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Current time:0:00Total duration:6:57

Relate multiplication with area models to the standard algorithm


Video transcript

what we're going to do in this video is multiply the numbers 352 and 481 and we're gonna do it in two different ways but realize that the underlying ideas are the same so first let's just appreciate that 352 can be re-written as 300 plus 50 plus 2 or we could think of it as 2 plus 50 plus 300 plus 300 you add these three numbers together you are going to have 352 and same idea 481 that's four hundreds for hundreds plus eight tens which is 80 so plus 80 and then we have 1 1 so plus 1 and you might have be familiar with multiplying like this in the past setting up this grid and it's essentially were applying the distributive property we're going to take the 2 and multiply it times 400 plus 80 plus 1 so we're gonna multiply 2 times each of those numbers and actually let me just draw some quick lines here so we have that and then we'll have we do it like this then we have this and then let me set up my grid I'm having trouble drawing straight lines ok there we go and then one more in this direction there you go and then in this direction let me draw some horizontal lines to have a neat clean grid here there we go now first we'll multiply 2 times 400 plus 80 plus 1 so 2 times 400 is 800 2 times in that same blue color so this is 800 2 times 80 is 160 and then 2 times 1 is 2 and then we can multiply 50 times these so what's 50 times 400 well 5 times 4 is 20 and then we have another 1 2 3 zeroes so 1 2 3 so that's 20,000 50 times 80 5 times 8 is 40 and then we have two zeros just like that and then we have 50 times 1 which is of course going to be equal to 50 and then we go to the 300 which we will distribute and multiply times each of these each of these numbers 300 times 400 3 times 4 is 12 and then we have 4 zeros 1 2 3 4 we get 120 thousand three hundred times 80 3 times 8 is 24 and then we have 1 2 3 zeroes 1 2 3 so we get 24,000 and then 300 times 1 is of course equal to 300 and then what we want to do is add up all of these numbers so let's actually add up the rows first so if we add up the rows let me draw another line going straight down like that and so if we sum this up this is going to be 960 to 800 plus 160 is 960 plus 2 so this is 962 this right over here is 24,000 50 20 4050 and then this right over here is what a hundred and a hundred and forty four thousand three hundred 144 thousand and three hundred 120 thousand plus 24 thousand is 144 thousand plus 300 there you have it and then you would add up these numbers just like that to get your final answer and I'm gonna hold off doing that for a second as we see the other way of multiplying these numbers so the other way of doing it we could have said 481 and this is sometimes called the standard algorithm 481 times [Music] 350 let me do the same colors 352 and in the standard algorithm the way that we do it is we start with this two in the ones place and then we multiply it times 481 so 2 times 1 is 2 2 times 8 is 16 so we put the 6 here and then we sometimes we say we'll carry the 1 we're really regrouping that as a hundreds that's 10 tens which is a hundreds and then two times four is eight which is really eight hundred plus one so that's nine or really nine hundred do you see a pattern here this 962 is the exact same thing as that 962 right over there why well because we multiply the 200 times the 1 times the 80 times the 400 we saw that over here and then we just added them all together to be 962 that's all the standard algorithm did just now and then we move over to the 5 but this is really five tens or 50 and that's why the standard algorithm we put a 0 here before that before saying all right what's 5 times 1 it's 5 what's 5 times 8 it is 40 we regroup the 4 let's complete this from before what's 5 times 4 well that's 20 plus 4 is 24 notice 24 thousand 50 that's exactly what we had over here and it makes sense because we're taking a 50 and we're multiplying it times 4 481 which is exactly what we did right over there and so you might guess what's going to happen when we take this 3 and we multiply it times 481 that's really a 300 times 481 let me delete that so I don't get confused so because it's a 300 in the standard algorithm we put two zeros here first so when I say algorithm it just means a method of doing something and so we'll say 3 times 1 is 3 3 times 8 is 24 and then 3 times 4 is 12 plus 2 is 14 and so notice I have a hundred forty-four thousand three hundred and the standard way of doing it at this point we just add them all up so whether we're doing it here or here we just add everything up so 2 plus 0 plus 0 is 2 6 plus 5 is 11 regroup that 1 so 1 plus 9 plus 3 is 13 and then 1 plus 4 plus 4 is 9 2 plus 4 is 6 and we have a 1 right over there so we get 169,000 312 and so when you just learn this method the standard algorithm we some people might call it it might seem like hey this just seemed like a little bit of a magic but all you're doing is you're going to each of these places and you're distributing it you're multiplying it times 400 plus 80 plus 1 to get this then you're multiplying 50 times 400 plus 80 plus 1 and then 300 times 400 plus 80 plus 1 exactly what we did right over here