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Current time:0:00Total duration:4:49

Introduction to remainders

CCSS.Math:

Video transcript

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 have 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 made 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 8/3 pause this video and see if you could 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 make can we divide this into groups that all have three in them and how many groups would we be able to make of three 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 groups of three and I 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 groups 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 of to another way to think about it is to this 2 times 3 6 and then if you were to put back that remainder that's how you can get to 8 now another way you could think about it is how we thought about in the second example with 8 divided by 2 let me draw eight objects again 1 2 3 4 5 6 7 8 and you could say hey let me divide that 8 into 3 equal groups so pause this video and see if you can divide this into 3 equal groups and then what might be left over alright so I'm going to try to divide this into 3 equal groups I'm not going to be able to put 4 in each of those groups because I can only make 2 equal groups of 4 I'm not gonna be able to put 3 into those 3 equal groups because that would actually be outing 9 4 doing that so each of my groups are gonna have to be 2 so I could make one group of two another group of 2 and there you go 3 equal groups of 2 so I was able to sort out 3 equal groups of 2 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 cuz I'm dividing by 3 then I have this leftover again let's do one more example what if I were to ask you what is what is 13 divided by divided by 4 pause this video and think about it and as you might imagine there's will be a remainder involved all right well let's draw 13 objects 1 2 3 4 5 6 7 8 9 10 11 12 13 and we could try to divide this into equal groups of 4 that's one way to think about it so let's see that's a group of 4 I got I have one group of 4 that's a group of four I have two groups of 4 and then that is a group of 4 so I'm able to find the equal groups of four so this is equal to three another way to think about it four goes into thirteen 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 twelve but then if you want to get to 13 well then you got to throw in that remainder there