W you said wow yeah and then the uh there was another one I had is it was the quiz was the quiz yeah see one and C but I think it's because I needed paper [Music] all [Music] right oh all right good morning everyone good morning hope everybody's doing great everybody is all right so uh hope everybody had a great weekend today we looking at uh 3.4 I know they're jumping all over the place with the sections but uh this is where we at 3.4 today uh the last class what was 5.1 two and three so now we at 3.4 but uh we're looking at percents we talked a little bit about percents in one of our previous sections um but this one right here just goes all the way into details that's converting between decimals to fractions to percents and so on so we want to make sure we okay with our conversions and then a couple words at the end as well matter of fact when we did the percent problems before we translate into the equation remember you know what percent is of you know we use the is and the of and the equals and all stuff like that so uh so we're going to going to show you a different way of solving those same type of problems and word problems as well so this time we'll look at using proportions but you'll see in a second so the word percent can be broken up into two two words per and Cent uh per 100 you know Cent is the prefix for 100 remember we talked about before how per uh represents Division I believe it this class I said miles per hour miles divided by hour so the percent sign is the same thing as 1 over 100 as a fraction or as a decimal 01 [Music] so the first conversion practice so the first conversion type that we're going to do is decimal to percent so it's no real calculation just process so uh locate the decimal then you going to move the decimal two places to the right and then place your percent sign e all right so here we have a couple examples of how to do that if we have 0.25 and we want to convert it to a percentage take the decimal move the two places to the right and that will be 25% if I have 1.8 once again take the decimal move it two places to the right notice there was only one uh data value or one number to the right of the decimal so we us a zero as a placeholder and that would be 180% question I don't know I get it all right and then for the number seven uh whenever you have a number and it has no decimal involved they assume you know that the decimal is to the right of the right most digit um so you take that value or that decimal move it two places to the right this time we're going to use uh two zeros as placeholders so seven would actually convert to 700% all right so here we're looking at going the other way oh no I was talking to the class you good so we went to decimal to% SN we going percent decimal so we located the decimal then we move the decimal two places to the left this time time and we remove our percent sign so about 37% mov be decimal two places to the left that would be 37 and right here all I was saying is that 0 0.37 and 37 are the same thing so just remind you that zero to the left of your decimal um it's fine whether you have it or not then 2.9% move your decimal two places to the left that be 0 029 using zero as a placeholder and then 6% once again moving decimal two places to left it's 06 that's a decimal [Music] that we use the [Music] because it's always two places no matter what's going on it's always two places yeah after class yes so so I want to mess up the leure and everything so I get you after class for sure just don't let me forget have you you EMA about any questions about this one still up next one so once again those first two processes to the right left accordingly um going from decimal to percent I always think about moving the two to the right and place my percent sign and then the other one Moving Two B to the right to the left um so just think about different ways of room my liit next one percents to fractions so we want to replace the percent sign with one over 100 remember we talked about that in the initial introduction of this uh discussion that percent sign is equal to 1 over 100 so we're going to replace our percent sign with 1 over 100 and it multiply and simplify if possible I know up top all right so looking at 56% once again you're going to start by taking the percent sign and replacing it with one over 100 from there just multiply across notice I rewrote 56 is 56 over one if you want to write it as a fraction that's the same thing 56 over one multiply across 56 * 1 is 56 1 * 100 is 100 so we have 56 over 100 as a fraction now so everybody go okay going up to this point so now from there you have to put your skills to use as far as reducing fractions um notice that 56 is 4 * 14 100 is 4 * 25 cancel out the fours and you left with 14 of 25 now you don't always have to find the largest number what you can do is find the number that you know and then just keep reducing down you know both of them are even so nothing else two can divide into both numbers so you can start there with two divide both of them by two still should have been even you can divide both by two again and ultimately you'll get down to 14 over 25 so if you didn't see that four that's in common with both top and bottom use what you do see and then continue to reduce down till you get your smaller numbers to the smallest numbers possible but you are expected to to reduce if possible before the common factor y greatest common [Music] factor h well when you look at breaking down 14 and 25 14 is 2 * 7 can't break it down in further 25 is five time five they can't break down in fur so they don't have nothing in common with top and bottom they can reduce down so that's where you stop so uh so we look at like I said 14 is 2 * 7 25 is five time five so nothing else can cancels remember the four could cancel because they were in common with top and bottom but nothing else didn't happen with at 14 25 so you just leave it like that same thing as if I had um 10 over let's say six that's 2 * 5 this is 2 * 3 the twos cancel and you just left with 5 over three I can write it and so that's all you have no I was just telling you why we couldn't go any further with the 14 and 25 because nothing else happens you know they don't have nothing else in common so you just Lev with the 14 and the 25 up [Music] another next one 125 125% that's 125 over1 * 1 over 100 same process just rewrite the 125 over one as a fraction so we see a clean multiplication um you don't need it if you understand the process I'm just doing it for Bard purposes but we do need to replace that percentage with one over 100 um so we can do our calculation that'll give us 125 over 100 and then the same thought process what do these two numbers have in common if anything what do they have in common so we see that they have 25 in common and 125 is 25 * 5 25 * 4 25s cancel leave 5 over 4 so we I think you just need it like that yeah all right last one and you may not even see one like this but it's worth talking about one with a decimal 4% so that once again following the same process you replace the percent with one over 100 multiply across that's 04 over 100 now uh a fraction is not truly in fraction form or not truly a fraction if it has a decimal involve so we do need to get rid of that 04 in the den uh in the numerator and the way we can do that is by multiplying by 104 time 10 is just four but when it comes to fractions whatever you do to the top you have to do to the bottom equivalency so that's why multiply both top and bottom by 10 so I can get rid of the decimal in that numerator and that gives me four over a th000 and then from there we can redas both top and bottom by four leav me one over 250 yes in order to get in order to get rid of the j y next conversion fr 2% so we convert a fraction to a decimal by division and then convert decimal to percent like we talked about the ear because once you cancel out that four completely then that's all you left with is one so in other words if you divide four by four you left with one if you divide 1,00 by four you left with 250 well then what are you canceling out in that 10,00 though are you canceling out two or four that you reduce it again and ultimately if you reduce it all the way down you still gonna have one over 250 so if you doing by twos or if you do all in once by by that four ultimately you still going to have that one50 all right so 3 over five 3 over five as a fraction the same thing as three divid by five a throw it in the calculator nobody's um checking your long division skills so you can just do 3 ID 5 and calculator that's 6 and if you move your decimal two places to the right that'll be 60% one more like this so if I have two and 1/4 that two is your whole number so it'll be to the left of your decimal at 1/4 if you um it will be to the right of your decimal actually be the deal part so 1 / 4 is25 and so that's 2.25 we be decimal two places to the right that would be to 25% back of the well these are two different examples that's what you saying soid by four you put that you can just put that in the calculator you get 0 25 n nope going too deep so the two is your whole number that's on the left of your decimal right here talking about that too the 1.4 is decimal to the numbers to the right of your decim and that's all it is so a no no other calculation after you do one divided four to get the 025 there's no other calculation it's just that the two the whole number is to the left of your decimal that two five is to the right of your decimal right here but that's the oneid four the 1/4 remember I saying right here fraction 3 over 5 is the same thing as 3id 5 so 1 over 4 is the same thing as 1id [Music] 4 all right so we're going to uh take those same type of problems that we did before like like what is 30% of 180 and we going to show you a different way of doing it using proportions remember before what we did was what our variable is equal sign 30% we3 of it multiplication than 180 so want to show you a different ways everybody done with that dark blue I want to SP look yeah so we're going to solve those same ones using proportions but uh something you how you want to solve you can use the other method or use this one just I just want to give you more than one way because when we look at the word problems that's right under this proportions might be easier for you to see you know maybe not real see so we have percent whatever your percent number you can just place that over 100 and remember we had is uh is and uh those numbers that we're dealing with you can just do is over U and when we get to the word problems that top number is going to be your part or the partial part of it and your base the bottom then will be your whole your base the uh they just different ways of looking at that top versus the bottom is over e so what is 30% of 180 so like I said the easiest part is the percentage you just place that over 100 that's 30 over 100 what is what is attached to the is of is attached to the 180 so it's just is over so that'll be X over 180 e so now when you have your proportion what you can do is what we call cross multiply think your denominator up to the opposite numerator so that 180 up to the 30 the 100 up to the X because if it's the true proportion that's supposed to be equ that way 30 * 180 is 5400 then of course on the right side we have 100x divide both sides by 100 x is 54 right try it again that was just me rewriting it but it's the same process 40% of what number is 25 so 40% 40 goes over 100 of is our what so that goes on bottom 25 it's attached to ear so that goes on top e cross multiply 40 * x 100 * 25 40x = 2500 IDE 40 62.5 all right I got one more like that before we go to the word problems got it good 12.4 miles is what number or what percent of 80 miles so our percent this time is the unknown so you place the X over 100 12.4 is connected to is 80 is connected to the of so once again it's is over that's 12.4 over 80 your cross multiplication 80x 100 * [Music] 12.4 8X = 1240 / 80 and may be 15.5 [Music] right what's go that couldn't wait to get to this word problem good good good all right so in a recent year the Freshman Class of a university had 18% Asian-American students if this represented 380 students how many students were admitted to the professional class round to the nearest stud somebody chance to write what they trying to do chok you up [Laughter] huh my bad e [Music] all right let's try it out so once again I'm trying this proportional uh setup so 18% is just 18 over 100 now this one the is and the of may not be as evident but what we recognizing is that we had a whole student body and that's what we want to know a whole student body well Freshman Class A whole a whole freshman class and we know that 380 was a part of the whole firstman class so that means when we look at part versus whole the 380 is the part of the freshman class and the whole amount of freshman students that were admitted is what we're trying to figure out or the total amount of freshman that were emitted so that's going to be your bottom number and so that's how we set it up 18 over 100 is equal 380 over than e so once you had a set up then um it's just the same process that you've done in the previous examples x to the 18 18x and then 100 * 380 that be 38,000 divide by 18 that would be 2,11 and then f r for the nearest student so you know that 2011 [Music] [Music] look at another one we got two more this one in one more and then that'll be it so a real estate broker receives a Commission of 3% of the selling price of a house if the broker receives a commission of $1,370 on a sale of the home what was the selling price of the home holding on to the red up top come all right so 3% is 3 over 100 and you're going to receive a 3% commission which is a part of the actual you know selling price so that's like a percentage of the actual selling price and so the commission that the broker receives is 14370 so it means the whole price of the selling of the home is what we're trying to figure out and so that's going to be the bottom number for is the unknown and that part is the 14370 same process do your cross multiplication take your X up to the three take the 100 up to the 14370 that will give you 3x to let's see 1,43 let me get it right 1, 437,000 and uh then divide by three that [Music] put a [Music] com want just try to think about comma shouldn't be necessary you should be a to put it in just like that now if a decimal was needed then yeah you need Comm are pretty much opposite all right questions before we look at the last one for the day see right one more so we got during strenous exercise an athlete may lose two liters of water per hour if the athlete has 55 lers of body water what perc decrease in water will the athlete experience in one hour of strenuous exercise m how you forn uh well first of all you need to look for you know what do you consider your unknown what are you looking for because that's going to be your variable um yeah so in this case it says what percent so we know that that's going to be X over 100 your percent is always over 100 so if you go back to what we had before come on there you go 3% 3% we got the three over 100 so your percentage is always over 100 now that one should be the easy part of establishing the easy the easier part of your fraction your proportion now the other part is recognizing what is the part what is the whole number what is the whole number versus what is the piece of you know the um total so uh that's what this is the part is always going to go over the whole so we say athlete may lose two laders of water but an athlete has 55 L of body water two of that is what you're talking about losing so two is the part the 55 is the whole and so there always the part over the total sobody say [Music] something did you give C1 and just C2 don't know what you mean by that are you talking about the the sections and when you say give what do you mean by give the tit in the chat anybody holding on to the black so once you set up your prop portion then it's all about solving it the same way we' done up to this point uh you cross multiply 55 * x 100 * 2 55x = 200 divide both sides by 55 that'll give you 3636 and what is you know to what decimal they want to the round so in this case they set to 10 place um I don't even know if they said actually in the exercise but I know I was looking at what they asked for in this problem ultimately it was the T they said that's what I sto right there math said 10 10th that's to the 10th place that's the only way the only reason so if they said 100th place you would did 3.64 you know because you around two places so it just depends on what mapb as any any other questions about anything we talked about um in this lecture everybody go [Music] let so everybody good this lecture I'll cut off this [Music] recording it's a decent one I can hold this one