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# Relate place value to standard algorithm for multi-digit subtraction

CCSS.Math:

## Video transcript

what we're going to do in this video is get some practice subtracting multi digit numbers I'm going to use one thousand minus five hundred twenty-eight as our example but it's really to understand different methods and how they all fit together and why it actually makes sense so if you wanted to visualize what this difference means imagine something that is has a length of a thousand some type of units so it's length right over here is 1,000 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 gonna do it using a table with place value and I'm also gonna 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 regrouping so I'm actually gonna do them simultaneously for your benefit all right 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's I have one thousand right over there that's one in the thousands place then you have your hundreds place hundreds place in 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 and in the tens place two tens right over there and then of course you have your ones place ones 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 one thousand and then I have zero hundreds I have 0 tens and I have zero ones and from that I am going to subtract five hundred five hundred two tens two tens and eight ones and eight ones so let's do both of these at the same time and let me make up 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 a thousand that's what we're subtracting from well on this table I would just represent as that is one thousand now we want to take five hundred s and two tens and eight ones from it how do we do that because 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 because we start in the ones place and we say hey we want to take eight ones from zero one similar problem here how do we take eight ones here similar 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 that we can start to fill in these other categories it's like exchanging money is that sometimes an example used so one thousand 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 one thousand or this one in the thousands place and give myself ten hundreds well that starts to solve my problem because 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 ten so let me do that so I'm gonna take let me do that in a color so I'm gonna take that one away and then that 100 is 10 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 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 tents and that's gonna give me one two three four five six seven eight nine ten ones and so over here I could take away one of my tents so I'm now going to have nine tens and then I'm that's gonna I'm gonna break that into 10 once 10 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 10 minus 8 that is going to be 2 how would I represent that over here I'm gonna do the subtraction in this yellow color well I want to take away 8 of these ones so I take away 1 2 3 4 5 6 7 8 and I am left with that 2 right over there that too is that too now I can move on to the tens place if I have nine tens and I take away two tens I'm gonna be left with seven I'm gonna 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 yeah that is seven tens right over there we have two ones seven tens and so this seven is exactly this 7 right over there the same 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 gonna 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 4 and this 4 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 10 hundreds and then we take one of those hundreds and we say hey that's 10 tens and then we take one of those tens and we say that's 10 ones and then we are able to subtract