Multi-digit subtraction with regrouping: 6798-3359

We've got 6,798 minus 3,359. So let's see how far we can get with the subtraction. So immediately, when we go into the ones place, we're going to try to subtract a 9 from an 8. So we immediately reach a little bit of a stumbling block. And to see what our options are here in terms of regrouping, I'm going to rewrite both of these numbers. So I'm going to rewrite 6,798 literally. So this is equal to 6,000. That's this right over here. That's 6,000, plus 700, plus 90, plus 8. Minus all of this. So I could subtract each of the places. So I could say this is going to be minus 3,000 minus 300 minus 50-- a 5 in a tens place is just 50-- minus 9. So here, we're just explicitly showing what those place values represent. A 6 in the thousands place is 6,000. A 3 in the hundreds place is 300. Let's go back to our problem. We wanted to subtract a 9 from an 8. Well, that's a little bit of a stumbling block. But what if we could take some of the value from some of these and give it to the 8? In particular, we could go one place value up to the 90. And what if we were to take 10 from the 90? So let's do that. If we were to take 10 from the 90, then 90 becomes 80. But we don't want to change the value of the entire number. So we're going to give that 10 to this 8. We're essentially regrouping right over here. And then that 8 can become an 18. Notice, I did not change the value of the number. I just essentially changed how I represented it. Instead of saying it's 6,000 plus 700 plus 90 plus 8, I'm just saying that it's 6,000 plus 700 plus 80 plus 18. Those are both going to give you 6,798. But now it becomes a little bit easier for us to actually subtract. Now, if we subtract, I have 18 minus 9, which is 9. I have 80-- not 90, now. I have 80 minus 50, which is 30. And these are all positive, so this is plus 9. This is a positive 30. 80 minus 50 is 30. I have 700 minus 300, which is 400. And I have 6,000 minus 3,000, which is 3,000. So this is literally going to be 3,000 plus 400 plus 30 plus 9, or 3,439. Now, how would you do it if you didn't want to write it out like this? And this is where you'll see a kind of shorthand notation. This is often called borrowing. So you say, look, I've got an 8 in the ones place. I want to take a 10 from this 90. So it's going to become an 80. But we'll just write it as an 8 because it's in the tens place. This 8 represents the 80. And I'm going to give that 10 to the ones place. So 10 plus 8 is 18. And now you can subtract. 18 minus 9 is 9. 8 minus 5 is 3. 7 minus 3 is 4. 6 minus 3 is 3-- 3,439.