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# Partial quotient method of division: introduction

## Video transcript

let's say we need to figure out how many times 16 goes into 1388 and what I want to do is first think about how we traditionally solve a problem like this and then introduce another method that allows for a little bit more approximation so traditionally you would say well 16 does not go into 1 any time so then you move over one spot well how many times does it go into 13 well it still does not go into 13 and then you go all the way to 138 you say well 16 does go into 138 you say how many times will it go into 138 and you might try 9 first and I'll do all my arithmetic here on the right side so you'll say 16 times 9 6 times 6 times 9 is 6 times 9 is 54 6 times 9 is 54 1 times 9 is 9 plus 5 is 14 so it goes 144 times so that's still that's still too big that's larger than 138 so it's going to go into it 8 times 8 times will be less than 138 so you would stick an 8 here notice I have to do this little trial and error here I have to make sure I got the right exact number I have to make sure I have put an 8 right over here then you say 8 times 6 is 48 and then 8 times 1 is 8 plus 4 is 12 so 8 times 16 is 128 so when I subtract I get the remainder from 138 so I get a remainder of 8 minus a to 0 3 minus 2 is 1 and then these cancel out so a remainder of 10 but I still have this 8 right over here so I bring that down so I have 108 and then I do the same thing again let me get rid of this one we don't get distracted we say how many times the 16 go into 108 and you can approximate you say well it's definitely not 8 times 8 times 128 is it maybe seven times and then you might do a little math on the side see 16 times 7 6 times 7 is 42 1 times 7 is 7 plus 4 is 12 or sorry plus 4 is 11 1 times yet 7 plus 4 is 11 so you 112 so that's still too large so it's going to be 6 but notice we have to do this little side work on the side right over here to come up to realize it wasn't 7 we now 6 is going to be the largest how many times you go into 108 without going over it so 6 times 6 is 36 carry the 3 or regroup the 3 depending on how you think about it 6 times 1 is 6 plus 3 is 9 plus 6 is a plus 3 is 9 then you subtract again 8 minus 6 is 2 and then you can just say 10 minus 9 is 1 or you could even borrow you can make this a 10 and then that goes away 10 minus 9 is 1 so then you have 12 and if we're not going to decimals you're kind of done because 16 does not go into 12 so 16 goes into 1388 86 times with a remainder of 12 that right over here is your remainder remainder and that's all all a decent way of doing it and that's the way you traditionally know how to do it but what I do is introduce another maybe a little more interesting way to solve a long division problem so once again let's do our 16 16 goes into 1388 and what we're going to do is give us a much more leeway for approximation or for essentially guessing and what we want to do is just guess we just we're going to make guesses for how many times 16 goes into the numbers without without overestimating without jumping too high and now we're not going to talk we're not just going to think about the one or the 13 or the 138 we're going to think about the whole number as a whole and before we do that I'm going to get two things out of the way just because it'll help us I'm just going to remind ourselves what 16 times 2 and 16 times 5 are and I'm just picking these as random numbers that we can use to approximate you don't have to use 2 & 5 you can use any numbers maybe I'll show other examples there so 16 times 2 we know is 32 and 16 times 5 is 50 plus 30 is 80 so let's just keep these these two results in mind while we try to tackle this right over here so the first thing to think about is how many times is 16 just our best guess our best guess for how many times the 16 go into 1388 or another way to think about how many times does 16 go into a thousand let's just let's just do something at a very very rough approximation well we know so we know it's not going to be 10 because 10 or it's not going to be 100 because 100 times 16 would be 1600 just throw those two zeros at the end of it and you say how many times is go into a thousand well we know 16 times 5 is 80 we know that 16 times 50 would be 816 times 50 would be 800 so let's use that and I'm using I'm using the 5 I'm multiplying it by another 10 to get 250 instead of the 2 because 800 is a lot closer than 320 to our thousand that we care about so what we could say is well 16 times 50 16 times 50 will get us to 800 will get us to 800 once again how did I know that well 16 times 5 I've know ahead of time is 80 so 16 times 50 I'm multiplied by 10 5 times 10 it'll get us to 800 and then I just subtract so I subtract here 8 minus 0 is 8 8 minus 0 is 8 and then you could say 13 minus 5 is 588 and now we ask ourselves how many times the 16 go into 588 how close can we get to that and let's just assume that we only know this stuff right over here or we could multiply 16 times a multiple of 10 so 800 once again be too big that gets us above 588 let's just go with 320 right over here so we know that 16 times 2 we know that 16 times 2 is 32 so 16 times 20 16 times 20 is going to be 320 I just multiplied the 2 times 10 which would give us our product times 10 and so we can subtract this right over here 8 minus 0 is 8 8 minus 2 is 6 and then 5 minus 3 is 2 so now I'm left with 268 and we say how many times does 16 go into 268 and well let's see 800 is too big even 320 is now too big well we could say let's see 10 times 16 will give us 100 60 let's just try that out we don't even have to get the exact right answer we don't have to get the highest multiple that's less than 260 we just have to make sure that we're still within 268 so if we multiply let me do a new color over here if we multiply 16 times 10 we get 160 160 we subtract again so 8 minus 0 is 8 6 minus 6 is 0 2 minus 1 is 1 and then we're left with well how many times does 16 go into 108 and we can go back to our we know 16 times 5 is 80 so let's just try out 5 so let's just try 5 16 times 5 is 80 we subtract right over here 8 minus 0 is 8 10 minus 8 is 2 so we're left with 28 and now it's pretty simple how many times the 16 go into 28 well it only goes into it one time you only go into it one time and then when you subtract 20 16 from 28 8 minus 6 is 2 2 minus 1 is 1 you're left with a remainder of 12 but you might say well how do we know how many times does 16 go into 13 88 or 1388 what goes 50 x + 20 x + 10 x + 5 x + 1 time so that's going to be we could just add up all of these things on the right hand side it's going to be 50 plus 20 is 70 + 10 is 80 + 5 is 80 5 plus 1 is 86 so there we have it it went into it 86 times with the remainder of 12 and what's cool about this method is it at every step I could have put a 60 over here and I could have done the math correctly or I could have done or I could have picked my two multiples to be 16 times 6 and 16 times 3 and I would have gotten different results here but at the end I still would have gotten the right answer so what it does is it gives us a method so that we're always thinking about we're always kind of biting away chunks of what we're dividing into so first we bit off an 800 piece chunk then we bit off a 320 piece chunk and we keep going until we until we essentially can't divide by 16 anymore so hopefully you found that kind of interesting