Understanding place value when subtracting

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 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 has a length of a thousand, some type of units. So its 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.

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 regrouping. So I'm actually going to 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 1000 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 gonna do it using the standard method. So I have one thousand, and then I have zero hundreds, I have zero tens, and I have zero ones. From that, I am going to subtract five hundreds, two tens, and eight ones.

So let's do both of these at the same time, and let me 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 hundreds, 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 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 so that we can start to fill in these other categories. It's like exchanging monies—that's sometimes an example used. So a one thousand is how many hundreds? Well, if we get rid of these 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 into 10 tens. So let me do that. I'm going to take—let me do that in a color—so I'm going to take that one away, and then that hundred 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 10 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 10 ones—10 ones. And so now things are pretty straightforward. What do I do? Well, I can now take my 8 ones from the 10 ones. So 10 minus 8, that is going to be 2.

How would I represent that over here? I'm going to 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, 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 gonna be left with 7. I'm going to be left with 7 tens. How would we see it over here? Well, I have 9 tens left over. I'm going to take away 2 of them. So take a 1, 2, and I am left with 7. 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 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 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 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 then we take one of those tens, and we say, "That's 10 ones." And then we are able to subtract.