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# Intro to long division (remainders)

## Video transcript

let's now see if we can divide into larger numbers and just as a starting point in order to divide into larger numbers you at least need to know your multiplication tables from the one multiplication tables all the way to at least the ten multiplication so I'll be up to ten times ten which you know is one hundred and starting at one times one and going up to you know two times three all the way up to ten times ten and at least when I was in school we learned through twelve times twelve but ten times ten will probably do the trick and that's really just the starting point because to do about multiplication problems like this for exams like this let's say I'm taking 25 and I want to divide it by five so I could draw 25 objects and then divide them into groups of five or divide them into five groups and see how many elements are in each group but the quick way to do it is just to think about well five times what is 25 right five times question mark is equal to 25 and if you know your multiplication tables especially your five multiplication tables you know that 5 times 5 is equal to 25 so something like this you'll immediately just be able to say because of your your knowledge of multiplication then 5 goes into 25 five times and you write the 5 right there not over the two because you still want to be careful of the place notation you want to write the 5 in the ones place it goes into it five ones times or exactly five times and the same thing if I said seven seven goes into 49 that's how many times well you say that's like saying 7 times what you could even instead of a question mark you could put a blank there seven times what is equal to 49 and if you know your multiplication tables you know that 7 times seven is equal to 49 all the examples I've done so far is the number multiplied by itself let me do another example let me do nine goes into 54 how many times once again you need to know your multiplication tables to do this 9 times what is equal to 54 and sometimes even if you don't have it memorized let's see nine times five is 45 and let's see nine times six would be nine more than that so that would be 54 so nine goes into 54 six times so just as a starting point you need to have your multiplications four tables from one times one all the way up to ten times ten memorize in order to be able to do at least these some of these more basic problems relatively relatively quickly now with that out of the way let's try to do some problems that might not fit completely cleanly into your multiplication tables so let's say I want to divide I am looking to divide three I'm looking divide three into forty three and once again I mean this is larger than three times ten or three times twelve actually look well let me let me do another problem let me do three into twenty three and if you know your three times tables you'll realize that there's three times nothing is exactly twenty three I'll do it right now three times one is three three times two is six let me just write them all out three times 3 is 9 12 15 18 21 24 right there's no 23 in the multiples of three so how do you do this division problem well what you do is you think of what is the largest multiple 3 that does go into 23 and that's 21 and 3 goes into 21 how many times well you know that 3 times 7 is equal to 21 so you say well 3 will go into 23 7 times but it doesn't go into it cleanly because 7 times 3 is 21 so there's a remainder left over so if you take 23-21 you have a remainder of 2 so you could write that 23 divided by 3 is equal to 7 remainder and then we all were just well write the whole word out remainder remainder 2 so it doesn't have to go in completely cleanly in the future we'll learn about decimals and fractions but for now you just say well it goes in cleanly 7 times but that only gets us to 21 but then there's 2 left over so you can even work the division problems where it's not exactly a multiple of the number that you're dividing into the larger number but let's do some practice with even larger numbers even larger numbers and I think you'll see a pattern here so let's do let's do for for going into I'm gonna pick a pretty large number here 344 and you immediately when you see that you might say hey Sal you know I know up to 4 times 10 or 4 times 12 4 times 12 is 48 this is a much larger number this is way out of bounds of what I know in my for multiplication tables and I'm going to show you right now is a way of doing this just knowing you're for multiplication tables so what you do is you say 4 goes into this 3 4 goes into this 3 how many times and you're actually saying 4 goes into this 3 how many hundred times so this is because this is 300 right this is 344 but 4 goes into 3 no hundred times or four goes into egg especially the thing that 4 goes into 3 zero times so you can just move on 4 goes into 34 so now we're going to focus on we're just going to focus on the 34 so 4 goes into 34 how many times and here we can use our for multiplication tables for let's see 4 times 8 is equal to 32 4 times 9 is equal to 36 so 4 goes into 34 39 is too many times right 36 is larger than 34 so 4 goes into 34 eight times there's going to be a little bit left over 4 goes into 34 eight times so let's figure out what's left over and really we're saying 4 goes into 340 how many 10 times so we're actually saying 4 goes into 340 80 times because notice we wrote this 8 in the tens place but just for our ability to do this problem quickly you just say ok 4 goes into 34 eight times but make sure you're at the 8 in the tens place right there 8 times 4 we already know what that is 8 times 4 is 32 and then we figure out the remainder 34 minus 32 well 4 minus 2 is 2 - and then these threes cancel out so you just left with a - but notice we're in the tens column right this whole column right here that's the tens column so really what we said is four goes into three hundred and forty-eight eighty times eighty times four is three hundred and twenty right because I wrote it in the three in the hundreds column and then there is and I don't want to make this look like a I don't want to make this look like a let me clean this up a little bit I just want to make that line there and look like when I was dividing the columns like a 1 but then there's a remainder of two but I wrote the two in the tens place so it's actually remainder of 20 but let me bring down this four because I didn't want to just divide into three hundred forty-eight divided into three hundred forty four so you bring down the four let me switch colors and then so another way to think about it we just said that four goes into three hundred and forty four eighty times right we wrote the eight in the tens place and then eight times four is 320 the remainder is now 24 so how many times does 4 go into 24 well we know that 4 times 6 is equal to 24 so 4 goes into 24 6 times we put that in the ones place 6 times 4 is 24 and then we subtract 24 minus 24 that's we subtract at that stage either case and we get 0 so there's no remainder so 4 goes into 344 exactly 86 times so if you took 344 objects and divided them into groups of four you would get 86 groups or if you divided them into groups of 86 you would get four groups let's do a couple more problems I think you're getting the hang of it let me do seven out of a simple one 7 goes into 91 so once again well this is beyond 7 times 12 which is 84 which we know from our multiplication table so we use the same system we did in the last problem seven goes into nine how many times 7 goes into nine one time 1 times 7 is 7 then you have 9 minus 7 is 2 and then you bring down the 121 and remember this might seem like magic but we're really said seven goes into 90 10 times 10 because we wrote the one in the tens place 10 times seven is 70 right you can almost put a zero there if you like and 90 with a remain 91-70 is 21 so 7 goes into 91 10 times remainder 21 and then you say 7 goes into 21 well you know that 7 times 3 is 21 so 7 goes into 21 3 times 3 times 7 is 21 you subtract these from each other remainder 0 so 91 divided by 7 is equal to 13 let's do another one and I won't I won't take that little break to explain the places and all of that I think you understand that I I want to at least either get the process down really really well in this video so let's do 7 all right keep using the number 7 let me do a different number let me do let me do 8 goes into 608 how many times so I go 8 goes into 6 how many times it goes into it 0 times so let me keep moving 8 goes into 60 how many times well let me write down the 8 let me draw a line here so we don't get confused let me scroll down a little bit I need some space above the number so 8 goes into 60 how many times we know that 8 times 7 is equal to 56 and that 8 times 8 is equal to 64 so 8 goes into 64 is too big so it's not this one so 8 goes into 60 seven times there's going to be a little bit left over so 8 goes into 60 seven times since we're doing the whole 60 we put the 7 above the ones place and the 60 which is the tens place and the whole thing 7 times 8 we know is 56 60 minus 56 that's 4 we could do that in our heads or if we wanted we can borrow that would be a 10 that would be a 5 10 minus 6 is 4 then you bring down this 8 you bring down that 8 8 goes into 48 how many times well what's 8 what is 8 times 6 well 8 times 6 exactly 48 so 8 times 8 goes into 48 6 times 6 times 8 is 48 and you subtract we subtract it up here as well 48 minus 48 is 0 so once again we get a remainder of 0 so hopefully that gives you the hang of how to do these larger division problems and all we really need to know to be able to do these to tackle these is our multiplication tables up to maybe 10 times 10 or 12 times 12