Hi and welcome to Math Antics. In this video we’re gonna learn how to do multi-digit subtraction. It’s similar to doing multi-digit addition like we learned in our last video, but there’s a few important differences. The main difference is, with subtraction the order of the problem matters. With addition, you can switch the order of the numbers you’re adding and you’ll still get the same answer. 5 + 2=7 and 2 + 5=7. But with subtraction, if you have the problem 5 minus 2, you’ll get 3. But you CAN’T switch the problem around. You won’t get the same answer if you try to do 2 minus 5 instead. In fact, you’ll probably get confused because you’ll be trying to subtract a bigger number from a smaller one. With multi-digit subtraction, it’s important to remember that order matters, especially when you’re re-writing your problem. Often you will be given a problem like this (38 – 25) and you’ll have to re-write it with the numbers stacked up like we did with addition. But you have to make sure that the first number, the one you’re taking FROM, goes on top and the number you are taking AWAY is on the bottom. Another hint is that the bigger number should always be on top. Okay, let’s go ahead and try this problem. We’ve got 38 on top and 25 below it, and the ones places are lined up, just like they should be. Now we draw our line so our answer can go below it, and we write a minus sign over here on the left to show that we’re subtracting. Now we can start getting our answer. And just like with addition, we ALWAYS start with the ones place column. Here we subtract the bottom number from the top: 8 – 5=3 So the ‘3’ goes in the ones place of our answer. Now we move to the next place column to the left, the tens place. There we have 3 – 2 which is 1. There, we just subtracted 25 from 38 and found out that the difference is 13. Alright, let’s see another example: 135 – 27 Ah-ha, this is where multi-digit subtraction can get a little tricky. Let’s re-write our problem: 135 on top, 27 below it, with the ones places lined up neatly, and our answer line and subtraction symbol in place. There… now we can start subtracting. Uh-oh! Look at this… In our ones place column, the digit on top is smaller than the digit on the bottom. How can we subtract a bigger digit from a smaller one? Did we make some kind of mistake? No, we wrote our problem correctly… the bigger number is on top. Sometimes this just happens… the top digit might be smaller than the bottom digit, so you can’t subtract it… unless… you borrow! Here’s how borrowing works… The top digit is 5, but the digit below it wants to take 7 away. “Sorry, I don’t have 7, I only have 5.” “Well, what about your neighbor? He’s in a bigger number place… he’s loaded! So you can just borrow from him.” “Excuse me, I’ve got a little problem… do you happen to have something I could borrow?” “Why of course. Here you go!” Great, that ‘1’ will help. But if you just add 1 to 5, you’d get 6. But fortunately, this ‘1’ came from the next number place and it really represents a 10. And when we add 10 to 5 we get 15 which is big enough. Now, instead of this column being 5 – 7, it’s 15 – 7 and 15 – 7=8. Okay, we’ve got the first digit of our answer. Now we can move on to the next column. But remember, we borrowed from that number place. It used to be a ‘3’, but now it’s a ‘2’. It went down by 1 because we borrowed from it. Well, remember… we really borrowed 10, because it was in the next number place, but it’s sometimes easier to just think of it as borrowing a ‘1’ and getting to stick that ‘1’ in front of the digit that needed to borrow. So in the tens place, we have 2 minus 2 which gives us zero in our answer. And then, our last column just has 1 minus nothing (or 1 minus zero) so that’s still just 1. There, we’ve calculated that the difference between 135 and 27 is 108. Alright, let’s try another example with borrowing (or re-grouping as some teachers call it). Let’s subtract 58 from 426. Again we start by subtracting the digits in the ones place column. Here we have 6 – 8, and since 6 it too small to subtract 8 from, we’ll need to borrow. We always borrow from the number place on the left. We’ll borrow a ‘1’ (which is really a ’10’) and we’ll write it in front of our borrowing digit (in this case 6) which gives us 16. And don’t forget to make the digit we borrowed from smaller by 1. You can just cross it out and write the new smaller number above it, like this. Okay, now we can subtract the first column: 16 – 8=8 Now for the tens place. Since we borrowed from this column, it’s become 1 – 5, but again, the top number is too small, so we’ll have to borrow again. We borrow a ‘1’ from the next number place over which mean that digit will change from a ‘4’ to a ‘3’. Then we put the ‘1’ in front of the borrowing digit which will make it 11. Now we can do the subtraction for that column: 11 – 5=6. And the last column is easy, we bring that leftover ‘3’ down to the answer line because there’s nothing there to subtract from it, and that means 368 is our answer. So now you know the basics of multi-digit subtraction. But before you move on to practicing with exercises, I want to show you one more important trick. Once in a while, you’ll come across a situation where you need to borrow from the next number place over, but that digit happens to be a zero! How can you borrow from a zero? Well, you can’t. So you’ll have have to borrow from the next TWO digits instead of just one. In this case, instead of borrowing from 0, borrow from 40. You’ll get the ‘1’ you need to borrow, and the 40 will become a 39. Or in this case… If the ‘3’ needs to borrow, don’t borrow from the ‘0’, borrow from the ’20’ and there will be 19 left over. Or, what if there’s two zeros in a row like this problem? Well, if the ‘2’ needs to borrow, then borrow from the whole 500 next door. The 2 will become 12, and the 500 will drop by one to become 499. Get the idea? You can do that no matter how many zeros are in a row. Just keep including the next digit to the left until you get a number you can really borrow from. Okay – that wraps up this lesson. Hopefully you have a better idea of how multi-digit subtraction works, but to really get it down, you’ve got to practice. So be sure to do those exercises. Thanks for watching and I’ll see you next time. Learn more at www.mathantics.com