Welcome back and in this video we're going to do a few more subtraction problems involving borrowing and I really want to make sure we do a lot of this because I think this is where, when people first learn it there is the most confusion but ones you really understand what you're doing, hopefully you find that it's pretty straight forward and then we’ll do a couple of word problems. So let's do the last couple of problems on page 33 in what is it the Primary Mathematics 3A book this is the US edition. So we, let's say we have and actually I'm going to do this on several ways because I want to show you that all of this ways are equivalent maybe what you learn in your school is a little bit different but they're all essentially doing the same thing and I want you to learn that. So we have 8,007 minus 3,429.

So how do we think about that this? Well three is less than eight but all of this numbers are greater than the numbers above them, right. So we're going to have to do some borrowing, so there’s a couple of ways you could do this, I'm actually I'm going to write the problem over again right here. Because I want to do it two different ways, one way I'm going to explain what's actually happening and one way is actually just really, really fast. So let's go over the fast way fist because it never hurts to know how do these problems really, really fast.

So let's say if I started at the ones place here and I have the seven but the seven is less than this nine so I have to take something from the rest of the number, right. And the only thing I ever take is you know, if I found in the ones place so everything I ever take is 10 right, so think of it this way. And then ignore it if confuses you but I have seven here and then this 8,000 or I could just, if I just look at those three places those—that 800 what is that? That’s 800 tenths right? Why do I say that? Well, because the last zero in the 800 is actually in the tenths place. So you can—and this is kind of Sal math, I don’t think this is really taught anywhere. But it's a really fast way of doing some of this borrowing problems, you could view this as 800 tenths, you need one tenth here, so that you can make the seven into a 17 so what do you do? Well you borrow one of those 800 tenths. So what's 800 tenths minus one tenths? What 800 minus one? Well it's 799, 799 and then you take that extra 10 and you add it to the ones place and you get 17, and then you're ready to subtract. 17 minus eight, I'm sorry, 17 minus nine is eight, nine minus two is seven, nine minus four is five, seven minus three is four and now you should only do what I just did, if you're really comfortable with how things are working and you understand the intuition.

Don’t try to skip steps if you're not sure what the step is. And on the left side now, I’ll do it kind of in the full proof way so that, so that you really make sure you understand what you’re doing. So we have the same problem because it's you know the numbers on top or smaller than the numbers on the bottom and of course the same problem because it's—well it's the same problem. So here we can actually start borrowing on, we can start going from left to right. It's going to have the exact same result as you’ll see in the second. I’m going to use the same color. So this zero is less than this four, right, the zero hundreds is less than 400, so—and we have 8,000 here so why don’t we take one of this 8,000 so we only have 7,000 left.

And convert it to 10 hundredths, so we convert hundredths. But now we have this zero tenths is less than two tenths. So let's take some of this 10 hundredths, well let's take one of this 10 hundredths so we only have nine hundredths left. And give one of those hundreds to the tenths place and now we have 10 tenths. All right, but we're almost done, but we see that the seven ones is less than the nine ones, so why don’t we borrow 10 form the tenths place. So if we borrow 10 we only have nine tenths left and then we add that 10 to the ones place so we have 17, notice the end product was the exact same thing, we now have a 7,000, a nine 900, a 90 and a 17 in the ones place and we could subtract 17 from nine, it's I'm sorry nine from 17 is eight, two from nine or nine minus two is seven, nine minus four is five and seven minus three is four. So the same result and they got the same place and I want you to think about why both of this worked and hopefully I gave a little intuition as far as why they worked.

Let's do a couple more, I'm not going to do all of them just depending on how much time we have. So let's say we have 9,403 minus 4,275. Four is less than nine, two is less than four but seven is not less than zero and three is not less than five. And actually let me do tit the two ways that we just learned because I think this will be instructive an it's good to, to see all the different ways and maybe you’ll come up with the new way of doing it. Actually my cousin when he was eight, he figured out a new way but—and then it actually it was pretty fast.

But anyway let's go back to this problem. So what's the conventional way or I guess nothing is a conventional way, they're teaching how they, they change how they teach this things every year it seems like. But we could say, well the four is less than a nine, so we're cool there. The two is less, well this is 4,000 and it's less than 9,000, the 200 is less than the 400 we're cool there but the 70 is not less than this zero tenths, right. So why don’t we borrow a hundred, so we only have 300 left and turn that into 10 tenths. And then we have the three is less than a five, so why don’t we borrow one of our 10 tenths and we have nine left and put that 10 in the ones place, we have 13. So that was kind of what I call the conventional way of doing it. The less conventional way of doing it is to actually start at the right hand side because we say well this three is less than that five, right.

The three is less than the five so let me borrow from here, wait but I can't borrow from zero tenths. But wait I could go one more space and I could borrow from 40 tenths, right. Four, this is 400 right, but 400 is the same thing as 40 tenths. So let me borrow one of those 40 tenths so then I have 39 tenths left. And add that extra 10 to this space and I get 13 and notice we have the exact same outcome when we could subtract. 13 minus five is eight, nine minus seven is two, three minus two is one, nine minus four is five. On this side 13 minus five is eight, nine minus seven is two, three minus two is one, and nine minus four is five. I encourage you to try to understand both things I did because neither of them are magic and they should make sense to you from a place value point of view.

But which ever one you're more comfortable with stick with that and just practice tons and tons and tons of problems and you know if you run out of problems your workbook, make up problems. That actually a good way to learn, so let's do one more and I think you’ll find that this one specially the quick using the technique that’s not necessarily condoned in your, condoned means encouraged or supported but it's not actually condoned by the Singapore math but I think it's good for you to learn every different possible way.

So we have 10,000 right, now we're doing a five digit number but hopefully you know this is a ones, tens, hundreds place, thousands place, 10 thousands place every place we go, we're just—it's 10 bigger, right. I mean hopefully if I give you a seven digit number we could, you could actually deal with it because you just know every time you go one place to the left that digit just represents something 10 times bigger than the digit to the right, 10 is 10 times bigger than one, 100 is 10 times bigger than tenths, 1,000 is 10 times bigger than a hundred and 10,000 is 10 times bigger than 1,000.

Well let's say 10,000 minus 5,721 I’ll do this one as both ways as well, 10,000 minus 5,721, so we have a zero here we need to borrow some—well not only I want to say because you have to take it right? But you can't take from zero you can't take from—so let's start at the left hand side. This 1,000 is zero thousands is less than 5,000 so let's borrow from the 10,000 spot. So let's—there's only one 10,000 there, so let's take it and let's put it into the 1,000 spot. So we have 10,000 down the 1,000. We don’t have enough hundreds here, so let's borrow one of the thousands and then we have 1,000 we don’t have enough tenths so let's borrow on of the hundreds now I’d borrow and take one of the 100 and then we have 10 tenths.

And then, well we have, we don’t have enough one so let's borrow one of the tenths and then we’ll have 10 ones and then we're ready to subtract 10 minus one is nine, nine minus two is seven, nine minus seven is two, nine minus five is four, sorry, nine minus five is four. My brain is malfunctioning. Let's do it this way, so how can we think about, well we could start at the right hand side. And say “Oh, well this is zero it's just not acceptable we need to get a 10 here somehow”.

So let's look to the left of it we can't borrow from here, we can't borrow from here and here. We can't borrow from here and here to there but if we bought, if we look at this entire number 10,000 is the same thing as 1,000 tenths, right. This is, this thing that look likes 1,000 since its starts to the tenths place here that’s 1,000 tenths, right. So why don’t we jut borrow this one of them, all we need is one tenth here, right. So if we, if we have a thousand of something and we take one of them how do we, how many do we have left? Well what’s 1,000 minus one, it's 999. So this has 1,000 tenths if we borrow one of them we have 999 tenths left and then we take that 10 that took or borrowed and we put it in the ones place. 10 minus one is nine, nine minus two is seven, nine minus seven is two, and nine minus five is four.

Do this only if you understand what's happening or otherwise do this since it was going to take you a little bit longer but either way, it's fine and they both should make intuitive sense to you, if you think about the number places and you know what if they don’t, I encourage you to draw out those diagrams like you have in the Singapore math book where you have to disks that with a thousand and hundreds in them. Or do the expanded notation like I have it where you know I’d write 5,721 as 5,000 plus 700 plus 20 plus one. Do it either way and you should find that things worked out and in all mathematics I encourage you even if you can get an A on the test, even if you find the homework easy play around with the numbers, experiment with them, really get a feel for them because if you really understand mathematics and the third grade or the fourth grade or either the fifth grade, the sixth grade or the 12 grade or college or you're in PhD in Physics, it's going to be that much easier. Anyway, I will see you in the next video.