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# Division using place value

CCSS.Math:

## Video transcript

let's say you want to figure out what 5,600 divided by 8 is now you might be tempted to do some type of long division 8 into 5,600 and you could do it this way and you using paper but what I want to show you is that you could maybe do this in your head or maybe even just use less paper to do it and the key realization here is like look if you got these two zeros here this is really the same thing as 56 times 100 divided by 8 56 times 100 is 5,600 you got the two zeros here you got the two zeros here and let me make it very clear to zeros here you got the two zeros here in fact sometimes people will call this number 5650 six hundreds so 5,600 is the same thing as 56 times 100 and when you write it this way then you might say hey well instead of doing 56 times 100 divided by 8 I can switch the order this is going to be the same thing this is going to be the same thing as this is going to be the same thing as 56 56 divided by 8 divided by 8 divided by 8 times 100 times 100 times 100 now why did I do this well it's pretty straightforward if you remember your multiplication tables what 56 divided by 8 is 8 times 7 is 56 so this right over here is going to be 7 and so then you're just left with figuring out what 7 times 100 is 7 times 100 well that's going to be seven hundreds or seven seven hundreds is just seven hundred seven hundred and you're done plus two more of these where we might be tempted to do some type of long division but if we really think about ways to break up the numbers we might be able to do it with less paper or possibly even in our heads so let's say that you had the number let's say you had the number 800 just in a different color let's say you had the number 846 846 and you want to divide that by two well the realization here or what you might think about is let's break this number up let's break up this 846 846 is the same thing this is going to be actually let me do it this way 846 is the same thing as this is the same thing as 800 800 plus 40 plus 40 plus 6 plus 6 and so 846 the same thing is 800 plus 40 plus 6 and so we can just divide that by 2 we can just divide that by 2 divided by 2 so notice didn't do anything too fancy here this is just the same thing as this over here and I just broke it up you have eight hundreds four tens which is 40 and six and you can divide that by two well how does that help us well now we can divide each of these separately by two one way to think about it is we can we can distribute the divide the division by two where you might be familiar with using the distributive property of multiplication but you could also do it with division so this thing right over here is going to be the same thing this is going to be equal to 800 divided by 2 800 divided by 2 divided by 2 plus 40 divided by 2 plus 40 divided by 2 and I'm going to add parentheses in a second to make it a little bit clearer plus 6 divided by 2 plus plus 6 divided by 2 so plus 6 divided by 2 divided plus 6 divided by 2 so once again you have 800 divided let me do that same you have 800 divided by 2 that's that right over there plus 40 divided by 2 40 divided by 2 plus 6 divided by 2 plus 6 divided by 2 so we distributed the division by two well 800 divided by two you should do in your head it's this is 800 s divide that by two you're going to get 400 400 410 s divided by two is going to be two tens is going to be two tens or 20 so eight to eight hundreds divided by two is four hundreds for tens divided by two is two tens and then six divided by two is three so you are left with four hundred plus twenty plus three which of course is equal to 400 and 423 now used a lot of my screen here to work this out for you so that you really digest what's going on here but once you get good at it you could say okay look eight divided by two is eight hundreds divided by two is four hundreds actually I could do it right over your eight hundreds divided by two is four hundreds for tens divided by two is two tens and six ones divided by two is three ones so you could say hey look if I just divide each of these numbers by 2 I get 423 but this is what you are really doing you are separating it out by place value you're dividing each of those places the hundreds the tens and the ones by the two by two and then you got 423 and by the way that's exactly what you would do if you actually did it through long division you're actually just dividing the two into each of the places let's do one more just to really make sure that we we are fully enjoying this so let's say let's say that I have nine hundred and nine hundred and sixty-three nine hundred and sixty-three and I want to divide that by and divide that by nine well over here you might make the realization well I can see parts of this that I know how to divide by nine so I could say this is the same thing as nine hundred and I'm breaking out the nine hundred because I know how to divide nine hundred divided by nine so that's nine hundred and then I know what I know that 63 is a multiple of nine so why don't I break out 63 separately I don't even have to break out the tens and the one separately so I could say this is same thing as nine +63 and all of that / / 9 well this is going to be the same thing as nine hundred divided by nine let me do that in the brown color nine hundred divided by nine plus 63 divided by nine plus 63 divided by nine I just distributed the division by nine so let me put some parentheses around this and what is this going to be equal to well nine hundred divided by nine is one hundred this is going to be one hundred and sixty-three divided by nine is seven is seven so this is going to be one hundred plus seven or one hundred 100 and 107 and so once again I wrote it all out like this but once you get some practice you'll say hey look nine goes into nine hundred a hundred times nine goes into 63 seven times so nine goes into nine hundred sixty-three 107 times hopefully you found that fun and this is this is this is useful stuff because one of the most important things you're going to have to find is it all the time we're going to find these numbers while you're doing you know your your finances or you're trying to calculate the the check at a restaurant and you're going to find it really valuable to be able to do this type of division and with some practice even without paper