okay we're going to look at exponents we had the idea of repeated addition a while back we had addition then we repeated it and we got multiplication out of it what would happen if we take multiplication and we repeat that so instead of like 5 + 5 + 5 we have 5 * 5 and we do that over and over and over and over and over again sure we can probably calculate that number and figure out how much that is that's going to be a spectacularly large number that's huge number but is there a better way that we can represent that and the answer is to that yeah there is there's a better way we can represent 5 * 5 * 5 if we keep repeating that five and multiplying it we can use what's called an exponent the way we use an exponent we have to identify something called the base then we have to identify how many times we're repeating that multiplication in our case the base is the number that's being multiplied over and over again so can you tell me what my base is here five is the the number itself yeah you're right number itself so five so we write that first that's called our base the number of times you've repeated that multiplication so you count up the number of fives you have how many was that seven seven that seven we write it just slightly smaller and we put it right here that's called our exponent these two things above my head above my head right these two things above my head say exactly the same thing this says five * 5 * 5 * 5 seven times this says you take five and you multiply it by itself seven times they say the same thing this is just a more concise way to write it we want to make things easy right to be able to do things like that so that's called our base the seven is our exponent we also have some ways to say things to say our exponents if I write this right here firstly what does that mean how what's our base here what's our exponent so what this means is five Time 5 Time 5 you know a lot of people do that and they say oh well this means 5 * 2 this is 10 this is not 10 how much is this this actually means 5 * 5 that's what the 5 to the second power means and there's two ways we can say it we can say this five we we can say it 5 squar you ever heard that five squar yeah 5 squared wouldn't that only be if it was like a two though a two or three we say 5 squar and the next one we're going to say is 5 Cub all the rest of them in including this one you could say as 5 to the 2 power that's how a lot of people say that so 5^ s or we can say 5 to the 2 5 to the second power hey someone who's with it today this is 53 or 5 cubed how much is that how' you get that 5 * 5 is 25 * 5 is so when when we have 53 it it literally means 5 * 5 * 5 right is it going to be 15 no they're huge numbers can you imagine how much this is now that's going to be massive you're just keep on multiplying times five that's a that's a big big number so this one I I want to get to how we say this this is going to be five we can say cubed or 5 to the 3 power blah blah blah blah blah the third power everything else doesn't have a special way like 5 to the 4th it's just said 5 to the 4th there's no no special word like 5 squ or 5 cubed you say 5 4th 5 the 5th and so on so on so on so everything after this is just five to the blank power we'll end with just a couple examples let's see if we can write these following repeated multiplications as exponents and we'll be uh we be on all right everybody what is our base right now on the board what's our exponent so we're going to write which number first perfect and how would you say that yeah I don't want to hear uh I know you said it this way but I know you didn't mean it I don't want to hear 8 to the four don't say that that's what what we're writing yeah but when we say this we go 8 to the 4th that's how we do it base three exponent oh that was nice could that 3 3 3B or 3 Cub very good 3 Cub or 3 the 3r can't you do that one okay can you write this as one base or do you need more than one more than one more than one yeah you can't multiply the seven times 10 what we do is we'd say seven is the first base to what power you say 7 squar or 7 to the 2 and then we just put a little multiplication and we do to the perfect very very good how we will understand our expon today feel okay about this stuff awesome we're going to end there today we'll continue on this next time so if you remember from last time what we were doing we we were talking about exponents and I think we did problems like something along these lines where we had a few numbers multiplied together and we were supposed to be able to put those in what's called exponent form and really all exponent form is is a simpler way to write repeated multiplication because this is just annoying to write over and over again so we had two two words that we we learn we had base and we had exponent can you tell me how many bases am I going to have up here okay what's my first base to the perfect or you could also sayare awesome and then we're going to have a little multiplication our other Bas is to the six all right perfect that's exactly how we need to write that can we evaluate by the way when I say evaluate it's always going to be mean the same thing if we have variables it's going to mean you plug in numbers and see what mathematical answer you get if I have just numbers you're going to see what mathematical answer you get can we evaluate some exponents for instance can you evaluate 4 squar we got to think about what four squ means though does four squar mean we're going to get eight no what's four squ mean how much is four squ then very good all right oh that one I know right you want to immediately say you want look at that and go oh that's 21 because we have that in our head multiply but if we do just 7 time 3 man we're going to be we're going to be way off okay let's let's all work on it here we're doing 7 time what it means is our 7 * 7 * 7 if we just do the first set here we're going to have 49 already right right so what would have 49 * 7 how much is our 49 * 7 I think you said it already 343 yeah it is so we say 7 cubed we're actually getting 343 that's a lot different than 21 so if you put 21 see for right now our problems they are these problems you get a couple like this on a test but if this were within a problem can you see how working with 21 is going to be way different than working with 20 or 343 got to really get these exponent things down what would happen if you did a number to the first Power how much is 11 to the first Power 11 so it really does you're not multiplying by anything it's just there we say we have 11 it's just one of them not me multiplied by another so 11 to the 1st anything to the first gives you back that number again last one I want to do with you for now we have 2 * 3 S we're going figure out what this is first thing I got to ask you is is it the two being squared the three being squared both of them being squared good you need to know that the exponent is a app just to the immediate base so what this says is okay I'm going to figure out what my exponent it how much is that by the way 3 S you know what a lot of people they give me six because it happens so quick they're trying to do it fast don't give me six on this problem so we're going to get 3 * 3 we get nine out of that so this really is 2 * 9 or how much is that perfect and this is a great step stepping stone right into our order of operations you see when we do mathematics we all want to be able to get the same answer and all of us be right in it correct we want that we don't want you to get one answer and you to get one answer and you both have different answers and you're both right that would make sense could well they'd both be wrong right I mean that that we we can't have that type of scenario in mathematics in other classes you can right you write a paper about an opinion paper and if you have different opinions doesn't mean you're necessarily wrong just means you have a different opinion there's no such thing as opinion in mathematics it's it's pretty much black or white you're right or you're wrong and the way we ensure that we're right all the time is that we stick with something called order of operations you guys have heard this before right okay so we have this thing called order of operations are there any questions on the exponents before we get into this you guys with me today right seems like you seem more awake today yeah took your coffee today or something huh what now the order of operations like our checklist for math every time you get a problem you go down the order of operations and say okay I did my number one step then I did my number two step then number three and then number four there's only four there's only four order of operations that we cover in here and the whole the whole idea is this we need to be able to get the appropriate answer if I give you a problem like this the question is what do you do first I'm going to do this two different ways the question is am I going to add this first and get like 7 * 5 No and then get 35 or am I going to multiply this first and get 4 + 15 you see we get drastically different answers right only one of them's correct though we can't be doing things out of our operations or else we get two completely conflicting answers that's not a good thing for us which way would you say is the right way 19 the second one the 35 or the 19 19 if you're familiar with order of operations you know this one's right but we're going to review those right now to make sure we're all on the same page so here's our order of operations the first thing that you do right off the bat number one you're going to take care of any operations Within These parenthesis remember how parenthesis when we said a while back said do this first remember that it still means that it means you do this first right off the bat parenthesis is number one so or of operations number one we're going to do operations within parenthesis first do all operations within parentheses first I do want to make you aware of something because uh I've had a lot of students come back and say you know what I didn't know how to do this problem because it didn't have parentheses what it had was these funny looking things like this these things being parentheses also okay they just they're going to be outside other parentheses so parentheses mean these guys or these guys either one mean this situation step number one you deal with these first notd your head if your can which one right on top like the same but we're going to find out why in a second it's a great question thank you for that one so first order of business we deal with our parentheses first we take care of all those operations then we move on to number two we're going to look for number two if you know this already you're going to look for any exponents the things we just covered and you're going to evaluate any exponents right then so parentheses come first but right after that we're going to simplify any exponents third step so if you want to keep track up here we look for parenthesis now let me set something straight for you please be be listening paying attention up here for a second um even though we have parentheses here do you see how there's nothing to do inside the parenthesis it's just the five do you see that that means they're done the the parenthesis aspect of this is completed it just means now a multiplication part are you with me on this then we look for exponents we don't have any exponents Now we move on to the next step the next step in our order of operations the next order is we're going to do all multiplication and division here's the deal a lot of people get this get this wrong a lot of people think that you have to absolutely do multiplication before you do division and that's not true what's true is you do multiplication and division please make sure you write this down you have this in your head as they occur from left to right so do you always do multiplication first the answer is no no you don't it might be that division came before multiplication okay so you look do your parenthesis you look you do your ex point you look again you do all your multiplication division but you have to do from left to right otherwise you're going to get the wrong answer not your head be okay so I'm put them on the same step we're going to do multiplication and division but it's got to be from left to right do multiplication and division from left to right that's kind of an important one for us we'll see why in a bit so let's see why this one's right and this one's wrong if we went through this example again and say parenthesis first you know what these parentheses don't really count there's nothing nothing to do inside of it we go to exponents well there's no exponents then we go to multiplication division is there any multiplication or division yeah it's a 3 * 5 so we went out of order here we went out of order here we added first that was wrong we had to multiply first that's why this one's right that one's wrong multiplication definitely comes before our addition does everyone with me on that one raise your hand if you're okay with this good all right so last step the last thing that you're going to have with have after you've done parentheses after youve done exponents after you've done all this the only thing that can possibly be left in your problem is addition and subtraction that's our last step we're going to add subtract but guess what addition doesn't necessarily come from before subtraction again it's as they occur from left to right so we're going to look at our problem we're just going to go from left to right and do whatever we have there whatever happens first between addition subtraction so do do addition and subtraction again from left to right would you guys like some examples on how to do this these type of problems you're good good we're going to do a whole bunch of them uh we really need to get this down if we don't have the order of operations down now when we get to negative numbers and things like that we're never going to have them down so we really want to get this just nailed so we can move on you guys with me on that so let's do a whole bunch of examples oh by the way a couple ways to remember or the order of operations youve heard maybe some of you heard the you heard the please excuse my dear an S it's a pneumonic that kind of Beats it into your head please excuse me please excuse me my dear Aunt Sally you've heard that one before right the other one I like is the pemos you've seen the pemos before yeah pemos is you just you just write it the only thing that I like better about this and please excuse my dear Sally is I can show you that these two things are linked it's not necessarily that the M comes before the D they come at the same time from left or right and these two are also linked have I ever told you my pemos story do you want to hear my pem do story yeah it's kind of stupid you still want to okay so here's my pem do story so I come from a place called Clovis I told you this right Clovis is kind of a sheltered little town where nothing really happens and so I went down to Long Beach which is not a shelter Town there's lots of things happen but I came back to Clovis and so my first teaching job ever was uh at a place called dos Palace high schools you know where dos Palace is and so I went out there and all my friends were were saying beforehand cuz off Club they don't really even know D house like man I heard the gangs are really bad there's not really there's only 5,000 people nothing happens and yeah the gangs are bad then you going get shot you better like you know be careful where your best so my first I think my first like month there I gave a test and uh and I taught him all about this stuff I'd never I I did the please excuse my dear a Sally thing I hadn't really the pemos was new for me at that at that time and so this girl turns in her homework and and uh and then her test comes and she she keeps writing this this gang name on her test I'm like what are you doing you can't write your gang what are you and so like I I bring her up I go and she's a real nice girl I mean she sits there she does all her work you know real sweet and everything and I bring her up I say look I I don't care what you do outside of class on the weekend whatever you just can't write your gang name on on my test and turn it in she goes are you talking about this this pemos I mean that that that is that your gang pendas I'm like what what is that that's or of operation like oh stupid but I swear that happened not even joking so I thought that pemos that's why I first learned it was from her anyway uh that's my pem duster I told you it was a little silly so if you write pm on your paper I'm not going to think it's your gang name I will understand now okay anyway but it it is a good reminder of how to do our or of operations we can write this however we want we use this as a checklist we check off our our parenthesis we check off our exponents multiplication division addition subtraction as long as you're doing this from left to right we got this down so let's go ahead and give a couple of these a try and see if we can kind of build on these problems we start simply at first then I'm start incorporating some parentheses and some brackets and we're going to make them kind of nasty looking at the end but they're all going to be doable for us because we have this idea okay I'm going to help you through the first two and I'm going to have you do two on your own before we start adding anything else up here uh so the first thing I'm looking at when I'm when I'm doing this problem I'm model this for you when I look at this problem I'm initially looking for any parentheses and if I don't have any then I move on if I did have some I would have to do those operations first so I look at this I go okay well I have no parentheses let's move on to the next one so I check for any exponents do we have any exponents okay no exponents I move on to the next one the next one is actually two of them it's multiplication and division so we look at this and we go do we have any multiplication and or division whatever one comes first left to right that's what we're going to do we're going to do that piece of it and then rewrite the problem so when we do this problem we go okay what comes first from left to right the multiplication or the division in this case multiplication so we're going to multiply we're going to say just ignore the rest of it do this part how much is the 9 * 3 and we'll rewrite the rest of our problem so we do that just piece by piece piece by piece that way at this stage in your math careers piece by piece is the way to go okay later on when you just get to hammer this stuff down you can do things different ways you do multi-steps at once okay but for right now it is piece by piece for us you're with me on this yeah okay so we're rewriting this the next thing we look for is do we have any more multiplication division we keep on doing that over and over again until we're done with all the multiplication and division do we have any more multiplication or division yes I see some division okay that came further on in the problem so we're good here are we going to subtract now no definitely not but we're not done with our division so we're going to rewrite the 27 and the minus but now we're going to ignore this part and do the 8 ID four piece how much is the 8 divided four piece so we've checked for parentheses there were none we've checked for exponents there were none we had some multiplication and division multiplication came first we did it first then we moved on go multiplication no division no oh division yes we did that little piece of it now we're down to where there's only either addition or subtraction we can look for addition subtraction of course we have the subtraction so we do the 27 minus 2 and get that's it and that's the correct answer this lets us do some of these problems and all get the same answer and is all the correct answer this one of my favorite ones this actually shows up on the final for your class this one cuz it shows me just in like 2 seconds whether you really understand the order of operations or not it really shows me that we're going to go through together we'll do it together I'll give you some on your own in just a second so together here we go firstly we check for any parentheses do we have any parenthesis okay next thing I'm going to check for is any exponents do we have any exponents yes when you do you ignore the rest of the problem you do just that little piece remember it's piece by piece so am I going to do 48 ID 3 right now no no no listen look at the am I going to do three 2 right now I'm going to do just this little piece so we're going to rewrite the whole problem 48 / 3 not plus three come on divid 3 times that times is still there what is our 2 to the second power yeah two two * self that's four then we move on we checked for parentheses there were none we just did we evaluated our exponent now we're down there's no more exponents we're down to multiplication division addition subtraction so multiplication division came first we do it from left to right so my question to you is am I supposed to multiply the 3 * the 4 or am I supposed to divide the 48 time divide by the three I have some conflicting oh I got arguments let's do this divide debate it out what do you think div divide 4 I covered this part up but that's important okay if you multiply first right now you will get the wrong answer okay you will why why it's it's okay you're learning right now but why it says that like you're reading yeah it's just like you're reading when you're down to multiplication division it has to come from left to right and you know what's what sucks about these type of problems is if you did this it's going to work out you're going to think you got the right answer let me show you if you did this this way and you got oh 48 ID that's 12 right 12 that looks like it's four you get a whole number answer you're thinking oh I did this right when in fact this is the incorrect way to do this problem are you all clear on this you have to go from left to right so this way no bueno we cannot do that okay the other way though we say we're going to do multiplication and division but we're going to do whatever occurs first from left to right that's not always this one I hope you're with me on this folks I really do hope you are uh because you are going to have some of these on your test I want you all to get the right answer we're going to do this part first the 48 divided by 3 how much is 48 divid good and then we multiply by four now we're down to the multiplication the only thing left we can do this and get that's our answer do you feel ready to try a couple on your own yeah let's do this now of course this is the one more one of the more important things I've taught you so far this semester uh so if you need help on this you're really not quite getting it I'm going to walk around for a couple minutes if you need help now is the time to get help on it promise don't wait okay there we go just two of them but there are two good ones it's good she if you got two on the second problem you got two on the second problem go back and look at that again something happened there you got two second problem okay let's see how we did on the things hopefully we did well first one of course we're looking for parenthesis there's none we look for exponents again there's none we look for multiplication division we're going to do it from left to right so the first thing that comes up is our multiplication we're going to do 8 - 3 / 3 we're just going piece by piece for now and then we're going to look for any more multiplication division you saw it we had the 3 divide by 3 that's our gives us our one and sure enough we're going to get seven as our answer how many we got seven good very very good next one same ideas but we we have some exponents here parentheses not so much exponents yeah so the first thing you should have done is done the four to the second power that's not eight that's now here's where people did two different things okay either you went the right way or you went the wrong way okay the right way is it's multiplication division from left to right the wrong way is you do multiplication the first the first every single time which in this case is going to give you the wrong answer can you always do multiplication first the answer is no no multiplication does not always come before division it matters whether one's before the other as you're reading like you said so from left to right we go oh you know what even though there's multiplication and division the first one I see is division I'm you know what it's so easy to fall into the Trap of multiplying because we always we see that easier in our head right it looks like multiplication is connected first it looks like that you go oh yeah I want to do this one first because it for some reason in our head it tricks and goes oh yeah multiplication comes first because you've been ingrained with that however if there in the this order you can't do it so we go okay so 16 ID two gives us8 and then we multiply the four that's your right answer how we've got 32 by the way good for you good for you if you didn't that's okay go back and fix it maybe try this one later now let's see what happens when we start incorporating some of these parentheses and these bracket Concepts see what we can do out of this thing does that like good enough for you right I get that the first day of class you're like whoa but now we we kind of know what to do with this stuff I hope we're going to work through this together so you can see how really I want you to do it and get all those ideas down so write down I'll give you a couple more seconds to write that down then we'll start on it as as a team as a group what's the first thing you should look for in this problemes do you see yeah in fact you know what those brackets count two so there's two sets of parentheses let me explain this to you those brackets count as your outer parentheses these count as your inner parentheses so here's how you would evaluate this problem check me out watch me on the board here real quick you look for for the innermost parentheses that you have so this one says yeah I'm going to do that first but inside this piece I also have another thing that says I'm going to do this first so this is like do this first this is like do this first first it's more even more first right off the bat you do that piece so if we're going to step by step it I'm going to leave this alone I'm going to leave this alone leaving that alone the only thing I'm really worried about right now is what is on the inside of those inner parentheses there so we're going do that just at little piece piece by piece what what are we going to get inside this parenthesis okay great so we just have a five it's kind of like having a problem with a problem you see that it's problem within a problem pieces within pieces so now that we've accomplished that parenthesis we can work on more parentheses so these brackets still count we're going to leave this 4 the 3 alone we're going to leave that plus alone in here in our bracket what's the first thing we're going to do in our bracket notice how it's a problem within a problem what's the first thing we're going to do great because it's like you're yeah exponent great you're going to go or of operations right through that mini problem just a mini problem so before we subtract we're going to have to have our 9 - 5 - 7 * 3 somebody tell me the next thing that I want to do very good yeah it's still in parentheses those brackets count and so we're going to leave the 4 the 3 alone we'll have plus notice how when you evaluate the parentheses you can actually drop them so for instance when you do the 9 minus 5 you're going to get how much we don't need a parenthesis around that anymore you can have one it really doesn't matter but you don't need it we can just write four there you okay with that yeah okay and then - 7 * 3 at the very end and now we're back to a problem that we've kind of been dealing with so far we've got all the parentheses out of the way no problem next thing we're looking for is and we have some so 4 to the 3 4 to the 3 or 4 Cub good yeah it's not 12 right we're not just multiplying we're multiplying 4 * 4 * 4 okay let's think through the order of operations again we now have our parentheses we've done our exponents the next thing I should do is definitely don't want to be subtracting here right that would not be the way to go now it is multiplication there's no division anywhere no multiplication before this guy hey what's going to come first uh when we do this addition is addition going to come first because we always do addition first from left to right good first thing we see so we're going to get our 68 68 - 21 how much you get there 47 oh yeah 47 perfect perfect perfect I would like you try one of your own it's very similar to this one but make sure you can go through those steps and really identify the order of operations are you guys ready for it all right we haven't fun yet no lie to me go yes this is awesome Try It Go that's pule no I don't need you to love math but I do need you to be good at it I don't care if you like it just want you to be good at it aren't you good at lots of things you don't like I'm really good at washing dishes but I hate washing dishes hate it but I'm good at it you know what it really doesn't work the other way around because if I was bad at it I probably wouldn't have to wash the dishes right it doesn't work that way with math if you're bad at it you still got to do it yeah unfortunately there we go that's a nice one okay what I'm going to do up here is I'm going to let you work on this on your own but I'm going to put the next step up about every 10 seconds or so so You' got 10 seconds a step let's see if you can finish this before I finish it and have the correct answer so we started now I'll give I'll put the first step up in about 10 seconds and you can continually check your steps this way so if you're if you're doing another step look up here make sure you have that okay for that's like 5 Seconds that was what now that was 5 Seconds oh well I I went quicker on the last one after the rest of them were tght how people got that got down to there good good for you give yourself a p on the back that's your sunburn read that really hurts okay I think we got time for a couple more what I'd like to do is one that's about as good as I can make it for you I want to show you one thing on this that you need to see a problem like this will be on your first test I tell that to you so you can put a little Mark next to it and study it it will be on your first test hint hint it's going to be on your first test okay so make a little Mark next to this one we're about to do also other ones we're going to deal with the what looks like fraction so okay this is our last one but I want your help with it okay so I want everyone participate and let's do this together okay now you tell me you tell me what's the first thing we should look for on this particular problem good why good uh watch carefully please would you listen up for a second there's one thing you can't do here one thing a lot of people do here this is one of the reasons why they have struggle desperately in math a and math C A lot of people think that we can take this exponent and move it here and here and we cannot do that are you with me on this you cannot do that uh you have to go or operations just like you see them we can't start inventing our own math cu chances are it's not going to work out real well for us all right you got to follow this stuff down so we can't do that with exponents the only thing we can do is follow order operations so the first step is as you guys said is the four + one do we do anything with a three no 4 + 1 is five to the that little two that two the second power that still is an exponent there that's that counts now do I absolutely need the parentheses here no since there's nothing inside of it I could I could have them or if you choose not to since there's no operations left what was it what it mean the three next to the parentheses multip times yeah so I could write that either way is fine all right it doesn't really matter and I'm going to rewrite the rest of our problem I've done the parentheses what else do I need to do expon start exp now we've got two of them here's one thing you can do with exponents you can do them both at the same time that's fine other stuff sometimes it depends on other operations with exponents that's usually not the case so we're going to do both exponents at the same time um firstly do I multiply the three times the five no no so I'm going to have the three times how much 25 25 good because we have 5 * 5 my how much is 2 to the 3 oh let's think about that six or eight definitely eight I give you this on the test two and a lot of people will give me six don't give me six we get 2 the3 power we're going to get eight okay next up we're rolling right along we've done parentheses we've done both of our exponents now we're going to look for which one's going to come first in this case mul multiply is you're right because multiplication is coming first how much are we going to get when we multiply you say a lot okay exactly exactly would that be awesome if math was that way you get a lot to put a little done 7 - 8 + 6 / two the next step is going to be definitely divide we still have that multiplication division go on we leave everything alone so 75 - 8 plus what was it perfect this is another one where people people always do this people always go oh I'm going to add first do we add first here no if you add first and get 11 and you subtract that you get or whatever that is 64 not good not good we we can't do that sort of thing it goes against the or of operations I can't explain to you exactly why right now cuz we don't have this our signs down I can't treat this like a negative 8 like I would I would show you that so on I will show you this for right now you just have to trust me that our operations have to be done this way so if they have to be done a certain way what's going to come first the Plus or the minus from left to right we do that 75 yeah last step is just to add that okay last one we're going to do today I just want to look at this problem for a second so that you don't you don't just kind of go what the come on Leonard what are you doing to me uh action mess up my whole method see now check this out these problems are pretty much like three problems in one watch watch on the board we're going to do this next time but I want to show you what what happens here when you have a division problem notice that this fraction it means division right that's what it means yeah it says what you have inherently is a parenthesis here and a parenthesis here so essentially what we're going to do I'm going show this next time we're going to start with this problem over here we're going to ignore the bottom of it we're going to do this problem all by itself till we get down to one number then we're going to ignore the top of it we're going to this problem down till we get to one number and then we're just going to divide it nod your head if you're with me on that it's like three problems in one that's really all it is so we'll start there next time what I'm going to do is I'm put some homework on the board uh this hey guess what this is not going to be due tomorrow y but it'll allow you to get started on it because it's it's a long assignment and so yeah least got two days this will be do on Friday we are almost done with the section uh so it'll be do on Friday don't hate don't hate don't hate he said don't wow poor stud no no I'm not cool I'm sorry I just look cool it's different all right I'll see you guys tomorrow all right so that's where we're going to get started today go ahead and write those down and get started on I'm going to be walking around cuz this order of operations stuff is really important for us if you're really not sure how we're doing these problems let me help you by the way is you're working on this what are the order oper what's the first one good what's the second one what's the third one good yeah yeah multiplication division is multiplication first or division first or does it 10 multiplication okay so left to right and then after multiplication division to right also you know what just a a point of order for the class I'm having some people trying to slip in late homework with current homework without letting me know they're going to be absent guys I'm just giving you zeros and handing it back um so if you're if you're not here for a day that homework is due you still need to get it into me somehow or at least let me know you're going to be absent beforehand otherwise I'm just going to put a zero on your paper and you get that back in the next few days okay so that's something to be aware of don't just slip in homework if you w't hear that day it needs to be oh you know what I'm sorry I meant 64 oh yeah right all right ask I got so excited drawing the eights they're fun to draw my bad get carried away there does that make it better yeah ah okay am for good good okay we're about to get started here take a few more seconds try to wrap this up all right so we reviewed or of operations we know we're looking at parenthesis first then exponents and multiplication from left to right and addition subtraction from left to right so when we look at our problem on the left over here we certainly don't have any parentheses we don't have any exponents but the multiplication and the division from left to right that's the important part of this problem if you got it you got it right if you missed it and you did the multiplication first well you probably got it wrong so in our case right here instead of going right for the multiplication even though it's easy to do and make that mistake stake we're going to go multiplication and division from left to right the first step is this 36 / 6 so we're going to do that little part we're going to get out of that 6 * 3 plus 5 so the 36id 6 is 6 then we still have the the rest of that problem the next thing we'll do is we'll look at multiplication division still in case we have any more we'll do that that piece of the puzzle so the 6 * 3 what's that give us 18 and the last operation is addition we're going to add that we're going to get the 23 did you get 23 good good fantastic okay next one's a little bit more involved right we got some parentheses and some exponents kind of attached to each other so we're going to ignore this part the first part of our problem we're going to go straight for our parentheses that's what we do first so I'll just rewrite it remember at this point we're really doing step by step just piece by piece until we get this stuff just down that we get right every time we don't want to be rushing this there's no reason for that this is is the problem we're working on right now it's okay so we're going to ignore everything else but that piece we're going to get instead of 8 - 6 that's going to give us two but remember that's still squared now you can choose to do a couple things here you can just put a two squared like this and multiply that's okay or you can if you want the parenthesis there you can have the parenthesis there it really doesn't make make that much of a difference so if you still want to do it like this which some of you might have that on your paper that's fine as long as you've done the operations inside the parentheses first you're fine on that do you understand that part of it okay so I'm going to leave it like this just for fun because this is super fun right yeah they're all saying yeah now you're on record okay so now we go for our Expo and since we're done with the parenthesis now I know there's still parentheses up there but what I mean by parenthesis is operations within those parentheses not just single numbers so here we have the 2^ squ we're going to do that how much is two squ again four so we'll rewrite the 64 all this stuff we still have the four and then the 2^ squar you're right that's four remember that the four next to the parentheses that means multiplication now we're going to go on since we've done the parenthesis and exponent we got multiplication and division from left to right what's the first thing we're going to do here a multiplication or a division in this case yeah so again we see that division comes first from left to right we'll do that piece of it we'll get eight as long as we're doing the the 64 ID 8 before the 8 * 2 that's the important part so notice that the 64 ID 8 give us 8 and then we still have the times two 8 * 2 plus we have some more multiplication we'll take care of that in just a second we got 16 plus the 4 * 4 gives us another 16 and lastly when we add those two pieces together we get do you feel okay with the order of operations idea yes no head yeah or no okay now I believe I did give you a problem that we haven't finished yet from last time the one with the fraction bar did we look at that one yet no we didn't I finished it you did but we didn't do it in class no I'll finish that up right now now what you need to know about these large fractions well that's that's what we have here is just a large fraction is that the fraction bar in implies parenthesis so whenever you see that it says do what's on the top then do what's on the bottom and then divide we can't do anything before that so what I want to write down right now is the fraction bar means parenthesis or implies parenthesis the fraction bar implies parentheses around the numerator the top and the denominator the bottom so what we're going to do on this problem the way you do this successfully you'd ignore either the top or the bottom first and do just one part just work on one part of this so what I'm going to do now I'm going to ignore the bottom I'm just going to work on the top of my fraction and do it piece by piece so when we look up there at the top we're ignoring this part okay we're just going to ignore that for now with the 25 + 8 * 2 - 3 Cub what's the first part we should do quickly we've done this several times now yes okay and 3 cubed is nine right yes 3 Cub some of you guys are not with me today you need to focus in on this stuff 27 very good how'd you get 27 3 * 3 = 9 and you add another 27 perfect so we're going to leave the 25 alone Plus 8 * 2 we realize we're subtracting 27 here and again I'm just ignoring that bottom part of my fraction I'll I'll keep going next step the next thing we do is try to keep going on this thing what's the next thing we would do in this problem great so we're going to have 25 I know that that's going to be 16 - 27 we've got two more steps on the top um quick question you said uh the FR right there fraction bars parentheses yeah but when isn't there already parentheses would you do that first like the bottom part because there's parentheses there it doesn't you get to choose it's like having a bracket it's like a a bracket around the top and a bracket around the bottom that's how I do you can do the bottom first it it really honestly Jeff doesn't matter as long as you do the top independently of the bottom so do the bottom first and then do the top that's fine as long as you're doing one of them all the way to one number and the other one all the way to one number and then together okay good question okay next up what do we have you add great so if I add these together can you tell me what I'm going to have what' you say 41 perfect only one more step we got 41 - 27 gives us 14 so right now we've worked the numerator or the top of our fraction all the way down to a single number that's really the process we want to do we want to stick with it just do it step by step till you get down there next we'll work on the denominator the denominator is going to take us less steps so we'll probably write the same number a couple times but that's okay what's the first thing we're going to do in the denominator parentheses and we're going to have the two stays the same but in the parenthesis how much so the 2 * the one how much does that give us we're going to keep rewriting the two because we had those extra steps here the two stays the same all the way through until we have both just a single number over single number on both the top and the bottom and now we can do what this problem says to do which is yeah we're going to divide 14 / two gives us we're done so it's not so bad if you really consider this to be like three problems in one you've got one problem you got another problem and then the final problem is put it together that's really it try one of these on your own and then we'll continue okay there we are so get corrected on that thing remember you can treat this like three problems do either the top or the bottom first then do the other one then put them together hey by the way how many people just out of my own curiosity have gone on to the website my website good for you how many people have actually watched one of the videos on there good awesome uh for the rest of you if you haven't gone to the website yet you're going to this evening I said this to the people who were here a little earlier um I'm going to put the homework assignments on the website only for the next few days to make sure that you can get on there and and find it okay that way you know that resource I have I do H we just sat The Home Room yesterday I don't think we'll make it through the next section I don't think so so it'll be just just the one I gave you yesterday okay and I'll give that website to you one more time at the end of this class to make sure you can find it did you guys finish up over here okay cool let's do this together then so I'm going to work on the top first I like doing that better than doing the bottom first because otherwise I have to write more fractions at the end I just don't like that so I'm going to start with the top of our fraction here so top of our fraction just like the last one the exponents comes first so we should have written on our papers 7 - 2 * 3 plus this one's going to give us 9 did you get N9 awesome over and we're going to five yeah we're going to fill that in later you can do it at the same time if you really want to if you're good at following those steps I don't really care as long as you know you do the top one and the bottom one independently that's really the key here then we'll do the seven time or minus 6 with our multiplication plus very good plus 9 what's going to come first here if we add if we look at this if we add right now we do 15 you're actually going to get a negative number that do you see that for those of you who have seen negative numbers before if you haven't you'd be like what do we do because it's that wrong thing it's the wrong thing we we do here so we are going to subtract first and get how much perfect we'll continue this on one + 9 that's going to give us 10 we stop there then we work on the bottom of our fraction so the bottom says we're going to do 5 * 2 - 1 that 2 - 1 comes first because it is in parenthesis that gives us 5 * 1 you can have parentheses or or not it doesn't matter 5 * 1 is 5 we'll write that a couple more times two that's exactly right how many we able to get two good if you didn't that's okay why don't you go back and try this again next time if you want to follow this on the video there's you can do that now the last thing that we're going to talk about in this section is just the area of a square now we talked about the area of a rectangle we can do the length times width do you remember that doing the area of a rectangle some of you no no not a bit that was a little while ago it was like last week if we're talking about the area of a square let me tell you a couple interesting things about a square that you probably already know but you probably never really thought about it what's a rectangle fourin four sides okay what makes a rectangle different than this shape that has four sides is that a rectangle no why not equal two equal sides two parallel well that has two parallel sides is that a rectangle no what else makes it a rectangle it's equal on like two different parts okay that's equal on two different parts it's a parallelogram say it louder right angles they are right angles you know what a right angle is a right angle means it's like the the 0 what was it 90° 90° like the the wall on the floor it's a 90° angle it means s sticking straight up perpendicular is another word for that so what we mean by a rectangle is okay rectangles you guys you had all the right stuff down you do you have two pairs of equal sides that are parallel and you also have some 90° angles in here that's a rectangle now can you tell me how's a square different than a rectangle all four sides are equal yeah they are does it still have 90° angles uhhuh and still has two pairs of pillar sides so guess what a square is a type of rectangle every square is a rectangle inherently that's the definition of it not every rectangle is a square here's a rectangle that's not a square every square is a type of rectangle a very special rectangle what that means for us if a square is a type of rectangle if a square is a type of rectangle we should be able to find the area exactly the same way the way we found the area of a rectangle let me erase this junk here the area was if you remember this like the base times the height well that's up to you you don't have to write anything down I would encourage you to but I don't really care so the area for a rectangle was base times height do you remember that from last time we did area well that means the area of a square is going to be the same thing we could could say base times height but watch watch on the board here when a square is well if a rectangle is a square like this we all know something about the sides they're all the same so the sides of this rectangle are S and S side and side they're the same length so when we do the area sure the area is s * s do you see where we're getting s * s that's still the base same as base and right the bases and the height are the same so this would still be base time height it's just we have the same value there is there a different way we can write s * s s Square s squ perfect that's where we actually get the word Square from s s so when we're looking for the area of a square why it's called a square we just take the side itself and square it brings me to my next question if I tell you something's a square how many sides do I need to give you for you to find the perimeter and the area one do you need two sides of it's Square two it's a square say it's 8 in okay I'm going to say this is a square you got me and one side is 8 in how much is this side 8 in this side this side so how many sides do you need if I tell you to a square one just one let's find the perimeter and the area here we'll do it we'll do I want you to do the perimeter on your own actually do them both on your own see if you can figure that out find the area and the perimeter that square it say it's a square a square okay let's get this done uh perimeter perimeter means what's perimeter mean to you okay so we're supposed to add it because it's the distance around that figure so it's the distance around that figure how much is the distance around this figure2 32 8 * 4 now if I'm talking about perimeter please pay attention up here for a second if I'm talking about perimeter should I say 32 Ines or 32 square in for perimeter just inches for perimeter inches that's what I ask you right that's what I'm asking is what should I say square inches or inches if it's the perimeter yeah cuz square inches will be everything right inside yeah that would be the surface right we're just talking about the perimeter means the distance around it so we'd just be like if you walked around this classroom you would get something in feet right you wouldn't get square feet if you walked around this classroom if you counted all the little squares in this okay hey notice squares right you're going to get square feet if you count all the surface of this room that's the area part of this so when we're talking about area I know that one side is 8 in so how much is the area oh how'd you get 64 well when we take remember it's base time height but they're the same number so we can actually just Square it to find the area so you times it yeah by itself on the area of a rectangle we did base time height area of a square we're doing the same thing we're doing base time height it's it just you still happen to have the same base and the same height so we're multiplying that number times itself twice or in other words we're squaring so we're going to get our 64 and in this case yall should have down there square inches or whatever units you used by show hands how many people feel okay with this perimeter and area idea okay if you're still a little rusty on this come and see me or go to the math lab um after this class I'll be there for an hour and I can clarify that for you at this point we're done with Section 1.7 that means your homework that I gave you last time is going to be due when that's right so if you got jump start on already good for you if not you have a lot of homework to do tonight um for the rest of our time here the next 20 minutes