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Relate place value to standard algorithm for multi-digit subtraction

Video transcript

- [Instructor] What we're going to do in this video is get some practice subtracting multi-digit numbers I'm going to use 1000 minus 528 as our example. But really to understand different methods and how they all fit together, why it actually makes sense. So if you wanted to visualize what this difference means, imagine something that has a length of 1000 some type of units, so it's length right over here is 1000 and we were to take away 528 from that. So 528 from that is what we take away and so this difference would be well what do we have left over. So this is equal to question mark. And I'm going to do it two different ways. I'm going to do it using a table with place value and I'm also going to do it using what's sometimes called the standard method it's the way that people often learn to subtract numbers like this especially if we're going to have to do some removing. So I'm actually going to do them simultaneously for your benefit, alright. So let me just write out our table with our place values. So first of all you have your thousands place, thousands. And let me square off the numbers here that are in the thousands place so that 1000 right over there, that's one in the thousands place. Then you have your hundreds place, hundreds place, and this number I have zero hundreds right now here I have five hundreds. And then you have your tens place, tens, zero tens right there in the tens place, two tens right over there. And then of course you have your ones place. Here I have zero ones, here I have eight ones. Now let me also rewrite these numbers and I'm going to do it using the standard method. So I have 1000 and then I have zero hundreds I have zero tens and I have zero ones. And from that I am going to subtract five hundreds, five hundreds, two tens, two tens, and eight ones, eight ones. So let's do both of these at the same time, make a little bit of a table right over here. So that is my table. So let's start with what we originally have, we have 1000 that's what we're subtracting from. Well on this table I would just represent as that as 1000, now we want to take five hundreds and two tens and eight ones from it, how do we do that? 'Cause right now we have no hundreds, we have no tens, and we have no ones. And with the standard method we have the same problem 'cause we start in the ones place we say hey we want to take eight ones from zero ones, similar problem here. How do we take eight ones here? Similarly we want to take two tens from zero tens, how do we do that here and the answer is regrouping. What we want to do is break up this thousand and so we can start to fill in these other categories it's like exchanging monies that's sometimes an example used. So 1000 is how many hundreds? Well if we get rid of this thousands I can break it up into ten hundreds, so one, two, three, four, five, six, seven, eight, nine, ten. And so that's equivalent of I could get rid of this 1000 or this one in the thousands place and give myself ten hundreds. Well that starts to solve my problem 'cause I could now take five hundreds from this, I could take five from ten. Five hundreds from ten hundreds, but I still have the problem in the tens and the ones place. And so what I could do is I could break up one of these hundreds and into ten tens so let me do that. So I'm going to take, (mumbles) so I'm going to take that one away and then that 100 is ten tens, one, two, three, four, five, six, seven, eight, nine, ten. And if I did that here, well if I take away one of the hundreds I'm now going to have nine hundreds left. Nine hundreds left, but now I have ten, now I have ten tens. So I'm in good shape now I can take some tens here but I still don't have any ones, remember I want to take eight ones from here, so you can imagine what's going on. I could take one of my tens and that's going to give me one, two, three, four, five, six, seven, eight, nine, ten ones and so over here I could take away one of my tens so I'm now going to have nine tens and I'm going to break that into ten ones, ten ones. And so now things are pretty straightforward. What do I do? Well I can now take my eight ones from the ten ones. So ten minus eight, that is going to be two. How would I represent that over here? I'm going to do the subtraction in this yellow color. I want to take away eight of these ones, so I take away one, two, three, four, five, six, seven, eight, and I am left with that two right over there, that two is that two. Now I can move on to the tens place. If I have nine tens and I take away two tens, I'm going to be left with seven, I'm going to be left with seven tens. How would we see it over here? Well I have nine tens left over, I'm going to take away two of them, so take a one two and I am left with seven. Is that seven? One, two, three, four, five, six, seven, yep that is seven tens right over there. We have two ones, seven tens and so this seven is exactly this seven right over there same colors. I think you see where this is going and the whole idea is not just to get the answer but to understand how we got this answer. So in the hundreds place if I have nine hundreds and I take away five hundreds then I'm going to be left with four hundreds, same idea over here. I have nine hundreds, I take away one, two, three, four five, I am going to be left with four hundreds, this four and this four is the same. And so there you get the general idea, with the standard method it sometimes seems like magic of how we're regrouping things but all we're doing is we're taking that thousand and saying hey that's ten hundreds and then we take one of those hundreds and we say hey that's ten tens and we take one of those tens and we say that's ten ones and then we are able to subtract.