Intro to remainders

let's take the number seven and divide it by three and I'm going to conceptualize dividing by three as let me see how many groups of three I can make out of the seven so let's imagine let me draw seven things one two three four five six seven so let me try to create groups of three so I can definitely create one group of three right over here I can definitely create another group of three so I'm able to create two groups of three and then I can't create any more full groups of three I have essentially this thing right over here left over so this right over here I have this thing remaining this right over here is my remainder after creating as many groups of three as I can and so when you see something like this people will often say 7 divided by 3 well I can create two groups of three but it doesn't it doesn't divide evenly or 3 doesn't divide evenly into seven I end up with something left over I have a left over have a remainder I have a remainder of 1 so this is literally saying 7 divided by 3 is 2 remainder 1 and that makes sense 2 times 3 is 6 so it doesn't get you all the way to 7 but and then if you have your extra remainder 6 plus that 1 remainder to get you all the way to 7 let's do another one let's imagine 15 divided by divided by 4 let me draw 15 objects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 now let me try to divide it into groups of 4 so let's see that's 1 group of 4 that's another group of 4 and then that's another group of 4 so I'm able to create 3 groups of 4 but I can't create a fourth full group of 4 I am then left with this remainder right over here I have a remainder of I have a remainder right over here of 3 I have 3 left over so we could say that 15 divided by 4 is 3 remainder 3 4 goes into 15 3 times but that only gets us to 12 four times three is 12 to get all the way to 15 we need to use our remainder we have to get three more so 15 divided by four I have three left over