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Partial quotient method of division: example using very large numbers

Video transcript

I thought I would do another example of the partial quotient method for long division and so that it actually has some positives to it it's actually kind of fun to do so let's say I want to do something really hairy like 291 it divided into divided into let me just throw some digits over here 300 and I knew actually let's store another digit right over here so this is how many times does 291 go into what is this nine million eight hundred seventy three thousand nine hundred and fifty-two and to just kind of get our bearings we know what 291 times one is that's pretty easy 291 times one is clearly just 291 we know what 291 times ten is that's clearly two thousand nine hundred and ten and let's get something some stuff in between here that'll help us as we try to approximate how many times 291 goes into this this crazy thing over here so let's just pick and in the last example I picked two and five you could just pick three and six if you want you could pick two and seven you could pick whatever you want you could even just do one one of them one of the above but let's just say 291 291 times let's try three out 291 times three so I could do this in my head or I could just to make sure I don't make a mistake let me do it right over here so 291 times 3 is 1 times 3 is 3 9 times 3 is 27 2 times 3 is 6 6 plus 2 is 8 so this is equal to 873 it's actually strange that that 873 showed up over there maybe my brain is doing strange things in the background but anyway that actually has no relevance to the actual solution of this problem and let's also try 291 let's also try 291 times 6 291 times 6 let's figure what that figure out what that is so 291 times 6 it's actually just going to be this thing times 2 but I'll just calculated it 291 times 6 1 times 6 is 6 9 times 6 is 54 2 times 6 is 12 plus 5 is 17 so it's 1746 746 and you might say Sal why did you go through the trouble of figuring out this and this and I'm just using these as some approximation tools when we try to figure out how many times 291 goes into this whole crazy mess so first of all let's just look at this whole thing this is nine million eight hundred seventy three thousand so let's just say how many times does 291 go into nine million nine million so 291 times 3 would be 873 we want to add up we want to have a bunch of zeros after the 873 so think of it this way and I'm picking 873 because it's leading digit is as close to the 9 as possible but it's definitely lower than the 9 so you say okay 873 and I'm gonna have one two three four zeros behind it so 291 times three will give me 873 but I have to multiply times three with one two three four zeros one two three four zeros to get this number eight point seven three eight point seven three millions have to multiply by 30,000 but I got that straight from this idea that 291 times 3 is 873 so let's subtract this right over here let's subtract this 2 minus 0 is 2 5 9 3 7 minus 3 is 4 8 minus 7 is 1 9 minus 8 is 1 so now we're left with 1 million one hundred forty three thousand nine hundred and fifty-two so which of these is which of these just gets us right under that so let's see if we we don't we can't go to something let's see if we want to go to we can't go straight to 1746 that will be too big over here we might want to do 873 again but this time we're gonna do eight hundred and seventy three thousand eight hundred and seventy-three thousand that is equal to 3 and then you have one two three zero so one two three three times 291 is 873 3000 is 873,000 let me write this a little bit neater my handwriting is so this is going to be this is going to be this is going to be three thousand three thousand times 291 and just let me make sure this is a 2 right over here 2 minus 0 is 2 and then you subtract again subtract again 2 minus 0 is 2 5 minus 0 is 5 9 minus 0 is 9 3 minus 3 is 0 and then you have 4 minus 7 so the way I like to do it when I have to start regrouping and borrowing is making sure I go from the left so I could this one I could borrow from there so that this becomes an 11 and then the 4 I can borrow one from here so that becomes a 10 and then this becomes a 14 so 14 minus 7 is 7 10 minus 8 is 2 so I'm down to 270 thousand nine hundred fifty-two so what's the the what's right below that so it seems like we can get pretty close if we do 291 times 6 so if you do a 1746 and then add two zeros to it this is going to be times six with two zeros so this is times 600 once again you subtract and one see I'm only using the sixes in the threes because I figured out those ahead of time so I didn't have to do any extra math so 2 minus 0 is 2 5 minus 0 is 5 9 minus 6 is 3 0 minus 4 well I can there's a couple of ways you could think about doing this you could borrow from here that'll become a 6 this becomes a 10 10 minus 4 is 6 now this one's lower so it has to borrow as well make this into a 16 16 minus 7 and I have multiple videos on how to borrow if I'm doing that part too fast but the idea is here to show you a different way of long division so 16 minus 7 is 9 so now we're at 90 6352 and once again it looks like the 873 is about as close as we can get so let me put an 8 7 3 over here with 2 zeros so that will literally be 291 times 3 with two zeros times 300 and so once again we want to subtract here 2-0 you get a 2 a 5 0 make this a 16 make this an 8 16 minus 7 is 9 and then we have to get close to 9000 52 once again that 873 those digits look pretty good 8 7 3 we still want to multiply we have 2 by three and then ten so this is going to be times thirty right over here we subtract again 2 minus 0 is 2 5 minus 3 is 2 and then you have 90-87 is 3 I'm doing the subtraction a little faster so that we can get the general idea then we have to go into 322 and how can we get close to that well actually 291 is pretty darn close to that so it's 200 you go into it one time one times 281 is 290 one two minus one is 132 minus twenty nine is three so you have a remainder of 31 291 cannot go into thirty-one anymore so that's our remainder but how many times did actually go into this big beastly number this 9 million eight hundred seventy three thousand nine hundred fifty-two well then we just have to add up all of these right over here 30 plus three thousand we could even do it in our head 30 plus three thousand is thirty three thousand thirty three thousand six hundred thirty three thousand nine hundred thirty three thousand nine hundred and thirty one thirty three thousand nine hundred and thirty-one and we are done assuming I haven't made some some silly mistake to her 91 goes into this thing thirty three thousand nine hundred thirty one times with the remainder of 31