Learn about Level 4 Subtraction

Khan Academy Presents: Subtraction of multi-digit numbers involving borrowing

Welcome to the presentation on level four subtraction. Let’s get started with some problems. So, the first problem I have here is 33,220-399. So, just like we did with, I believe that we also did borrowing in the level three subtraction. We have to go through all of the digits in the top number, starting with the top-right digit. And make sure that they are larger than the digit below it because you can only subtract a smaller from a larger number, you can’t do the other way until all this will turn into negative numbers. So, let’s go through this and check which are all the top numbers are larger. Well, immediately we see none of this, zero is not larger nine so we have to borrow to make the zero bigger. So, what we do is we borrow one, well some people say we’re borrowing a one, some people say, I mean borrowing a one from the tens place is really like borrowing a ten. First, we simply say let’s just borrowing a one. So, we borrow one from this two, and this zero will become a ten. And since we borrow that one, this two will become a one. We took one away from this two and we gave it to the zero to make ten. We actually took ten away from this two because two is in the tens place, I don’t want you to confuse you too much. If just the mechanics of it all, we took one away from the two and we put it in front of the zero to make ten. Now, let’s keep checking. So now, we have a one in this place. One is smaller than nine so we have to borrow again. So, we borrow one from this two now, so, this two now becomes one, and this one will now become an eleven. So now, we have a ten is larger than nine, eleven is larger than nine, one is not larger than three, so we have to borrow again. This is a good problem. It’s a, maybe I should warm that up a little bit more because it involves a lot of borrowing. So, in order to borrow, we do the same thing over again. This one will become an eleven. It’s going to borrow from this three which will become at two. I think we’re done now. Ten is larger than nine, eleven is larger than nine, eleven is larger than three, two is larger than nothing, and three is larger than nothing. So now, we’re ready to subtract. It’s the easy part. 10-9=1, 11-9=2, 11-3=8, 2-0=2,3-0=3, so we get, 32,821. So, the important thing to- the only thing that makes this harder than just normal subtraction is that you have to how to do the borrowing. And the way I do the borrowing, it might be different than the way you learned in school but I think it’s easier because you do all of the borrowing at once instead of switching back and forth between borrowing and subtracting. So, all we did here, we said than zero is less than nine, let’s borrow one, then zero becomes a ten, could you got this one right here? We got this one from this two, and this two became a one. I think you might see the patter if you do a couple more problems. So, let’s do a couple more. If I had 25,633-578, so, same drill. Let’s start at the top-right, and we make sure that the digits on top are larger than the digit below it. Immediately, we see three is more than eight, so we have to borrow. This three will become thirteen, and we borrow from this three which now become two. We took a one away from this three. We came to two at this one that’s right here. Thirteen is now larger than eight but two is smaller than seven, so we have to borrow again. This two becomes a twelve and this six will become a five. Thirteen is larger than eight, twelve is larger than seven, and five is the same as five, so you can actually do the subtraction because five minus five is zero. As long as the top number is not smaller than the number below it, and I’ve seen this five is larger than this zero, and this two is lager than this nothing here. So now, I'm ready to subtract, 13-8=5, 12-7=5, 5-5=0, 5-0=5, bring down the two. So, the answer is 25,055. Then, let’s do a problem now that I think will confuse you a little bit more because at borrowing isn’t as easy. You have to actually borrow from a couple places. Let’s say I had 37,002-155. So, it’s the same drill. So, this two is less than five, we have to borrow. This two will become a twelve. But there’s a zero here, you can’t borrow from the zero. Some people will let you borrow from the zero but I think that just confuse this things because you can’t borrow from the zero, there’s nothing there. Instead of borrowing from the zero, we look to this zero, well, there’s still nothing there. So now, we look - Oh there’s a seven here. So, what we do is, instead of borrowing a one from this zero which is hard to do, we borrow one from the 700, from this whole 700. And what is 700-1? Right, it’s 699. So, that 700 becomes 699. We’ll cross all of these out. And now let’s check our numbers again, twelve is larger than five, nine is larger than five, nine is larger than one, six is larger than nothing, and three is larger than nothing, so we’re ready to subtract. 12-5=7, 9-5=4, 9-1=8, 6-0=6, 3-0=3, so there, we’re done. The answer is 36,847. I think we could have time for one more problem. Let’s say I had 3,201-502. Same drill. One is less than two, so we have to borrow. Turn that into eleven. But you can’t borrow from this zero, so you’re going to have to borrow from this entire 20. Well, what’s 20-1? Right, it’s 19. So, let’s check again. Eleven is greater than two, check. Nine is greater than zero, check. One is not greater than five, so we have to borrow again. This one becomes an eleven. We borrowed from this three which becomes a two. Eleven is greater than two, nine is greater than zero, eleven is greater than five, and two is up as grade in nothing below it, so we subtract; 11-2=9, 9-0=9, 11-5=6, and 2-0=2. So, 3,201-502 is equal to 2,699. I think you’re now ready to try of some the level four subtraction problems. You just always have to remember, do your borrowing first, make sure all the numbers on top are larger than all them or at least as large as all the numbers on the bottom, and then we can just do your subtraction like the normal subtraction problem. I hope you have some fun doing this. Talk to you later.