Multi-digit subtraction with regrouping: 7329-6278

We have 7,329 minus 6,278. So let's go place by place and see if we can subtract. 6,278 is clearly less than 7,329, so we should be able to do this. So first, we go to the ones place. We're subtracting an 8 from a 9. That seems pretty straightforward. That's just going to be a 1, a 1 in the ones place. It literally just represents 1. Then we go to the tens place. And we're trying to subtract a 7 from a 2. And this is really representing 70. And this is really representing 20. Well, now we're hitting a bit of a stumbling block. So we're going to have to regroup or borrow. And to understand what we're doing, let's rewrite both of these numbers. So 7,329-- 7 we can rewrite as being equal to 7,000. Plus 300-- so this 3 in the hundreds place is representing 300. The 7 in the thousands place is 7,000. 3 in the hundreds place is 300. The 2 in the tens place, that's two 10's, or 20. And then the 9 in the ones place is just going to be 9. So this is another way of representing 7,329. And then down here, we have the 6 in the thousands place. Well, that's going to be 6,000. And we're subtracting, so minus 6,000. And then here, we have a 2 in the hundreds place. And once again, we're going to be subtracting all of these. So we're going to be subtracting 200. And then here in the tens place, we have our 7. And we're subtracting it. So seven 10's, that's 70. And then we are subtracting that 8. And what we've already done is said, hey, look. Subtracting 8 from 9? That's just going to be 1. But then we got over here, and we said, hey, how are we going to subtract 70 from 20? And the key here is to regroup some of the value up here and give it to the tens place, so that we can subtract 70 from it. And the most natural place to go is one place value above. So we could take 100 from the 300. So then it will become 200. We're going to give 100-- we're going to give that 100 to the tens place. So it is going to become 120. Notice, 200 plus 120 is 320. 300 plus 20 is 320. We have not changed the value of the number. We've just changed what place we're representing it in. If we wanted to do it here, we could say-- and when you think of it this way, this is really regrouping, and this is really what's happening. But if you want to think of it in a borrowing framework, you could say, hey, let's take 1 from the 3. Although it's a 300, so you're really taking 100. That becomes a 2. And you give that 1 to the tens place. And so that becomes a 12. Now, what was really happening is you took 100. You gave it to the 20. It became 120. But now you can subtract. Here, you'd say, well, what's 120 minus 70? Well, 120 minus 70 is going to be 50. Over here you could say, well, what's 12 minus 7? Well, that's 5. But it's still representing the same thing. 12 10's is 120. Seven 10's is 70. And they give you five 10's, which is the same thing as 50. This 5 represents that 50. And then we can go to the other places. You say 2 minus 2. Well, that's zero 100's. And then 7,000 minus 6,000 is 1,000. And once again, right over here, 200 minus 200 is zero 100's. And then 7,000 minus 6,000 is 1,000. So this is going to be 1,000 plus 0 plus 50 plus 1, which is the exact same thing as 1,051. The important thing is to visualize-- you don't have to write this out every time. But to make sure you visualize in your head that this 3 is representing 300, that this 2 represents 20, that when you're taking 100 from the 300, then you would represent that as a 2 in the hundreds place. And then when you give 100 to the tens place, it's essentially that the two 10's will become 12 10's. Because you're giving it 10 more 10's. You're giving it 100. So hopefully, that makes some sense.