# ve/n3EtyIaFgp0N.xml.gz
# za/n3EtyIaFgp0N.xml.gz

(src)="1"> OK , now that you’ve mastered decimals , & lt; br / & gt ; you now get the next hurdle, which is fractions . & lt; br / & gt ; Now , when we do fractions , & lt; br / & gt ; the same principles that appliedwith decimals apply with fractions . & lt; br / & gt ; So let’s review what some of those were , & lt; br / & gt ; specifically when we wereadding decimals . & lt; br / & gt ; We did stuff like & lt; br / & gt ; 238 . 51 plus 4 . 29 . & lt; br / & gt ; Now you’ve done enough of theseproblems , you’re like, “Uhh , that’s not gonna work . ” & lt; br / & gt ; Right here the decimals aren’t lined up, you can’t really do that problem , & lt; br / & gt ; so you move it over here and you say , & lt; br / & gt ; “OK , 238 . 51 plus 4 . 29 . ”& lt; br / & gt ; Now as you recall , why thatwas so important . & lt; br / & gt ; Here we have the tenths column . Here we have the hundredths column . & lt; br / & gt ; And , like we learned in the beginning, you cannot& lt; br / & gt ; take something like five apples& lt; br / & gt ; plus seven penguins & lt; br / & gt ; and get anything . & lt; br / & gt ; They need to be alike in orderfor adding to occur . & lt; br / & gt ; So here we have five- tenths and two- tenths, that’s where we get the seven- tenths . & lt; br / & gt ; One- hundredth plus nine- hundredths , that would be ten , & lt; br / & gt ; and that’s where we carried the one , & lt; br / & gt ; and so then we would carry on like that . & lt; br / & gt ; Now I’m gonna write out that problemjust a little bit differently . & lt; br / & gt ; We had 238& lt; br / & gt ; and five- tenths& lt; br / & gt ; and one- hundredth , & lt; br / & gt ; and we added it to four& lt; br / & gt ; and two- tenths& lt; br / & gt ; and nine- hundredths . & lt; br / & gt ; Now what really happened over here, we took one- hundredth& lt; br / & gt ; plus nine- hundredths was& lt; br / & gt ; ten- hundredths . & lt; br / & gt ; And that became zero- hundredthsand one- tenth . & lt; br / & gt ; So there was a carrying that happened . & lt; br / & gt ; Remember what we did here : five plus two was seven , & lt; br / & gt ; and we worried about carrying, but here notice we do& lt; br / & gt ; five- tenths plus two- tenths , that’s& lt; br / & gt ; seven- tenths , and then we wouldcarry the one from over there . & lt; br / & gt ; But this actually forms a basis ofwhat’s going on with fractions . & lt; br / & gt ; Right here we were able to add thesebecause they were exactly alike . & lt; br / & gt ; They were both tenths . Here they’re exactly the same, being hundredths . & lt; br / & gt ; And so we are able to leave the realm oftens , hundreds , thousands , millions , & lt; br / & gt ; and we can determineany denominator we want . & lt; br / & gt ; We can determine sevenths , & lt; br / & gt ; eighths , fifths , fourths , & lt; br / & gt ; but the same principle applies . & lt; br / & gt ; So , we can do a problemvery similar to these , & lt; br / & gt ; but instead of saying “tenths” we can say , & lt; br / & gt ; “OK , so two and three- sevenths & lt; br / & gt ; plus five and one- seventh . ”& lt; br / & gt ; Doing this problem , & lt; br / & gt ; we now have the ones column, just like normal , & lt; br / & gt ; tens column , hundreds column , going this way , & lt; br / & gt ; but right here, this is not the tenths column, it’s the sevenths column . & lt; br / & gt ; So we have three- seventhsplus one- seventh , & lt; br / & gt ; and that’s where we get four- sevenths . & lt; br / & gt ; And seven . & lt; br / & gt ; So we’re able to do thatthe exact same way we did before . & lt; br / & gt ; Trying another one : & lt; br / & gt ; 136 and seven- elevenths & lt; br / & gt ; plus & lt; br / & gt ; 251 and & lt; br / & gt ; three- elevenths . & lt; br / & gt ; We’re gonna do this exactly likewe did with decimals , & lt; br / & gt ; except now , instead of the tenths column, we now have the elevenths column . & lt; br / & gt ; So seven- elevenths plusthree- elevenths is & lt; br / & gt ; ten- elevenths . & lt; br / & gt ; Six ones and one one : seven ones . & lt; br / & gt ; Three tens and five tens : eight tens . & lt; br / & gt ; 100 and 200 :
(trg)="2"> I 'm Amber Wild , and I am a BYU- Idaho Pathway student . & lt; br / & gt ; & lt; br / & gt; I had known that I wanted to go back to school for& lt; br / & gt ; & lt; br / & gt; awhile , was at Rhode Island College , but then I& lt; br / & gt ; & lt; br / & gt; stopped to serve my mission .
(src)="4"> We have two divided by two , & lt; br / & gt ; three divided by three, four divided by four , & lt; br / & gt ; five divided by five, six divided by six , & lt; br / & gt ; eighteen divided by eighteen , & lt; br / & gt ; square root of three divided bythe square root of three , & lt; br / & gt ; pi divided by pi . & lt; br / & gt ; We get any number over itself is one . & lt; br / & gt ; And it’s not that it means one , & lt; br / & gt ; but it means that numberthat we call one , & lt; br / & gt ; we call two over two, three over three , four over four—& lt; br / & gt ; they’re all exactly the same thing . & lt; br / & gt ; So we’re gonna do another one here . & lt; br / & gt ; Let’s try to find new names forsomething like two- thirds . & lt; br / & gt ; Now as you look at thisyou’re like , two- thirds , & lt; br / & gt ; same name as two- thirds , & lt; br / & gt ; and you have & lt; br / & gt ; four- sixths . & lt; br / & gt ; You’ll notice what happened isI times by two hereand times by two there . & lt; br / & gt ; Well I just times by two and two, that’s another name for one . & lt; br / & gt ; So I just times this guy by one . That means he’s the same thing . They’re exactly the same thing . & lt; br / & gt ; Here we have six- ninths, if you times by three and three . & lt; br / & gt ; If you times by four and four, times by five over five . & lt; br / & gt ; So we’re using all thesedifferent names to get all thedifferent names for this guy . & lt; br / & gt ; Five over five looks like that . & lt; br / & gt ; Six over six . & lt; br / & gt ; So let’s get some new namesfor this one . & lt; br / & gt ; Two- fifths . & lt; br / & gt ; Times by eight over eight . & lt; br / & gt ; That’s a new name . & lt; br / & gt ; Times by eleven over eleven . & lt; br / & gt ; Times by three over three . & lt; br / & gt ; And you may wonder, “Where are you getting those numbers ? ”& lt; br / & gt ; I’m just pulling them out of the air . & lt; br / & gt ; You can pull out any number : seven . & lt; br / & gt ; Times on top and the bottom & lt; br / & gt ; and there we have it . & lt; br / & gt ; A new name for two- fifths . & lt; br / & gt ; You can go and makea whole bunch of these . & lt; br / & gt ; Let’s do this one . & lt; br / & gt ; New name for three- elevenths, let’s just make a couple of them . & lt; br / & gt ; Times by two over two, we get six over 22 . & lt; br / & gt ; Times by three over three, we’ll get nine over 33 . & lt; br / & gt ; Times by four over four : twelve over 44 . & lt; br / & gt ; Times by five , we get fifteen over 55 . & lt; br / & gt ; Now if you’re able to take theseand transform them into other& lt; br / & gt ; names and vice versa , & lt; br / & gt ; the whole world of fractions& lt; br / & gt ; isn’t so tough anymore . & lt; br / & gt ; I’ll show you what I mean . & lt; br / & gt ; If you look at this problem, we ran into an issue with—they’re not the same thing . & lt; br / & gt ; However , this hasa whole bunch of names . & lt; br / & gt ; It can have a bottom of ten , fifteen , & lt; br / & gt ; 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 . & lt; br / & gt ; This could have a whole bunch ofdifferent denominators as well , & lt; br / & gt ; and you see some of them listed here . & lt; br / & gt ; Notice that that guy andthat guy right there , & lt; br / & gt ; they can add together—they’re like things . & lt; br / & gt ; Here you have 22 fifty- fifths, there you have fifteen fifty- fifths . & lt; br / & gt ; It’s a different name forthe same number . & lt; br / & gt ; So this guy 22 fifty- fifthsand fifteen fifty- fifths . & lt; br / & gt ; Those two add together just fine . & lt; br / & gt ; You have 22 of them andfifteen of them would be & lt; br / & gt ; 37 fifty- fifths . & lt; br / & gt ; So let’s write it downhow we’ve got this . & lt; br / & gt ; When you’re adding fractions—& lt; br / & gt ; step number one : & lt; br / & gt ; you have to get common denominators . & lt; br / & gt ; Now most of the time, like in this one , you’re like , & lt; br / & gt ; “Oh five and eleven , what can I turnboth five and eleven into ? & lt; br / & gt ; Five times eleven—huh, fifty- five they both go into it . ”& lt; br / & gt ; So you can do this based on observation . & lt; br / & gt ; You can do this based onthose two timesing together . & lt; br / & gt ; And then there’s another onethat I’m gonna show you , & lt; br / & gt ; and it’s called prime factorization . & lt; br / & gt ; This is for the big problems . & lt; br / & gt ; But let’s do a couple morethat you can see what thedenominator would be . & lt; br / & gt ; Let’s take one- half plus one- third . & lt; br / & gt ; OK , one- half has a whole bunchof different names . & lt; br / & gt ; It could be two- fourths , three- sixths , & lt; br / & gt ; four- eighths , five- tenths , and so on . & lt; br / & gt ; This guy could be two- sixths , & lt; br / & gt ; three- ninths , & lt; br / & gt ; four- twelfths , & lt; br / & gt ; five- fifteenths , and so on and so forth . & lt; br / & gt ; You notice that there are a coupleof them—this name and that name—& lt; br / & gt ; they’ll work .
(src)="5"> You’ll be able to do it . & lt; br / & gt ; One- half is the same as three- sixths, one third is the same as two- sixthsand you can take , & lt; br / & gt ; “Ah , three- sixths and- two sixths, that’s five- sixths . ”& lt; br / & gt ; Let’s do one more down here . & lt; br / & gt ; If you have & lt; br / & gt ; three- eighths plus—& lt; br / & gt ; three- eighths plus one- sixth . & lt; br / & gt ; Again , think of all the numbers thateight can go into : & lt; br / & gt ; eight , sixteen , 24—and you’re like , & lt; br / & gt ; “Oh wait !
(src)="6"> 24 .
(trg)="4"> But I have found being in it& lt; br / & gt ; & lt; br / & gt; that yes , it was definitely the right decision . & lt; br / & gt ; & lt; br / & gt; I found that when I took the first course , Pathway& lt; br / & gt ; & lt; br / & gt; Life- skills , I got so many answers for just being a mom . & lt; br / & gt ; & lt; br / & gt; And I didn 't expect that at all .
(src)="7"> I’m going to that . ”& lt; br / & gt ; You’ll notice that’s justby observation . & lt; br / & gt ; You’re like , “Hey they both happento go into 24 , that’s great . ”& lt; br / & gt ; You could also do it by multiplying . & lt; br / & gt ; Let’s do it this way first . If we’re gonna make this a 24 , & lt; br / & gt ; it’s gotta times by three and by three , & lt; br / & gt ; so that’s gonna be nine twenty- fourths . & lt; br / & gt ; Right here we’re going to timesby four and four . & lt; br / & gt ; So we get & lt; br / & gt ; thirteen twenty- fourths . & lt; br / & gt ; If we multiplied and we’dget forty- eighths—forty- eight as the denominator . & lt; br / & gt ; Well that’s true , let’s look at that . & lt; br / & gt ; So another name for this, if we timesed by six and six , & lt; br / & gt ; would be eighteen forty- eighths . & lt; br / & gt ; And this one , & lt; br / & gt ; times by eight and eight : & lt; br / & gt ; eight forty- eighths . & lt; br / & gt ; So if we add those two together , we get & lt; br / & gt ; 26 forty- eighths . & lt; br / & gt ; That might bother some of you, that it appears that we gota different answer . & lt; br / & gt ; Well , those two are the same number . & lt; br / & gt ; And this is part of the process that you’re going to do with fractions , & lt; br / & gt ; is make sure you can identifythat those two areexactly the same thing . & lt; br / & gt ; You’ll notice that this guytimesed by two is 26 , & lt; br / & gt ; that guy times by two is 48 . & lt; br / & gt ; That means that this one is anew name for that one right there, they’re the exact the same thing . & lt; br / & gt ; When you take it and take outall the numbers you can& lt; br / & gt ; so you get the simplest form , & lt; br / & gt ; that is called “simplifying . ”& lt; br / & gt ; When you take the simple oneand you make it bigger , & lt; br / & gt ; they don’t have a name for that , & lt; br / & gt ; so I call it “complexifying . ”& lt; br / & gt ; Com- plex- i- fy- ing . & lt; br / & gt ; Because you’re making it lookmore complex even thoughit’s really all the same number . & lt; br / & gt ; So that’s the thing, sometimes when you do the multiplying , & lt; br / & gt ; you might have to do some simplifyingat the very end of the problem . & lt; br / & gt ; So , I’m going to show youprime factors right now . & lt; br / & gt ; This one is a little bit tougher , & lt; br / & gt ; and usually should be reservedfor the harder problems , & lt; br / & gt ; but you need to see it now so thatyou’ll be able to do stuff later on . & lt; br / & gt ; So we’re gonna get a big one here . & lt; br / & gt ; Seven over 72 plus eleven over 96 . & lt; br / & gt ; If you’re anything like me , & lt; br / & gt ; I don’t happen to know my72 times tables off the top of my head . & lt; br / & gt ; I don’t know the 96 times tablesoff the top of my head either . & lt; br / & gt ; Being able to just say , “Oh yeah look, I have a number here that both of thosego into” ?
(src)="8"> Not a chance ! & lt; br / & gt ; I could you know, there’s a good number& lt; br / & gt ; that would work for both of them, and that is whatever 72 times 96 is , & lt; br / & gt ; I don’t know, it’s up in the 6000´s somewhere . & lt; br / & gt ; There’s probably gonna bea lot of simplifying . & lt; br / & gt ; Kind of like on that last problem, we had to simplify once , this isprobably going to give us a lot of them . & lt; br / & gt ; So here , prime factors . & lt; br / & gt ; I have to tell you , & lt; br / & gt ; prime factorization& lt; br / & gt ; allows a mathematician to do to a number& lt; br / & gt ; what a biologist does to uh , & lt; br / & gt ; a worm , or an organism that he’s cuttingup and he sees how it works inside , & lt; br / & gt ; that’s the microscope . & lt; br / & gt ; What a chemist does to chemical compounds . & lt; br / & gt ; Prime factorization is where wesplit the number open and we seewhat it’s made of . & lt; br / & gt ; We find out its genetic code . & lt; br / & gt ; In this case , 72 , if we factor this & lt; br / & gt ; what makes 72 ? & lt; br / & gt ; Six times twelve , or eight times nine, either one of them . & lt; br / & gt ; And then what makes up the six ? It’s a two and a three . & lt; br / & gt ; Twelve is a two and a six , & lt; br / & gt ; and a two and a three . & lt; br / & gt ; So here at the end , we gettwo , two , two , three , three . & lt; br / & gt ; I just kind of like to put themin order , so you know, get the smallest ones first , & lt; br / & gt ; but this right here is the code for 72 . & lt; br / & gt ; You break it down into the numbersuntil you can’t break it down any moreand these are the—& lt; br / & gt ; these are prime . & lt; br / & gt ; That’s what that means, it goes all the way down , & lt; br / & gt ; and you can’t break a prime number downany further . & lt; br / & gt ; So , here’s its genetic code : two , two , two , three , three . & lt; br / & gt ; When we do 96 & lt; br / & gt ; that is , um eight times twelve . & lt; br / & gt ; That’s four times two .
(src)="9"> Two times two . & lt; br / & gt ; Four times three .
(trg)="5"> The answers to my& lt; br / & gt ; & lt; br / & gt; prayers have been , you know , it 's been very evident& lt; br / & gt ; & lt; br / & gt; that the Lord has been answering them through& lt; br / & gt ; & lt; br / & gt; this program .
(src)="10"> Two times two . & lt; br / & gt ; So we get & lt; br / & gt ; two , two , two , two—one , two , three , four , five of them—times a three . & lt; br / & gt ; Now , as we look at these, they’re very similar , really close . & lt; br / & gt ; So what we’re going to do & lt; br / & gt ; If I put any number on here , & lt; br / & gt ; like a five or something like that , & lt; br / & gt ; I could now take and, if I times 72 by five , I get this number . & lt; br / & gt ; If I put a seven on thereI get that number . & lt; br / & gt ; If I put a six on there—six is this , two times three—& lt; br / & gt ; I would get that number . & lt; br / & gt ; So here we’re able to find out& lt; br / & gt ; and create this denominatorthat both of them can go into . & lt; br / & gt ; So I’m going to write it up here, right here I have& lt; br / & gt ; a two times a two times a twotimes a three times a three . & lt; br / & gt ; And over here I have & lt; br / & gt ; Now , if I look at this , & lt; br / & gt ; this guy has plenty of twos , & lt; br / & gt ; but if I put one more three on there , & lt; br / & gt ; then I know that 72 goes intothis number right here . & lt; br / & gt ; But 96 doesn’t go into this one yet . & lt; br / & gt ; I would need—one , two , three , four , five twosin order for that to happen . & lt; br / & gt ; We’ve just created our monster . & lt; br / & gt ; This is how you createa common denominator . & lt; br / & gt ; We’ve split it open, we’ve looked at what it’s made of . & lt; br / & gt ; Now , this number , whatever it is, it’s the same on both of them , & lt; br / & gt ; is our common denominator . & lt; br / & gt ; And I know I have to times 72 by four& lt; br / & gt ; to get this common denominator, so I do it on the top& lt; br / & gt ; and this guy had to be timesed by three . & lt; br / & gt ; So this is 28 over & lt; br / & gt ; four times 72 is going to be 288 & lt; br / & gt ; plus & lt; br / & gt ; 33 & lt; br / & gt ; three times 96 & lt; br / & gt ; is a 288 . & lt; br / & gt ; So that saved me from simplifying a lot . & lt; br / & gt ; So when I add these two together, I get & lt; br / & gt ; 61 over 288 . & lt; br / & gt ; Now while on the subject ofprime factorization , & lt; br / & gt ; this will also help you& lt; br / & gt ; in simplifying very , verylarge fractions . & lt; br / & gt ; At the end , you noticed, we simplified just a little bit . & lt; br / & gt ; I want to talk to you just a little bitabout simplifying right now . & lt; br / & gt ; If you have a very largefraction , such as & lt; br / & gt ; 144 & lt; br / & gt ; over 196 , & lt; br / & gt ; something like that, and you’re not able to tell exactlywhat’s going on with it , & lt; br / & gt ; this prime factorization willallow you to& lt; br / & gt ; get rid of some of those& lt; br / & gt ; common terms that people have takena small number and complexified up . & lt; br / & gt ; You may wonder, “Why in the world do we simplify things ? ”& lt; br / & gt ; Well have you ever thoughtthat if you got a recipe& lt; br / & gt ; and the recipe actually said& lt; br / & gt ; you need to add & lt; br / & gt ; 72 ninety- sixths cup of sugar , & lt; br / & gt ; you’d probably think , & lt; br / & gt ; “That’s dumb . Why would anybody say that ? & lt; br / & gt ; It’s just another name for three- fourths . & lt; br / & gt ; Well , then why not just saythree- fourths ?
(trg)="6"> The reason why I 'm in Pathways , and& lt; br / & gt ; & lt; br / & gt; eventually going into Business Management , is my& lt; br / & gt ; & lt; br / & gt; parents have a business .
(src)="11"> And that’s the idea . & lt; br / & gt ; The simplified version of a numberis the one everybody uses . & lt; br / & gt ; You’re attending college right now , & lt; br / & gt ; people probably ask you your agequite often . & lt; br / & gt ; Can you imaginewalking around and saying , & lt; br / & gt ; “Oh yes , I’m the square root of 361 . ”& lt; br / & gt ; And they would justlook at you very odd . & lt; br / & gt ; It’s the same as nineteen , & lt; br / & gt ; but nobody ever says that . & lt; br / & gt ; I mean , they really think you’rekind of a geek . & lt; br / & gt ; So , simplifying a number& lt; br / & gt ; is just a way to be able to communicate and say , & lt; br / & gt ; “Ah , we really do have the same number, ”when everybody& lt; br / & gt ; on what the simplified version is . & lt; br / & gt ; So you take this thing right here , & lt; br / & gt ; now normally we could see—Oh !
(src)="12"> Hey , look . & lt; br / & gt ; I think a two willgo into top and bottom , & lt; br / & gt ; that’ll be kind of a nice onebecause they’re both even . & lt; br / & gt ; But this prime factorization, if you can pull out & lt; br / & gt ; everything that it’s made of, you’ll be able to tell exactly& lt; br / & gt ; how well it can—it can be simplified . & lt; br / & gt ; So , on this one , & lt; br / & gt ; So , on this one, we would break it down like this—& lt; br / & gt ; I’ll let you do that—144 is , like , twelve , twelve . & lt; br / & gt ; And so , this would be the same as & lt; br / & gt ; twelve & lt; br / & gt ; times twelve . & lt; br / & gt ; So I did twelve and twelve . & lt; br / & gt ; And then on the bottom, this is fourteen times fourteen , so & lt; br / & gt ; Now what this is , we broke it downas far as we couldwith the prime factorization& lt; br / & gt ; and now it’s very easy to see :
(src)="13"> Oh ! & lt; br / & gt ; Here’s a two over twothat somebody put on there—take it off . & lt; br / & gt ; Here’s another two over two . & lt; br / & gt ; Take that one off . & lt; br / & gt ; And so we’re left with& lt; br / & gt ; four times nine is 36 & lt; br / & gt ; seven times seven is 49 . & lt; br / & gt ; And what this does is tell you for sure& lt; br / & gt ; there is nothing elsethat will ever come out of those numbers& lt; br / & gt ; because we broke it downto its very basic form . & lt; br / & gt ; OK , so minor digression on simplifying, let’s come back here, this is how we’re adding fractions . & lt; br / & gt ; Common denominators . Observation’s gonna be the easiest one, by all means . & lt; br / & gt ; You’re going to be able to say , & lt; br / & gt ; “Oh yeah , common denominatorlooks like twelve, or looks like fifteen , or 24 . ”& lt; br / & gt ; If you’re not able to tell exactly , & lt; br / & gt ; you can always multiply the two numbers, and that will get you& lt; br / & gt ; a number that they both go into . & lt; br / & gt ; You may have to do some simplifyingwith this one , and on the big ones—& lt; br / & gt ; I think there’s only a couple ofproblems on your assignments , & lt; br / & gt ; but this’ll be one to work together on . & lt; br / & gt ; OK , so get common denominators . & lt; br / & gt ; Two now , the denominators , & lt; br / & gt ; they’re the ones on the bottom . & lt; br / & gt ; If nobody’s ever told you yet& lt; br / & gt ; why they’re called “denominators, ”you need to know . & lt; br / & gt ; When you have a fraction , like & lt; br / & gt ; three- fifths , & lt; br / & gt ; I’m gonna write it out like this, “three- fifths . ”& lt; br / & gt ; When you cut up something intofive parts , each one of them is a fifth . & lt; br / & gt ; And this is telling you what you have . & lt; br / & gt ; Like in currency , & lt; br / & gt ; you can have a twenty- markdenomination bill , & lt; br / & gt ; a twenty- dollar denomination , & lt; br / & gt ; ten- dollar denomination , & lt; br / & gt ; two hundred- peso denomination . & lt; br / & gt ; Denomination is how you are telling& lt; br / & gt ; what you’re dealing with , & lt; br / & gt ; and this is telling how many you have , & lt; br / & gt ; so you are enumerating these things . & lt; br / & gt ; So that denotes & lt; br / & gt ; that’s why it’s a denominator, it’s saying , & lt; br / & gt ; “Aha , this is a denomination, we’re talking about fifths . ”& lt; br / & gt ; And this is how many there are , & lt; br / & gt ; and so that is why thisis called a “numerator . ”& lt; br / & gt ; That’s why this one is called a numerator & lt; br / & gt ; and this is a denominator . & lt; br / & gt ; So , once you have the same denominator , & lt; br / & gt ; that means you’re now adding like things . & lt; br / & gt ; So when we do it, when we have like things , & lt; br / & gt ; we count up the total ofhow much we have . & lt; br / & gt ; So in this case , you add the numerators & lt; br / & gt ; also known as adding the tops . & lt; br / & gt ; And then & lt; br / & gt ; like we did before , & lt; br / & gt ; if you’re gonna carry , you have to carryby what you’re talking about . & lt; br / & gt ; If it’s fifths, once you get five of them, you have a whole thing and you carry . & lt; br / & gt ; If you have twelfths, you carry with that . & lt; br / & gt ; An easy way to remember this& lt; br / & gt ; is if you’re dealing withdays of the week , & lt; br / & gt ; each day of the week is a seventh . & lt; br / & gt ; And so if you talk about& lt; br / & gt ; how many days make a week, once you get seven- sevenths of a week , & lt; br / & gt ; it carries over and it’s a whole week . & lt; br / & gt ; So you’re gonna carry& lt; br / & gt ; by the denominator . & lt; br / & gt ; And then finally & lt; br / & gt ; you have to simplify& lt; br / & gt ; at the end so everybody’son the same page as to what numberyou’re really talking about . & lt; br / & gt ; This is very similar to whatyou’re gonna do with subtraction , & lt; br / & gt ; so we better do a coupleof subtraction problems to make sureyou’re OK with that . & lt; br / & gt ; You know in subtraction , we have & lt; br / & gt ; two- thirds minus one- fourth . & lt; br / & gt ; You can do the same thing, we’ve got to get common denominators—& lt; br / & gt ; addition and subtraction we alwayshave to do like things . & lt; br / & gt ; So , two- thirds minus one- fourth, can you think about what thecommon denominator might be ? & lt; br / & gt ; Two- thirds minus a fourth . & lt; br / & gt ; If you can’t , go aheadand write out a few of these : & lt; br / & gt ; two- thirds , four- sixths , & lt; br / & gt ; you keep going but you’re like, “Wait ! ” Three , six , nine , twelve , & lt; br / & gt ; “Ah , twelve is what it’s gonna be . ”& lt; br / & gt ; So , on this guy I’d have totimes by a four , & lt; br / & gt ; times by a four, so you get eight- twelfths minus & lt; br / & gt ; minus , in this case, I’d have to times by three , & lt; br / & gt ; times by three : three- twelfths . & lt; br / & gt ; So , eight- twelfths minus three- twelfthsbetter be five- twelfths . & lt; br / & gt ; Good deal . & lt; br / & gt ; Let’s see if you remembernegative numbers really well . & lt; br / & gt ; If you had & lt; br / & gt ; two- fifths minus seven- eighths . & lt; br / & gt ; Here we’ve got to get acommon denominator , very first thing . & lt; br / & gt ; You can do it by observation . If you can’t think about it, go ahead and multiply the two . & lt; br / & gt ; Five times eight :
(trg)="7"> They own a gymnastics school , & lt; br / & gt ; & lt; br / & gt; and so I feel like it 's a really good course of study& lt; br / & gt ; & lt; br / & gt; for me to take to help us help it grow . & lt; br / & gt ; & lt; br / & gt; I would say changes that I' ve noticed in myself , & lt; br / & gt ; & lt; br / & gt; is being able to manage my time better because I& lt; br / & gt ; & lt; br / & gt; have to .
(src)="14"> 40 . & lt; br / & gt ; That is what’ll be a nicecommon denominator , & lt; br / & gt ; you get—times by eight , times by eight—& lt; br / & gt ; sixteen over 40 minus—times by five times by five—& lt; br / & gt ; 35 over 40 . & lt; br / & gt ; Ooh !
(src)="15"> Sixteen minus 35, how well do you remember your negatives ? & lt; br / & gt ; You’re starting at sixteen andyou’re subtracting 35 , & lt; br / & gt ; which means you’re gonna go past zero, you’re gonna end up down in the negatives , & lt; br / & gt ; and that’s what happens—this number’s really bigger , & lt; br / & gt ; so it’s stronger—they’re tug of warringagainst each other , & lt; br / & gt ; you have sixteen fortiethspulling positive , & lt; br / & gt ; 35 fortieths pulling negative—& lt; br / & gt ; this guy wins . And so you subtract these two—& lt; br / & gt ; 35 minus sixteen—& lt; br / & gt ; and the negative guy wins . & lt; br / & gt ; So negative nineteen fortieths . & lt; br / & gt ; So if we do this with subtraction , & lt; br / & gt ; there are a couple thingswe have to add here . & lt; br / & gt ; So , you’re going to add orsubtract numerators . & lt; br / & gt ; We’re gonna do a problemwhere we’re gonna borrow now . & lt; br / & gt ; 428 and & lt; br / & gt ; two- sevenths minus& lt; br / & gt ; fifteen and & lt; br / & gt ; four- sevenths . & lt; br / & gt ; So we have this age- old debate now . & lt; br / & gt ; We’re doing the same thingbut just decimals , & lt; br / & gt ; we can’t—we don’t have a decimal point , & lt; br / & gt ; we’re now dealing witha sevenths column . & lt; br / & gt ; So this could be considereddays of the week . & lt; br / & gt ; If this is 428 weeks and two days , & lt; br / & gt ; that’s 428 and two- sevenths weeks , & lt; br / & gt ; minus fifteen weeks and four days, that’s fifteen and four- sevenths weeks . & lt; br / & gt ; This is the age- old debate : & lt; br / & gt ; two minus four , can you really geta number from two minus four ? & lt; br / & gt ; I mean , you take & lt; br / & gt ; If I have two carrots on the tableand I go and steal four of them , & lt; br / & gt ; you think, “It doesn’t quite make sense . ”& lt; br / & gt ; That’s exactly what’s going on , is—& lt; br / & gt ; that we have to takea whole thing right here , & lt; br / & gt ; so we’re down to seven whole weeks . & lt; br / & gt ; How many days does it make ? It makes seven of them .
(src)="16"> Notice & lt; br / & gt ; it turns this into nine- sevenths . & lt; br / & gt ; You’re not going to cancel thisand put a one out here , & lt; br / & gt ; you’re not borrowing tenof them at a time , & lt; br / & gt ; you’re cashing in a whole thing hereand you’re getting out so many sevenths , & lt; br / & gt ; you 're getting out seven sevenths . & lt; br / & gt ; Now you’re able to go : nine minus four , that’s five- sevenths , & lt; br / & gt ; seven minus five is two, two minus one is one , & lt; br / & gt ; four minus zero is four . & lt; br / & gt ; 412 and five- sevenths . & lt; br / & gt ; So & lt; br / & gt ; see if we can do one more of those . & lt; br / & gt ; 300 uh , yeah 35& lt; br / & gt ; and & lt; br / & gt ; eight- elevenths minus & lt; br / & gt ; 149& lt; br / & gt ; and three- elevenths . & lt; br / & gt ; Now , at first glance, this doesn’t look so bad . & lt; br / & gt ; You’re like , “Oh , that’s not so bad . Look , eight minus three, that’s five- elevenths , good deal . & lt; br / & gt ; Five minus nine—OK, we’d have to borrow from the three ”& lt; br / & gt ; But then you start walking out hereand you’re like , & lt; br / & gt ; “What do—there’s nothingto borrow from out here . ”& lt; br / & gt ; When we’re doing subtraction , & lt; br / & gt ; there’s kind of a first step, step zero , up here , & lt; br / & gt ; You’ve got to set it up . & lt; br / & gt ; You’ve got to get—& lt; br / & gt ; subtract with the big guy on top . & lt; br / & gt ; So step zero , you’ve got to subtract & lt; br / & gt ; with the biggest on top , & lt; br / & gt ; Or the strongest, if you want to [ call it ] . & lt; br / & gt ; We’re gonna rewrite this . & lt; br / & gt ; You have a negative 149and three- elevenths& lt; br / & gt ; and 35 and eight- elevenths . & lt; br / & gt ; Now I put the minus sign here, we’re still going to be subtracting , & lt; br / & gt ; there’s still a minus sign here, but just put the biggest one up on top . & lt; br / & gt ; It’s gonna make life a lot easier for us . & lt; br / & gt ; Now we can borrow, there 's eight of those and it gives us—& lt; br / & gt ; we’re talking about elevenths now, not tenths—& lt; br / & gt ; so it gives us eleven of them, so we really have fourteen- eleventhsout here now . & lt; br / & gt ; Fourteen minus eight : six- elevenths . & lt; br / & gt ; Eight minus five is three, four minus three is one, and then you have a one . & lt; br / & gt ; Now the idea—we just subtracted , & lt; br / & gt ; but this guy—in the tug of war between thesetwo numbers , this guy wins & lt; br / & gt ; so the overall answer will be negative . & lt; br / & gt ; And that should take care of addition, subtraction of fractions , & lt; br / & gt ; so remember we’re carrying—& lt; br / & gt ; or in this case borrowing—& lt; br / & gt ; by the denominator , & lt; br / & gt ; and then we’ll simplify . Now we’ve always got to remember& lt; br / & gt ; that when you’re subtracting, the biggest guy will win . & lt; br / & gt ; So that takes care ofaddition , subtraction of fractions, now we get the easy part . & lt; br / & gt ; We get & lt; br / & gt ; multiplication and divisionof fractions . & lt; br / & gt ; Now , we’re also gonna go back to decimals& lt; br / & gt ; for how we learn this one . & lt; br / & gt ; When we have something like& lt; br / & gt ; 2, 000& lt; br / & gt ; times 40 , & lt; br / & gt ; and you could actually do this out2, 000 plus 2, 000 plus 2, 000 plus 2, 000and see what you get . & lt; br / & gt ; We ended up with eight and four zeros : & lt; br / & gt ; 80, 000 . & lt; br / & gt ; Now we’re going to break that upa little bit .
(trg)="8"> You know , I have to be on top of everything& lt; br / & gt ; & lt; br / & gt; or else the house is a disaster , especially this& lt; br / & gt ; & lt; br / & gt; semester there 's a ton of work , there 's no way& lt; br / & gt ; & lt; br / & gt; I should able to get it done and yet , it is done . & lt; br / & gt ; & lt; br / & gt; Besides that , there 's such an increase of the Spirit in& lt; br / & gt ; & lt; br / & gt; my life because each semester we 've had Institute , & lt; br / & gt ; & lt; br / & gt; and now it 's Teachings of the Living Prophets , & lt; br / & gt ; & lt; br / & gt; and besides that in the other courses , you know English , & lt; br / & gt ; & lt; br / & gt; Math , Life- skills , it 's not just recommended that you& lt; br / & gt ; & lt; br / & gt; learn by the Spirit , but it 's absolutely necessary . & lt; br / & gt ; & lt; br / & gt; It 's such a blessing to be able to increase my education& lt; br / & gt ; & lt; br / & gt; and get my degree at this time in my life .