Introduction to remainders

- [Instructor] We're already somewhat familiar with the idea of division. If I were to say eight divided by two you could think of that as eight objects. So one, two, three, four, five, six, seven, eight divided into equal groups of two. And so how many equal groups of two could you have? Well you could have one, two, three, or four groups of two and so you'd say eight divided by two is equal to four. Another way we could've thought about that is you have one, two, three, four, five, six, seven, eight and if you were to divide it into two equal groups well you could have one group of four. Let me get a little bit cleaner. One group of four and then a second group of four. So two equal groups. How many in each of those equal groups? Well they're four in each of those groups. And so once again eight divided by two is equal to four. Now we're going to extend our knowledge of division by starting to think about things that don't divide evenly. So what if we were to say what is eight divided by three? Pause this video and see if you can think about that a little bit. All right so let's draw eight objects again. One, two, three, four, five, six, seven, eight and one way to think about it is how we thought about it here is can we divide this into groups that all have three in them and how many groups would we be able to make of three? Well let's try it out. I can make this group of three, I can make this second group of three but I can't make any more group of three and what I have left over are these two. And so the way that you would describe this or one way to describe this is hey I was able to make two group of three so it's equal to two and there's some left over, there's a remainder. Let me write that down. Important concept. There is a remainder of two as well and so sometimes it's written as just a lowercase r or remainder of two. Another way to think about it is two, this two times three is six and then if you were to put back that remainder that's how you can get to eight. Now another way you can think about it is how we thought about it in the second example with eight divided by two. Let me draw eight objects again. One, two, three, four, five, six, seven, eight and you could say hey let me divide that eight into three equal groups. So pause this video and see if you can divide this into three equal groups and then what might be left over. All right, so I'm going to try to divide this into three equal groups. I'm not going to be able to put four in each of those groups 'cause I can only make two equal groups of four. I'm not going to be able to put three into those, three equal groups 'cause I would actually be outing nine for doing that so each of my groups are going to have to be two. So I could make one group of two, another group of two, and there you go three equal groups of two. So I was able to sort out three equal groups of two with just these six but once again I have a remainder. I'm not able to make use of these two, they're not able to fit into one of in this case one of the three equal groups. If I said four equal groups then they would fit in, but if I just said three equal groups 'cause I'm dividing by three then I have this left over again. Let's do one more example. What if I were to ask you what is, what is 13 divided by divided by four? Pause this video and think about it and as you might imagine there will be a remainder involved. All right, well let's draw 13 objects, one, two, three, four, five, six, seven, eight nine, ten, eleven, twelve, thirteen and we could try to divide this into equal groups of four, that's one way to think about it so let's see. That's a group of four, I have one group of four. That's a group of four, I have two groups of four and then that is a group of four so I'm able to find three equal groups of four so this is equal to three. Another way to think about it four goes into 13 three times but then I have this little lonely circle here, I have one left over I have a remainder of one because four times three that gets you to 12 but then if you wanna get to 13 well then you gotta throw in that remainder there.