWatch at: 29:20 / 29:40so we say let X be a certain quantitytypically X a letter from the alphabetrepresents a number now that brings usto preconceptions about numbers most ofyou in taking some notes right now haveWatch at: 29:40 / 30:00a piece of paper in front of you and Iwant you to do the next process if youhave paper in front of you in less thanthree seconds write the first numberthat comes into your head now pleasefirst number that's in your head okaythat's more than three seconds youshould now have a number written downWatch at: 30:00 / 30:20now it in a sense in a very simplisticway represents a kind of preconceptionthat we all have when we come into aclass in mathematics if I ask mygrandson that I get to see weekly howWatch at: 30:20 / 30:40old he is very soon he'll say thisyou know the number without saying andit'll be his fixation at his birthdayfor some time I'm old now there areWatch at: 30:40 / 31:00other situations that are equallyobsessive the 16 year old is veryconscious of being 16 because that's arite of passage agreed that's when youcan legally reckon go out and drive andWatch at: 31:00 / 31:20think of the insanity in McHenry Avenuea few days before Christmas try doingthat at sixteen your first solo flightokaytwenty-one right of passage and we focusWatch at: 31:20 / 31:40on those numbers and then there's somewe try to delay 55mmsixty-five numbers that we focus on youwrote down my guess is a counting numberWatch at: 31:40 / 32:00and most of you probably did that and alot of you did a number between one andten how many of you wrote a numberbetween one and ten may I see your handslook around you okay pull out the camerain that can't yell pointed holder let'sWatch at: 32:00 / 32:20keep up let me get it this is chaos andits best but you'll see if Debbie canget drainages good buddy there we go gotthose hands up Thank You Debbie now whatis numberhow many of you wrote a fraction that'sWatch at: 32:20 / 32:39interestingnada nobody wrote a fraction how about adecimal I said it numb oh yayprecisely the point I said number afaction is a number no it is a numberWatch at: 32:39 / 33:00not a part of it is a number 3/4 is acool number how many loaded decimal 3.14name the number hiWatch at: 33:00 / 33:20very good we use it in geometry if youdid math tenon you did it now what doyou did it that's pre-algebra youlearned about PI 3.14159 at a nauseagoes on foreverevery piece do you buddy have a negativenumber it doneWatch at: 33:20 / 33:39so you're very biased they have to bepositive or you don't want them and yourhead a number is a counting number whatyou did is a kid still there now thatbrings up the question of what aboutWatch at: 33:39 / 34:00something like 3.14159 the number pijust as a reminder the number that werepresent with the symbol that's calledpi let me write that on the board foryou one of the most famous symbols sorryWatch at: 34:00 / 34:20Debbie I didn't Telegraph that well atall but the symbol for pi now thatrepresents a certain ratio what is thatratio this is a time to shine or maybenot what this pi represent fromWatch at: 34:20 / 34:40pre-algebra circumference overokay for the magic carpet rideover what close radius is an excellentWatch at: 34:40 / 35:00wrong answer it's a very close mannerdiameter very good cross multiply incircumference is pi D you didn't knowwhat you can do with the CD before justtake C over D and get PI that was prettyWatch at: 35:00 / 35:20badokay you're familiar with the formulasfor the area of a circleanybody one more chance to redeemyourself as a group area for a circle isfor your background I've asked threequestions so far and we're getting gooseWatch at: 35:20 / 35:40eggs here and this is sort of my pretestfor whether you belong hereokay area of a circle formula maybe sixhow's the radio is it that's goodguess it has pie in it too I have iswhere yes PI R squaredvery good that's one of the few bits ofWatch at: 35:40 / 36:00humor in mathematics what's the joke PIR round circle R squaredthis with pie around not square okayWatch at: 36:00 / 36:20it's quarter ready swear now what aboutthe circumference for a circle theformula Lois it's up on the board theygive it to me in terms of ourcircumference misterwhat is the diameter in terms of theWatch at: 36:20 / 36:40radius okay one of us half the other oneis twice the other which is it theradius is half the diameter so thediameter is how much of the radiusdouble to our D is 2r that's importantWatch at: 36:40 / 37:00to R so cross multiply and thecircumference is 2 pi R now folks thosethree are supposed to be part of yourbackground when you walk through thedoor this morning and the fact that theyWatch at: 37:00 / 37:20aren't is a great concern to me okaynumbers pi is a number it is aparticular generic number it's called areal number now to say that we have realWatch at: 37:20 / 37:40numbers tells us that it is a collectiona set of numbers that can be a countingnumber a fraction a decimal can bepositive or negative and there are 11properties of the real number systemthat you should have studied inWatch at: 37:40 / 38:00pre-algebra and should be part of yourbackground today and must be memorizedby tomorrowsection 1/7 of your textWatch at: 38:00 / 38:20there are 11 of them let me ask you aquestion if I add two odd numbers whatdo I get two odd integers I be carefulto whole numbers that are both odd likea 3 and a 5 what do I get and even rightWatch at: 38:20 / 38:40I don't get what I started with Istarted with odds out of the might noteven I'm sure you're sitting theresaying who cares that means that I hadan operation with two numbers that didWatch at: 38:40 / 39:00not give me a number in the original setI started with two odds atom togetherand got an even we guarantee that if youtake two real numbers and add themtogether or multiply them together youget a real number I started with twoodds added them and I didn't get an oddWatch at: 39:00 / 39:20so this property called closure does notautomatically occur for us now I'm goingto consider a B and C contained in thisset called R so I have three symbols a BWatch at: 39:20 / 39:40and C meaning they're different numbersand they belong to our closure says thata plus B belongs to R and the product aB belongs to R also add and multiply andWatch at: 39:40 / 40:00you get a number in the reals that'simportant first two properties they're11 um of you're keeping count what aboutadding two numbers we talked aboutadding one in three and you get an evenbut one plus three is the same as 3 plus1 2 times 3 is the same as 3 times 2 weWatch at: 40:00 / 40:20say you can reverse the order ofaddition to multiplication and you're inbusiness and it may seem trivial can youdo it with division no can you do itwith subtractionno you get different answers so we referto that as the community property andWatch at: 40:20 / 40:40that says that a plus B will equal Bplus a and a times B will equal B timesa those are the community properties foraddition and for multiplication now if IWatch at: 40:40 / 41:00give you 3 numbers 2 3 & 5 then you knowwhen you add them you get 10 2 3 & 5 bythe way if you can't do that quickly inyour head it's another acid test if youcan't add 2 3 & 5 in your head without acalculator you're over your headday one now how do we write 2 + 3 + 5Watch at: 41:00 / 41:20you add 2 + 3 first and then add 5that's how you get your 10 can yourearrange it mix and match you betso we say that there is an associativeproperty and the associative propertysays that a plus B plus C can be done inWatch at: 41:20 / 41:40parenthesis first that way or add the Band C first and then add a get the sameresults Thank You Debbie what aboutmultiplication same argument ABC nownotice a and B together me multiply thisWatch at: 41:40 / 42:00is something you should come in with asa background from either 10 or 20 and itsays that you could have multiplied Band C first and then multiply by a andget the same answer associative propertyokay how many we up to now we're up tosix total three total different ones butthere's two in each so there's a closureWatch at: 42:00 / 42:20for addition close your multiplicationcommunity addition communitymultiplication associative additionassociative multiplication more to goand your goal to have these memorized bytomorrow and know them on demand okayso we have associativity now somethingWatch at: 42:20 / 42:40that you already know about if you addzero to something you get the number youstarted with five plus zero is fivethat's called the identity property foraddition identity so it says that if youWatch at: 42:40 / 43:00start with any number in the real numbersystem and add zero to it you'll getwhat a now technically because we havecommunity you could say zero plus a isequal to a plus zero but I'll just writeit this way and what aboutmultiplication what's the identity formultiplication one right one times threeWatch at: 43:00 / 43:20is three so we say a times one I'm usinga little dot between the a and the onerounded parenthesis is equal to add aand of course the assumption here isthat 0 m1 are members of our realWatch at: 43:20 / 43:40numbers so a times 1 is 1 times a equalsa identity so we're up to 8 3 more to gothe inverse for every number a there isanother number called - a not just aWatch at: 43:40 / 44:00comment here - a could be positive andif you have trouble with that part of itis because in your head a number is whata counting number you think of it as apositivebut if number could be negative forWatch at: 44:00 / 44:20example if you have minus 3 as yournumber a negative of minus 3 is positive3 and with the pre-algebra backgroundthis should not be something ofdifficulty for you so we're saying thata plus negative a is equal to zero youWatch at: 44:20 / 44:40can add the inverse to a so you startwith a out of ten verse and you get zerojust as an examplemake sure you understand that minusthree plus a negative of minus three isWatch at: 44:40 / 45:00zerowhat about the inverse formultiplicationit's what you call the reciprocal 1 overa so what we sometimes say is for everya looks like an upside down a means forWatch at: 45:00 / 45:20every for every a comma a not equal tozeroa times 1 over a is equal to 1 noticethe inverse gets us back to the identityso that's for every a a not equal to 0 atimes 1 over a equals 1 that's what getsWatch at: 45:20 / 45:40us fractions we're up to 10 by the waypart of pre-algebra is to go through allthese properties and know them so thisis not supposed to be new materialdistributive property the one propertythat pulls everything togetherdistributing the distributive propertyWatch at: 45:40 / 46:00says a times in parentheses B plus C isequal to a times B plus a times C andI'll step aside so double you can getthat one distributive property a time'sWatch at: 46:00 / 46:20the quantity B plus C equals a B plus ACdistributing addition or it should saymultiplication over addition now thoseare your 11 properties you need to knowWatch at: 46:20 / 46:40them have them memorized and be able towrite them in the form that I've had inthe front board by tomorrow that's insection one seven to facilitate thatthere are 82 problems in section oneseven they start on page 67 68 69 I wantWatch at: 46:40 / 47:00one282 done odd the odd numbers so thatmeans one three five seven nine eleventhirteen and so on means you have 41problems in homework plus memorized theWatch at: 47:00 / 47:20real number system properties the elevenproperties by tomorrow yes one through82 odd section one seven page sixty yesit starts on 67 68 and 69 now I'm goingWatch at: 47:20 / 47:40to close at this point with the formalpart of the presentation which meansDebbie is going to go ahead and go to aslide and music stay in your seat pleaseuntil the slides up and the music startsand with that have a pleasant day I'llsee you tomorrow