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Pre-Algebra 7.3 Using the Percent Proportion

Added May 16, 2021 •

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there's a formula on how to use a percent cuz if I'm like you know some number is blank percent of some other number so that's pretty much what it comes but what about those two numbers how to differentiate so the noon 10% time original equals the new number what percent of this number is that number that's the formula percent times OG equals new percent X original equals new that this came from and that's what we're doing today that's called the percent proportion so someone even call this like cuz that's the whole thing there are percents that are bigger than 100 that shows versus you know what it is it's like a you can have 275% of an original means it's a bigger number instead of a fraction 7% this is still a proportional equation and I'm going to try this in algebra one you're going to come across in a lot is called well this year we call that y equals k x k is the constant of proportionality button actually becomes y equals MX M and K are the same thing it just depends on the type of equation we use it or so it switches up so there's no real difference between emmentaler technically the same but if you look at this right here it's y equals percent X it's the same thing you know sometimes they called the but that's the whole thing what if your percent is bigger than 100 it's a growth a lot of people are stuck thinking the percent is 100% or less don't get caught up in that just think about what's the original number one to begin with what's the new number that we're going to use but in a it's but all of this started with upper portion so proportion 8% is just a fraction we have the parts Over the Hole it's a fraction a piece of something over the whole amount and when we call based on a hundred percent a percentage based on 100 and your percent whatever you the number is up here that's your percent so if you look at this and leave this your whole and your 100 are based on pretty much the same thing so jumping ahead how does this become this this is what we're going to play with we're going to take all right what's the piece that we have what is it out of it as a whole and then we're going to do a cross product 102c what are percentage and its bad easy but how does this become this I take a percent of a number another number if we want to use this wording right here if you want to use this wording percent X percent time the hole holy original equals your part which is your name this right here is based this is pretty much what makes algebra hard for a lot of people notice I didn't throw any number these are ideas what I'm creating our rules math laws math for me using words in place of numbers and so when you have numbers that's what makes algebra heart do you know where to place them when it gets further and further lawn algebra to calculus trigonometry discrete mathematics better than what we're doing now and then you know you got to be weird like Elon Musk figure out stuff like that cuz the whole thing is I'm going to try this our basic propulsion system is Antiquated compared to the UFO aliens I believe in them cuz our basic jet propulsion system does not I will not give us quote-unquote Lightspeed technology and that's how we're going to actually become what are they call it voyager's of space in a 2 floor Space Explorers of spaces go with that cuz it's too slow and then some people talk about you watch all these movies where they have a cryogenic chamber of cryogenic chamber and watched enough movies those I'd be scared what is the cryo cryo system gets messed up and then it doesn't you can't wake up your Frozen Anna Anna Anna Anna and I might as well call it a coffin or oxygen not a horror movie it's just a thriller what if you wake up in your cryo chamber cuz there was a malfunction and you can't get out something when he goes to do chaos theory and figure out how to use black holes or attic Lightspeed technology or warp speed AKA give me the holy say hey what's the percent you can always figure out percent by going part divided by whole equals percent over 100 and it's just a cross product so let's look at this find the percent 12 is what percent of 32 and if you translate this question it literally he comes this formula watch this right here what is the word is in math what is the word is in math Tran this is stuff you get in yes will do that in a bit thanks for letting me know. Equal 12 equals that means the 12 by itself notice the number sometimes they sometimes they slip it around so yeah the part comes first then use Flash part equal and look at this and the word of means multiply percent x 32 we're missing the percent so how do you find the percent look at this right here start over the whole the new think about this how would you get the percent by itself and this is algebra right here how do you get percent by myself I would divide both sides by 32 and look at this percent X 32% x one that leaves you the percent and then we get this fraction 12 over 32 Your Parts over your whole equals your percent now the whole thing is the percent is literally the percent you're going to get a decimal 12 / 32 is a decimal the decimal equivalent of your percent that's why you got to go in and put it over 100 and whatever that number is your percent you get rid of the decimals divided by a hundred on this side and what do you got to do all you got to do is take the cross product so cross product is 12 * 112 hundred equals 32% but you know let's divide internet mean fly bites we call it pee should have called it plmp cuz we don't want to think that number should you be sent 32p so let's get peed myself / 32 / 32 and if I / 4 / 4 I get paid if I divided by 4 I get 300 then I can / 8 60 / 4 / 4 / 2 I get 150 and 4 / 150 while I'm not good enough so I should do the division algorithm 150 / 43 * 12 bring that down with a 3/4 goes into 37 * 28 bring it down I get a zero 37.5 equals P totally correct you people that put it in the chat but P stands for percent so 37.5% this is algebra and this is where people get mixed up where and what season number is mean is if you understand word problems and Lexa plugging things in is not an issue and do you need to go do all of this know you can go straight to the this setting it up as a fraction equals a percent over 100 you don't need to do all this I'm just showing you where it comes from him what we're going to end up doing in the next lesson so try these two out on your own to make sure you know what you're doing 15 equals what percent equals what percent 20 and I'll set it up for you and then the next one what percent 5 is 12 social problems do these to make sure you know what you're doing if you have a 15 is what percent remember you just got to know the formula part or news up to you I like to use new and original but they let's go with the stairs so let's stick with their name part equals percent time the whole and of course it is part over whole heart over the whole equals percent over 100 the park 15 over the 20 equals your percent and I'll call it pee over 100 keep it simple leave this right here 15/21 thing you can easily do if you have it over 100 you don't need to do the cross product another thing I'll do the crossfire II but if you can make an equal fraction you can find what that number is 20 times what gets you a hundred 20 * 5 what you do in the denominator do in the numerator whatever that is equals / 115 * 5 that's seventy-five 75% some people simplified it some people simplifying at 3 or over 4 and you knew that was 75% lot of different ways to do this but let's do the cross product has a lot of people went and did that one if I was going to cross product I would always simplify my fraction first then take the cross product let's say you didn't do that Cash 5 is 20 p equals 15 * 100 is 1500 / 20 cross that out what's half of a 5075 Kiest and 4% in this case so 75% all right what percent of 5 is 12 so we're looking for percents do but I arranged it this is percent X Pole equals part so then let's switch it up now my percent let's call it pee equals part over the whole my part is 12 over the hole is 5 so it is a mixed number or improper fraction or over a hundred more than 100% 5p equals 1200 / 5 / 5 was 1200 / 5 of the top of my head imma do my division 5 goes in at 12 two times and that's 10 bring down a 0 foot was in that for 240 so P equals 240 percent watch out don't flip it don't automatically think that the smaller numbers on top that's why you got to watch that and read to those two guys that got the 41 play 66 or 67 yeah you got to watch out it's Lexa don't remember what is the part what is the original that's why I go so we we thought that well was the whole but five was the whole it increased so read Lexa super important right Leslie the next one instead of finding the percent let's find one of the other pieces so this next one talks about finding the part find the parts and the part is the peace by what is equal to song if its 15.5 percent let me rewrite it 15.5% 450 is what and that's why you want to write down that formula translated so you can tell what's what so you got 15 let's translated 15.5% of 450 is which is equal and one right there where it is equal to what and remember your percent times our whole equals your part and that's all we're looking for and some people want to put an X there instead of the word part I'm going to leave the word in the variable and this was all we got to do is you can change it to a decimal times 4500 equals a part and that's what I would have done in years and years past I was just X move it over 450 x .155 and then I do that multiplication I hear that but I'm going to show you the person set up most of the time easier over your whole I'm looking for my part I have my whole 450 equal my percent my percent is 15 25 / 100 that's pretty much my thing right there so I take my cross product is my part times 100 equals 50 18.5 * 450 all I'm doing is getting myself and then I / 100 I just rewrite it whatever this is is my part I don't deal with you know and the whole thing is what's good about this is I do deal with side percents so look at this right here I can simplify this I could cross this is zero out cuz it gets rid of that zero right there / 10 / 10 15.5 / left but hey I don't want to deal with this decimal so if I multiply it by 10 and move it over one space while then I got to move this back one space so I get to 155 5 * 45 / 100 and then I simplify this hot mess whatever that is what is that 6000 975 someone said over 100 and that's the whole thing Adesa places right here if you want to get rid of your zeros and that's why that's the only reason why I don't like this the proportion changing it from this to the 66975 / 100. Is the part my PC 69.75 it's all that the vision work you could have just multiplied that right away and then the but you could have just multiplied up here it would have been quicker but this right here for some reason people don't like decimals it's how you like it let's go with that it's a preferential place you know they like milk chocolate do you like chocolate plane Eminem Eminem's with peanuts you know you still get the same thing in the end try these two make sure you know what you're doing what's is 11.4% of 330 and then find 15.3% 425 should I was once that as a question where the other ones said as a statement and use the same thing learn how to do percents cuz it's what number is so let's set up as a proportion so we know we're looking for the part part over the whole art over the hole which is 3:30 equals 11.4 / 100 it's a nice way of setting it up but like I said some people like to set it up as this equation you can do it this way I will never trip if you do it this way cuz it's the same things when people get let's go what number is part equals 7.4% * 330 but we never met find Westside % you can change it to a decimal remember twice right is bright and I forget that acronym party quiz move the decimal place over to time point 11 for 3:30 look at that right there and all I can do is multiply this proportion a lot of people like that and look at 3:30 * 11.4 cross product equals 100 times my part and I get a divide 100 technically the same thing right here and if I get rid of my decimal places and I move it over whatnot times it by a hundred you get this right here it's the same sing 7 set of dealing with one decimal places with two decimal places that 3 1 vs. 3 Let's just that's where that came in so I'll just do that right there so you know 330 device zero and then I got three times for that's a to carry 1343 yes I put in 202-433-0267 and then how many decimal places three decimal places so my part is 37.62 super easy and this is what we're going to do next lesson technically you know but the proportion is just sometimes you can tell when the proportion is a betterment when you get a messed up when you get a messed up percent this way when you get a nice hole clean percent the proportion method is better what's 15.3 over 100 equals I don't know I'm looking for the part 4/25 / this over so technically it's a hundred fifty three over a thousand equals my part at 4:25 and then I take my cross product it's time is this 425 equals my part * 1000 + / and then I can simplify 17 17 17 if I buy 25 or that + 40 40 and then I just do that so I get 153 * 17 what is that twenty one two I got a 35 37 carry a 310-0351 added going to get 110 Carolina 2601 / 40 this goes in that 6 * 242 get 22 a woman goes into a 5 x I get 200 I get a one at I'm going there at 10 but it goes into 100 2 * 2 * 80 240 goes into 205 times 65.025 serious if I was going to do this in real life I would estimate instead you know I would not go 15 points that's the exact number but you could come close to it but estimating 15 15.3% I would have did 15 / at 4:25 and then I would say okay 15% 15 is 10 and 510 percent of 425 is 42.5 and then half of that would be 5% at 42 will be 21 21 25 21 + 42 would be 6363 7563 75 50% I noticed that right there 65 you're off by a little bit so if you guys are going to do stuff like this on the SAT calculated I use Simple Mental Math my estimate and multiple choice multiple choice is the mated at 15% to get about 63.75% I know I'm going to be off but which ones close a 65 is closed to 63 and I know it has to be bigger cuz it's three more scn the next one find the whole number this is the one that takes the most time 78 is 60% of what and just to see why it's set up in the proportion the way it is remember if part over whole equals percent over 100 where does songs from is from the literal translation 78 equals 60% of blank x o x at The X X Pole to get the 60% by Subway / I should have / the percent cuz I want to figure out what the whole is but let's just set up as a proportion / 60 / whole 78 / your hole and what's left is your percent 60% change 60% into a fraction 60 / 100 and then you just take your price product 7800 equals 60 whole / 60 equals your hole crossout my zeros 780 / 6 wasn't it one time 830 South 138th Circle not too bad it's just a bunch of manipulation of numbers so try these last two out to see your what you're doing this so 30% what is 63 and then 45 is 3% of what and the thing about percent problems all that is plug-and-play you're off and this is most of algebra you have three different variables we have the whole number we have the part number and we have the percent three variables in almost all of mash even if you have more buried you're always given everything but one that sounds super one in algebra one you're giving all your variables but missing one that's what you're solving for and algebra two you're going to be learned what if you're not given all the various but you're given the variables in different situations you're going to be able to come up with an expression for one of the missing Ones based on another variable so then you can buy those two expressions a lot now I know but when you get there you'll see and then you're left with only one unknown and once you find that one unknown you plug it back in to find that second and known you were basing it on another variable yeah a lot of things trust me it'll be easy when you get there but I understand you're always given almost all your variables plug it in and comes out okay let's go do it so 5% and easy thing to do if you want to change a percent to a fraction remember percent over 130 over 100 that is equal to my piece is 63 over what and that's my whole 45 equals 3% 3% of 3 over 100 times that while that's my whole that's how you see any of the stuff is just setting it up notice it's only one another that's all it was not always an algebra one is always one unknown an answer you're going to have to on and you'll learn how to solve it Beth the systems of equations you'll get there 6300 equals 30 whole and then we divide 30 / 30 cross that out like a 120 110 210 210 watch what that's why you got to set it up read it look at this the percent is the easy part that's a percent so rude Amber gray hair heart over the whole equals percent 130% of what 30% that means of what is my original number that's my whole number 30% of what is 6363 is my so Parts over the whole and change your percent over 100 so you set it up as that and then take the cross product 63 * 160 330 * your hole whole 6300 equals 30 whole but then I got the whole number by myself so I divided by 30 divided by 30 so then 30 over 30 is at 1 and then this is 0 + 0 across is 630 / 3 210 and then this right here 45 take a cross product 4500 equals 3 times my whole divided by 3 divided by 1500 thousand five hundred I get it while you guys mixed up the numbers that's the most common thing to do but don't just don't just look at it and do the cross product understand the placement that's the next level have higher level math word problems and even if it's not a word problem the stinking is word problem like don't just do stuff with the numbers thanks where they go and how to set it up here there's a shortage of remembering which doesn't really help you learn but if you're looking for the percent if you're looking for the percent you setup your fraction is p over 100 the unknown is your percent so you have your fraction you just got to make sure your fraction setup your part over your whole is percent over 100 what if you're looking for the part I'm looking for the part I'm looking for the new thing it's always been Raider over the whole equals your percent over a hundred what if I'm looking for the whole number it's your part over the whole week was your percent notice how it's always only one variable you're looking for and that's it right here the table shows the the table shows batting statistics for one season for Derek Jeter of the Yankees if he had 639 at-bats what percent of his at-bat were singles round to the nearest so they give you a list right here some of these are totally worthless right here we're not going to use all of them so he had 639 at-bats we're looking for a percent and what percent his at-bats were singles you had a hundred fifty-one 151 out of his hole 639 South 151 out of 639 looking for what percent and we're looking for the percent percent out of 100 so cross product 151 what's up is what I'll put it in a second and it's then and that's the whole thing but I want the percent by itself across from right here what's a percent so then can I simplify this that's a messed up looking number right there 1000 front 150,000 100 / 639 calculating that your percent is just this hot mess right here I'm just going to give it to you it's 23.6% s o hot mess up simplifying that all right so let me go look at when I put it so let's read let's read this carefully. And we'll do the number four on top of it if you want to sell the whole thing is understanding remember the percent proportion is the part Over the Hole your percent number to technically just meet that telling you that's your percent but to change this percent you want to change it to a fraction when you change a percent to a fraction member a percent is just a watching over 100 without the percent start so it is technically it is the percent number we get rid of the percent sign it's the percent number over 100 I'm using that not to close so it's like if I had 73% what is that as a fraction is 73 over 100 if I had some messed-up decimal percent like 68.4 2% that is 68.42 over 100 so change a percent to the fraction so that's what they're asking us to do as a proportion when they say Over the Hole it is part Over the Hole equals the percent number without the percent sign percent number over 100 let's go to the start so it tells us that Derek Jeter had 630 and this is science using science 639 at-bats that's not a percent it's not a dozen that's literally how many times he stepped up to the plate and that's the thing it helps if you know baseball well if you do understand that you might change things so 639 at-bats and it says how many were singles round to the nearest tenth all we got to run to the nearest 10 I didn't do that looking at this right here here are his stats and singles is doubles and triples home runs walks strikeouts that stuff there's just to confuse you but if you add all of this stuff up if you a dog that should be 639 akeno is there a pop-up and flies that doesn't even count so it's actually lesson 6:39 so but we don't care about the rest of the singles so 151 out of what a hundred 51 out of 639 at-bats 151 we're singles out of 639 at bat so right now it's not a smoke and then we have some percent we don't know what it is I'm a right-to-work percent cuz that's all we're looking for out of a hundred cuz that's the number that's going to be the percent and then we take a cross product 151 * 100 equals 639 * 2% so this is 15100 equals 639 percent then I got to get percent by itself divided by 639 and then that's a one whatever this number is / Alaska 15100 / 639 so we get this jacked-up decimal 23 find 6306 Madison round to the nearest tenth tenth is one decimal place so we got to look at 1 back that's a 3 that's less than 5 so we just cut it off 23 .6 but it's supposed to be a South since that's a percent 23.6% it's not there's no decimal at all there's no decimal for the point is that we're not that's not a bad thing I was just how many times he's a tad late but are you just plug it in don't change anything until you got to do something with it. Only time it becomes a decimals when we divide 639 noticed none of these numbers are decimals yet nothing's a decimal nothing is a decimal nothing is a decimal now we got the percent by so let's change this into a decimal so that means we divide still not a decimal and then we just got to go in how many times does 8 go into 151 with 639 goes into it was it one time so we subtract 639 and we get some messed-up thing we get one that's ten 7 and then we got to borrow 7 turn down a zero goes into a 5 x that's my fault I messed up to Sienna Safari subtracted by 2.2 3 mag goes on so so on and so forth so that right there you keep on going to get 23.6 there's your decimal and then that's supposed to represent your percent don't just do math is to try and the number understand which part it is this represents the percent that's why whatever we get is the percent the pieces what's a whole piece what's up heartbeat but it got nothing else.

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Pre-Algebra 7.3 Using the Percent Proportion

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