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so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | maybe spiral it around snugly like this . maybe make it into a square . maybe wrap it into a hexagon with a nice symmetric sort of cycle to the flappy parts . | how do you make the six sided hexaflexagon ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and by you , i mean arthur h. stone in 1939 . anyway , there 's lots of cool things you do with a strip of paper . you can fold it into shapes and more shapes . | what 's a mobius strip ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | maybe spiral it around snugly like this . maybe make it into a square . maybe wrap it into a hexagon with a nice symmetric sort of cycle to the flappy parts . | how do you make equilateral triangles ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and by you , i mean arthur h. stone in 1939 . anyway , there 's lots of cool things you do with a strip of paper . you can fold it into shapes and more shapes . | what is a `` mobius strip '' ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | maybe spiral it around snugly like this . maybe make it into a square . maybe wrap it into a hexagon with a nice symmetric sort of cycle to the flappy parts . | how to make a fexagon ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | now you can flip from yellow side to white side . yellow side , white side , yellow side , white side hmm . white side ? | if you made a hexaflexagon from paper with one side colored how many sides would end up colored when you finish it ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | during lunch you want to show this off to one of your new friends , bryant tuckerman . you start with the original , simple , three-faced hexaflexagon , which you call the trihexaflexagon . and he 's like , whoa ! | is it possible to have more than a six sided hexaflexagon ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and by you , i mean arthur h. stone in 1939 . anyway , there 's lots of cool things you do with a strip of paper . you can fold it into shapes and more shapes . | is there any relationship between a hexaflexagon and a mobius strip ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and you are like , it 's easy ! just start with a paper strip , fold it into equilateral traingles , and you 'll need nine of them , and you fold them around into this cycle and make sure it 's all symmetric . the flat parts are diamonds , and if they 're not , then you 're doing it wrong . | how do you make a 60 degree fold without a protractor ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and by you , i mean arthur h. stone in 1939 . anyway , there 's lots of cool things you do with a strip of paper . you can fold it into shapes and more shapes . | what is a mobius strip ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | you can fold it into shapes and more shapes . maybe spiral it around snugly like this . maybe make it into a square . | i heard of something called a `` tri '' -hexaflexagon - is that like around the same thing as a regular hexaflexagon or like , totally different ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and you 're like . `` i do n't know , hexagons are n't too exciting , but i guess it has symmetry or something . '' maybe you could kinda fold it so the flappy parts are down and the unflappy parts are up . | i did n't have the volume on so starting what is the point ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | maybe spiral it around snugly like this . maybe make it into a square . maybe wrap it into a hexagon with a nice symmetric sort of cycle to the flappy parts . | can you show me how to make a hexaflexagon in slow motion ? |
so say you just moved from england to the us and you 've got your old school supplies from england and your new school supplies from the us and it 's your first day of school and you get to class and find that your new american paper does n't fit in your old english binder . the paper is too wide , and hangs out . so y... | and you want to make one that 's a little less messy , so you try with another strip and tape it nicely into a twisty-foldy loop . you decide that it would be cool to colour the sides , so you get out a highlighter and make one yellow . now you can flip from yellow side to white side . | how do you make a hexaflexagon with more than 3 sides ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | another way you could think about it is 4 , if you do a prime factorization , is 2 times 2 . and 3 -- it 's already a prime number , so you ca n't prime factorize it any more . so what you want to do is think of a number that has all of the prime factors of 4 and 3 . | what if the denominator is a prime number ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . and we can divide -- so let me make the numerator -- and we can divide the denominator by 7 . we 're doing the same thing to the numerator and the denominator , so we 're not going to change the value of the fraction . | does anyone know how to divide a pie into 5 equal slices ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21/28 -- you can see that they are both divisible by 7 . so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . | what do you call the line between the numerator and the denominator ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . | what does lcd stand for ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so their least common multiple is really just going to be the product of the two . so we can write 3/4 as something over 12 . and we can write 2/3 as something over 12 . | why did sal write a dot instead of a multiplication sign 3 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | so prime factorization is to make a composite number prime ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | here we could do fairly small numbers . the common denominator of 3/4 and 2/3 is going to be the least common multiple of 4 and 3 . and 4 and 3 do n't share any prime factors with each other . | when you said the least common denominator is the product of the denominators 4 & 3 , in future problems can i just multiply the two denominators to find the least common denominator or do i need to make sure they do not share prime factors first ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | another way you could think about it is 4 , if you do a prime factorization , is 2 times 2 . and 3 -- it 's already a prime number , so you ca n't prime factorize it any more . so what you want to do is think of a number that has all of the prime factors of 4 and 3 . | and what exactly is a prime a number anyways ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | what is the point of prime numbers ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | 9 times 2 is 18 . 18 plus 7 is 25 . so we get 252 . | is 7/11 considered a simplified fraction ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21/28 -- you can see that they are both divisible by 7 . so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . | what is the difference between the numerator and the denominator ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | another way you could think about it is 4 , if you do a prime factorization , is 2 times 2 . and 3 -- it 's already a prime number , so you ca n't prime factorize it any more . so what you want to do is think of a number that has all of the prime factors of 4 and 3 . | what 's a prime number ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21 divided by 7 is 3 , and 28 divided by 7 is 4 . so 21/28 is the exact same fraction as 3/4 . 3/4 is the simplified version of it . | how do you turn a fraction in to a percentage ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | or we could just multiply it out if that confuses you . so let 's just do the second way . 9 times 8 is 72 . | will a number line be a good way or a bar ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | 6 divided by 3 is 2 , and 9 divided by 3 is 3 . so 21/28 is 3/4 . they 're the exact same fraction , just written a different way . | cant 21/28 be simplified more ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | they have no common factors . another way you could think about it is 4 , if you do a prime factorization , is 2 times 2 . and 3 -- it 's already a prime number , so you ca n't prime factorize it any more . so what you want to do is think of a number that has all of the prime factors of 4 and 3 . | could someone explain what a prime number is please ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | there 's a couple of ways you could do it . you could multiply in your head 28 times 10 , which would be 280 , and then subtract 28 from that , which would be what ? 252 . | what would you do with negative fractions ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so what we could do is we can find a common denominator for both of them and convert both of these fractions to have the same denominator and then compare the numerators . or even more simply , we could simplify them first and then try to do it . so let me do that last one , because i have a feeling that 'll be the fas... | do you divide first or multiply first ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and the real benefit of doing this is now this is much easier to find a common denominator for than 28 and 9 . then we would have to multiply big numbers . here we could do fairly small numbers . | do i have to multiply the numbers ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21/28 -- you can see that they are both divisible by 7 . so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . | what happens if the numerator and the denominator can not be devided by the same number ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so let me do that last one , because i have a feeling that 'll be the fastest way to do it . so 21/28 -- you can see that they are both divisible by 7 . so let 's divide both the numerator and the denominator by 7 . | how are you do you find that 21 and 28 is divisible by 7 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | what is the point of using prime numbers ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . | how do you do the sum ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . | what is short term division ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | another way you could think about it is 4 , if you do a prime factorization , is 2 times 2 . and 3 -- it 's already a prime number , so you ca n't prime factorize it any more . so what you want to do is think of a number that has all of the prime factors of 4 and 3 . | can a prime number be a multiple of any number except itself ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | what the hell is prime factor ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | well , clearly , we have the same denominator right now . we have 9/12 is clearly greater than 8/12 . so 9/12 is clearly greater than 8/12 . or if you go back and you realize that 9/12 is the exact same thing as 21/28 , we could say 21/28 is definitely greater than -- and 8/12 is the same thing as 6/9 -- is definitely ... | what is the simplified version of 12/6 and 27/9 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so we get 168 . let me write that out just to make sure i did n't make a mistake . so 28 times 6 -- 8 times 6 is 48 . | how can you make a pie chart out of fractions ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21 divided by 7 is 3 , and 28 divided by 7 is 4 . so 21/28 is the exact same fraction as 3/4 . 3/4 is the simplified version of it . | what is a equivalent fraction ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | when did you introduce factoring , prime numbers , etc ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so if we were doing it with -- if we did n't think to simplify our two numbers first . i 'm trying to find a color i have n't used yet . so 21/28 and 6/9 . | how do i find th area of a base ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so we get 8 . and so now when we compare the fractions , it 's pretty straightforward . 21/28 is the exact same thing as 9/12 , and 6/9 is the exact same thing as 8/12 . | can u compare the fractions with a different denominator with decimals or only with fractions ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | well , to go from 28 to 252 , we had to multiply it by 9 . we had to multiply 28 times 9 . so we 're multiplying 28 times 9 . | how do you know what to number to multiply ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | did we learn prime factorization before ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | we 're doing the same thing to the numerator and the denominator , so we 're not going to change the value of the fraction . so 21 divided by 7 is 3 , and 28 divided by 7 is 4 . so 21/28 is the exact same fraction as 3/4 . | how do i show 4/6 & 5/7 on a number line ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so i 'm saying the common denominator here is going to be 252 . least common multiple of 28 and 9 . well , to go from 28 to 252 , we had to multiply it by 9 . | what does the `` common '' thingy and the `` least common '' thingy mean ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | i 'm trying to find a color i have n't used yet . so 21/28 and 6/9 . so we could just find a least common multiple in the traditional way without simplifying first . | sal is dividing by different numbers for example hes dividing 21/28 by 7 and hes dividing 6/9 by 3 but when i do that i get it wrong how is that possible ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 6/9 is the exact same fraction as 2/3 . so we really can compare 3/4 and 2/3 . so this is really comparing 3/4 and 2/3 . | if you have 2/8 and 3/89 could you cross multiply and then compare the products ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . and we can divide -- so let me make the numerator -- and we can divide the denominator by 7 . | why did sal do all that complicated figuring , when he could just reduce the fractions ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so we also have to multiply the numerator by 4 . so we get 8 . and so now when we compare the fractions , it 's pretty straightforward . | what is 16 *8 equal to ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 6/9 is the exact same fraction as 2/3 . so we really can compare 3/4 and 2/3 . so this is really comparing 3/4 and 2/3 . and the real benefit of doing this is now this is much easier to find a common denominator for than 28 and 9 . | so my question is would n't the answer be 2/3 is greater than 3/4 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | the common denominator of 3/4 and 2/3 is going to be the least common multiple of 4 and 3 . and 4 and 3 do n't share any prime factors with each other . so their least common multiple is really just going to be the product of the two . | what are the prime factors ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | there 's a couple of ways you could do it . you could multiply in your head 28 times 10 , which would be 280 , and then subtract 28 from that , which would be what ? 252 . | how would we use comparing fractions in the real world ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so right , 168 . so now we have a common denominator here . and so we can really just compare the numerators . | do i have to do the harder way ( which i quite frankly ca n't grasp ) because i can not simplify the fractions before finding a common denominator ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 6/9 is the exact same fraction as 2/3 . so we really can compare 3/4 and 2/3 . so this is really comparing 3/4 and 2/3 . | by what % is 1/4 from 3/8 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | 20 times 9 is 180 . and then 1 times 9 is 9 . so this is going to be 189 . | so is 4/9 -- 7/12is 48/108 lessthan 63/108 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | is there any way to avoid introducing new concepts like prime factorization in the 4th grade fractions playlist ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | the common denominator of 3/4 and 2/3 is going to be the least common multiple of 4 and 3 . and 4 and 3 do n't share any prime factors with each other . so their least common multiple is really just going to be the product of the two . | so , if the numbers do n't share any prime factors , it 's the same of saying that they do not have a gcd ( greatest common divisor ) ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so 21/28 -- you can see that they are both divisible by 7 . so let 's divide both the numerator and the denominator by 7 . so we could divide 21 by 7 . | you know how if you multiply or divide the numerator or denominator of a fraction ( if you 're comparing it with another fraction ) you have to do the same to the same to both the top and bottom ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | well , 2 times 2 times 3 is 12 . and either way you think about it , that 's how you would get the least common multiple or the common denominator for 4 and 3 . well , to get from 4 to 12 , you 've got to multiply by 3 . | how do u get the common denominaors when you have to find out which one is smaller ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | 20 times 9 is 180 . and then 1 times 9 is 9 . so this is going to be 189 . | during the eclipse sal taks about t why is the moon the exact size of the sun , offering complete 1 for 1 coverage ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and 14 is 2 times 7 . that 's its prime factorization . prime factorization of 9 is 3 times 3 . | what was the point of doing a prime factorization tree when you just ended up multiplying the denominators to find the lcm ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so we really can compare 3/4 and 2/3 . so this is really comparing 3/4 and 2/3 . and the real benefit of doing this is now this is much easier to find a common denominator for than 28 and 9 . | when in the real world is comparing fractions useful ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | so we get 8 . and so now when we compare the fractions , it 's pretty straightforward . 21/28 is the exact same thing as 9/12 , and 6/9 is the exact same thing as 8/12 . | what would happen if one or both fractions were improper fractions ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | i 'm trying to find a color i have n't used yet . so 21/28 and 6/9 . so we could just find a least common multiple in the traditional way without simplifying first . | today you dusted and vacuumed your home if your dusted your house every 6 days and run the vacuumed every 9 days when is the next time you will do both chores again ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | and let me show you that just for fun . so if we were doing it with -- if we did n't think to simplify our two numbers first . i 'm trying to find a color i have n't used yet . | can you use smaller numbers for the first question , like 4x7 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | we 're doing the same thing to the numerator and the denominator , so we 're not going to change the value of the fraction . so 21 divided by 7 is 3 , and 28 divided by 7 is 4 . so 21/28 is the exact same fraction as 3/4 . | what is 600 divided by 22 ? |
use less than , greater than , or equal to compare the two fractions 21/28 , or 21 over 28 , and 6/9 , or 6 over 9 . so there 's a bunch of ways to do this . the easiest way is if they had the same denominator , you could just compare the numerators . unlucky for us , we do not have the same denominator . so what we co... | it 's 2 times 14 . and 14 is 2 times 7 . that 's its prime factorization . | how do we order fractions because for example 1/2 7/2 4/5 it is 1/2 first 4/5 next and finally 7/2 but the thing says no it is incorrect ? |
we are here in the portland art museum in the jubilee center for modern and contemporary art in front of marcel duchamp 's landmark boite-en-valise the red box , series f when i hear the word `` valise '' i think of could carry around like a suitcase . yeah . like a suitcase . i think my grandmother used `` valise '' f... | we are here in the portland art museum in the jubilee center for modern and contemporary art in front of marcel duchamp 's landmark boite-en-valise the red box , series f when i hear the word `` valise '' i think of could carry around like a suitcase . yeah . | what is mona lisa doing in his collection ? |
- you know , there 's that saying that it takes a village to raise a kid . well , i guess you could say that it takes an entire body , and i mean every single organ of a body , to make a baby . it 's like the best example of teamwork that there is , all the organs in the body working together to support the growth and ... | okay . oxygen consumption increases in pregnancy . right ? | what is the physiologic explanation for the unusual , insistent food cravings that some women experience during pregnancy ? |
- you know , there 's that saying that it takes a village to raise a kid . well , i guess you could say that it takes an entire body , and i mean every single organ of a body , to make a baby . it 's like the best example of teamwork that there is , all the organs in the body working together to support the growth and ... | because we know urinary stasis is a risk factor for bacterial growth . and that 's perhaps why pregnant women are more susceptible to developing pyelonephritis , or infection of the kidney , than are non-pregnant women . it 's because of that urinary stasis that occurs as a result of the large uterus putting pressure o... | as pregnant women are more likely to get kidney infections , what postures or exercises are recommended to drain out the stagnant urine into the bladder ? |
- you know , there 's that saying that it takes a village to raise a kid . well , i guess you could say that it takes an entire body , and i mean every single organ of a body , to make a baby . it 's like the best example of teamwork that there is , all the organs in the body working together to support the growth and ... | and that includes the smooth muscle that surrounds all of the blood vessels . so that relaxation causes dilation of the blood vessels , which then lowers the blood pressure . so that 's a first cause , sort of , of the decrease in blood pressure through pregnancy . | heart beat rate is inversely proportional to blood pressure , is this law not applicable to all normal situations ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | would n't the derivative of a^x be just x ( a^ ( x-1 ) ) according to the product rule ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . so what we will do is we will first take the derivative of the outside function . | how come when using the chain rule and taking the derivative ( ( ln a ) * x ) = ln a ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | where does the x go ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | well natural log of a , it might not immediately jump out to you , but that 's just going to be a number . so that 's just going to be , so times the derivative . if it was the derivative of three x , it would just be three . if it 's the derivative of natural log a times x , it 's just going to be natural log of a . | 0 would n't derivative of 8 equal to 0 ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | now , what power does 2 need to be to raised to get 2 ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | should n't we use the power rule ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | why did n't he use the product rule to get the result of [ 8 * 3^x ] = -ln ( x ) * 3^x * 8/3^2x ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . so what we will do is we will first take the derivative of the outside function . | how come when using the chain rule and taking the derivative ( ln a ) * x we get ln ( a ) ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so that 's going to be the same thing as e to the natural log of a , natural log of a times x power . times x power . and now we can use the chain rule to evaluate this derivative . | just like x. would n't we use the product rule here , or at least convert ln ( a ) to 1/a ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . | how can ln ( a ) be treated as a constant ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | so really think about this . do n't just accept this as a leap of faith . it should make sense to you . | is n't differentiation of ln ( a ) =1/ ? |
what i want to do in this video is explore taking the derivatives of exponential functions . so we 've already seen that the derivative with respect to x of e to the x is equal to e to x , which is a pretty amazing thing . one of the many things that makes e somewhat special . though when you have an exponential with ... | and then we take the derivative of that inside function with respect to x . well natural log of a , it might not immediately jump out to you , but that 's just going to be a number . so that 's just going to be , so times the derivative . | is `` a '' should be an real number ? |
how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . so , i 'm gon na choose six . this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . wan na scroll down and make su... | one , two , three , four , five , six , seven , eight . wan na scroll down and make sure i do n't miss these over here , nine , 10 , 11 , 12 , 13 , 14 , 15 , 16 wheels . there are 16 wheels . | what will the solar system be like if we did n't have a jupiter ? |
how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . so , i 'm gon na choose six . this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . wan na scroll down and make su... | how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . | how do we pronounce numbers more than 1000 ? |
how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . so , i 'm gon na choose six . this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . wan na scroll down and make su... | how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . | what is an easy way of carrying decimals in my head ? |
how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . so , i 'm gon na choose six . this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . wan na scroll down and make su... | wan na scroll down and make sure i do n't miss these over here , nine , 10 , 11 , 12 , 13 , 14 , 15 , 16 wheels . there are 16 wheels . these four cars have 16 wheels . | why did steering wheels not count as wheels ? |
how many people do you see in this picture ? let 's see , i see one , two , three , four , five , six people in this picture . so , i 'm gon na choose six . this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . wan na scroll down and make su... | this is fun , lem me keep going . how many wheels do i see in the picture ? one , two , three , four , five , six , seven , eight . | what happens if the picture is blurry and you can not count ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | this carbon is just a methyl group . so this right here does look like a chiral center . it does look like a chiral carbon , and the other ones do n't . | at the very end , when the compound is finally named , should the prefix be 2s instead of s , because we must specify the chiral center ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | and then finally , you have your number four group in yellow , which is just a hydrogen that 's coming straight out . so that is coming straight out of -- well , not straight out , but at an angle out of the page . so that 's our number four group , i 'll just label it number four . | how does the molecule go from sticking out of the page to going into the page , while the others just move from the plane of the page to sticking out ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | so let me scroll over a little bit . so we have our chiral carbon . i put the little asterisk there to say that that 's our chiral carbon . | what 's the actual difference between chiral molecules or chirality and enantiomers ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclature rules and we 'd be done . | how do you decide on the r/s configuration when given a flat skeletal or lewis structure that does n't have the substituents pre-oriented in 3d like the example in this video ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | we have to differentiate between this carbon group , that carbon group , and that carbon group . and the way you do it , if there 's a tie on the three carbons , you then look at what is attached to those carbons , and you compare the highest thing attached to each of those carbons to the highest things attached to the... | when substituents are in a tie while we are ranking them , you look at the highest atom attached to each , but how do double or triple bonds get counted in the ranking process ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . | is it possible for a molecule to have multiple chiral centres ? |
let 's see if we can name this molecule using the -- sometimes called the r-s system , or the cahn-ingold-prelog system . and the first thing to do is just to see if there are any chiral centers in this molecule . if there are n't , then we do n't even have to use the r-s system . we can just use our standard nomenclat... | we 've named it using the r-s system . this molecule is ( s ) -- sinister -- 1-bromo-3-fluoro-2,3-di -- | once you have determined that the chiral center for c2 is s , to fully name the molecule could it be correct to say ( 2s ) 1-bromo-3-fluoro-2,3-dimethylbutane ? |
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