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Video transcript

we're going to do in this videos get some practice doing division with numbers that are multiples of ten 101,000 things like that so let's say we wanted to compute what two thousand four hundred divided by 30 is pause this video and see if you can calculate it using whatever strategy makes sense to you all right so let's think about this together and I'm going to show you how my brain likes to handle this will do this out on my little digital blackboard but eventually you'll be able to do things like this in your head so 2400 or 2,400 divided by 30 that is the same thing as 2,400 2,400 over over 30 so this is just another way of saying 2,400 divided by 30 now the reason why I wrote it this way is because you can now write each of these the numerator and the denominators as the product of some number and either ten or a hundred or a thousand so two thousand four hundred that's the same thing as 24 times 124 times 100 and I knew that I was like okay I've got these two zeros at the end so you could view this literally as 24 hundreds and then 30 you can view as we got one zero here so it's three tens the three is in the tens place so three times ten now what's valuable about thinking of it this way as you can separately divide the 24 by the three and then the hundred by the ten so this is the same thing as let me do this this way as that times that and so we have 24 divided by three 24 divided by 3 times 100 100 divided by 10 now 24 divided by 3 you might already know that is going to be 8 3 times 8 is 24 so this is going to be and this is going to be equal to eight and what's 100 divided by 10 well 100 divided by 10 is just going to be 10 so our our quotient I guess you could say is going to be 8 times 10 or it's going to be equal to its going to be equal to 80 and we're done and you might notice something interesting here so if I take my 24 and divide it by my and divide it by my 3 I'm going to get this 8 and then if I take 2 zeroes and if I take away another 0 I'm going to be left with 1 0 right over here so you get 80 but why did that thing with the zeroes work because you're really taking 24 hundreds divided by 3 tens so 100 divided by 10 what you're going to lose a 0 that's going to be equal to 10 which has only one zero let's do another example just to hit the point home and try to do this next example the way we just did it maybe in your head or maybe on a piece of paper so let's say we wanted to calculate 3500 which could also think of as 3500 and we want to divide that we want to divide that by write the division symbol a little bit nicer than that so we want to divide that by 700 pause this video and see if you can compute that so as we just did we could view this as 3500 over 700 3500 we can view as 35 35 times 100 over over this is going to be over let me get the right color here over 7 times 100 now the 100's cancel out and we're just left with 35 over 7 now with 35 divided by 7 well that is going to be equal to 5 and notice you could just say 35 divided by 7 is 5 and if you're saying how many zeroes do I have left over well I have two zeros here but since I'm dividing by something with two zeros those two zeros are going to be cancelled out I don't want you to just memorize that the reason why that happens is because that's those two zeros here represent hundreds 3,500 these two zeros represent hundreds if you divide 100 by hundreds they're all going to cancel out so you had two zeros before but you're dividing by something with the two zeros so you don't have any zeros after the five here let me do one more example just to really hit that point home but I want you to appreciate that it's not just some magical trick it just makes sense out of things that you might already know so it's someone and I'm going to give this I'm gonna get a crazy one let's say we had 42 million 42 million divided by 42 million divided by let's say 60,000 what is that going to be pause the video and see if you can think about it on your own well using the the notions that we just talked about you could say all right 42 divided by 6 is going to be 7 and then if I let's see over here I have 6 zeroes so we're talking about millions and I'm going to draw divided by 4 zeros right over here which is 10,000 so if you had six zeroes then you divide by if you have millions with six zeroes and you divide by ten thousands with four zeroes six minus four is going to be two so your answer is going to have two zeros in it so this is going to be equal to 700 now once again not a magical trick the way that we got this is that this is equal to 42 times a million we got our six zeroes right over there divided by divided by six ten thousands six times 10,000 so our 42 divided by six and that's where we get the seven from and now if we one way to think about it we divide the numerator in the denominator by 10 we lose zero then we do it again we lose zeroes we do it again we lose zeroes we do it again we lose zeroes and so this thing just all becomes one or another way to think about it we if we divide the numerator and the denominator by 10,000 this becomes 1 this thing loses four zeroes and you're left with 42 divided by six is seven hundreds because we have a 1 now in the denominator 100 divided by 1 so 700