Learn to Divide Decimals (Long Division with Decimals) - [19]

hello welcome back the title of this lesson is called dividing decimals this is part one it's a long lesson we have a lot of problems here but it's a very very important skill to master so we're going to get a lot of practice now before you have uh before you conquer this i really would like you to do two things first i'd like you to watch the previous lessons on understanding what a decimal division is using pictures so in the back of your mind i want you to have the picture a picture of what's going on as we do our problems second of all you really need to be pretty good at long division already long division of whole numbers we've done that many many times in the past many many many problems if you are fuzzy on how to do long division please stop and go do that right now so once we have those two things out of the way what we want to do is divide a decimal by another decimal so for instance let's say we have the decimal 20.4 we have 20 whole sandwiches and 0.4 of another which is a little bit less than half of another sandwich and we want to divide it by 1.7 so we have a decimal divided by another decimal now in the picture model that we had in the last lesson we could draw a picture of 20 whole things and then 0.4 of a fraction of another thing and then we can divide by 1.7 we could draw a picture of that and we could see how many times 1.7 is going to fit in there how many times will it fit in to 20.4 that would work but that's not going to be a great way to solve a lot of problems so what i want to do is i'm going to show you how to do this you will have some questions the first time you'll be like why can't we do that how do we do that why is that okay i want you to kind of keep your questions but let me cycle through the first couple of problems so i can cycle through all of your questions and then at the end you'll understand everything now dividing by 1.7 in long form is difficult to do so what we're actually going to do is we're going to change this problem a little bit what we want to divide by on the outside we always want it to be a whole number it just makes the math easier so what we want to do is take this nasty little decimal point and we want to move it over here but if we move the decimal spot one position over this way then we must also move what is under the the the um division symbol uh one spot as well so we move the decimal one spot this way and then one spot that way you might say why are you allowed to move decimals just hold your questions i will explain why we are allowed to move decimals in just a second but for now just know that we want a whole number out here so we move it one spot and if we move it one spot out here then we must also move this one spot as well so then what happens is we're not going to solve this problem what we really will do is solve a very closely related problem which is 20 i'm sorry 204 divided by 17. you see the original decimal was here and we moved it one spot to the right so now we have 17. the original decimal was here and we moved it also one spot to the right which means we have a decimal point here and now a decimal point here exactly as we've shown here so what we're saying is now we're going to solve the problem 204 divided by 17. we already know how to solve that problem you already know how to do that right um the uh only trick is knowing that we that trick but the only thing we have to know is that we have we want a whole number on the outside of the division symbol so we move one spot move one spot now let's solve this problem the answer that we get to this problem whatever we get is the answer is the same answer as what we would get if we just drew a picture and divided this it just so happens that this is much easier to do and it gives us the same answer again i will explain why we're moving the decimal in just a minute let me finish the problem all right how do we do long division 17 divided into two it can't go it's it's not 2 is not big enough so consider 17 dividing into 20. it can only go one time 17 is very close to 20. so we'll put a 1 right here and we put it over the 0 because we're dividing into the 20. the next step is 1 times 17 we just put the 17 here and subtract now you can do the borrowing and all that to subtract or you can just think that you're subtracting 20 minus 17. you can start at 17 and count up to 20 to do the subtraction if you want to go subtract 20 minus 17 on the side that's fine or you can count up from 17 18 19 20. there's only three uh units between 17 and 20 so we can just put a 3 down here to do it long form we'd have to borrow here and all this stuff and that will make it cluttered so we know the answer is 3. after we subtract grab the next digit bring it down now what do we do we have to figure out 17 times something is 34. we know that 17 times 1 is 17. what is 17 times 2 17 times 2 7 times 2 is 14 and 2 times 1 is 2 plus 1 is 3. 17 times 2 is exactly 34. so this has to be a 2. 2 times 17 is 34. subtract 34 minus 34 is 0. and so we grab the next digit but there is no next digit so we're basically done and the remainder is zero so what have we figured out here we figured out that if we take 204 and divide it by 17 we get 12 times it fits in there exactly 12 times so the answer to this problem is 12. the answer to this problem is 12. and that is exactly the same answer as we get when we take 20.4 and divide by 1.7 we convert it to this because when we don't have nasty decimals here on the outside it makes doing the long division process easier so what we're going to do every single time is when we're dividing by a decimal we're going to move the decimal as many spots as it takes so that we only have a whole number out here and however many spots we move it we must also move the inner decimal the same number of spots because if you move one but not the other then you've changed the problem but if you move one of them and then also move another one then they're the same let me give you a couple of a couple of reasons why it's okay to do this picture you have a teeter-totter or a seesaw right and you have it's balanced in the middle you have one person on this side and one person on this side and it's perfectly balanced it's not moving it's perfectly flat now if i put a bag of sand on one side of course it's going to do this but i can keep it balanced by also putting another bag of sand on the other side and then i can keep the exact balancing the same of the seesaw if i take one bag of sand off this course is going to move but if i take both sands off at the same time then the children are still there and the seesaw is still exactly balanced if we move one of these decimals by itself then we've unbalanced everything and changed everything but if we move both of these decimals the same then the problem looks different but actually gives exactly the same answer as if we do this so that's one way of thinking about it let me tell you another way a better way of thinking about it when we do division like this you really need to start thinking about division as being kind of like a fraction it is a fraction fractions and division are basically the same thing so what we have here is the fraction uh two let me do it yeah i'll do it here 20.4 divided by 1.7 22.4 divided by 1.7 i know that you may not be thinking of fractions in terms of division yet so because we talk about fractions as parts of a whole but as we go more and more into fractions you need to start thinking about fractions as being division the fraction bar is basically a division symbol actually the bar here with something on top and something on the bottom doesn't look a whole lot like this a bar with something on the top and something on the bottom a bar with something on the top and something on the bottom so a fraction is division it's the top thing divided by the bottom thing now we're dividing taking this and dividing by this now remember we said that when we deal with fractions we can multiply or divide the top and the bottom by the fraction of the fraction by any number we want that's how we simplify fractions remember we can divide the top by 2 and the bottom by 2. we can divide the top by 4 and the bottom by 4. i can divide the top by 10 and the bottom by 10 as long as i do it to this to both the top and the bottom i have not changed the fraction the same thing is true of multiplication i can multiply a fraction by 2 or three or four as long as i do it to the top and the bottom at the same time so let's see what happens since i can do whatever i want what would happen if let me extend this fraction bar here what would happen if i multiply the top of this fraction and the bottom of this fraction by 10 i'll multiply the top and the bottom of the fraction by 10. multiplying by the same number does not change the fraction it just changed the way the fraction looks and then what would we have remember we talked about what happens when you multiply by 10. all that happens is you move the decimal right so when you multiply by 10 you move the decimal to the right making it 10 times bigger and when you divide by 10 you move the decimal the other way we talked about that before so 20.4 times 10 is 204 and 1.7 times 10 is 17. so what we're saying here is that this fraction 204 over 17 looks different than 20.4 divided by over 1.7 but it's the same fraction because we've multiplied the fraction top and bottom by 10 and all that does is move the decimal so this is why i can take 204 and divide by 17 and it gives me the same answer because this thing is the same exact thing as this thing it means the same thing we multiply top and bottom by 10 when when i tell you to move the decimal all you're doing is multiplying this one by 10 and multiplying this one by 10 which you already know that you can do that for fractions but most of the time in in learning long division the teacher doesn't tell you what you're doing they just tell you move the decimal move the decimal on the inside and on the outside and you don't know why it's because this is really a fraction and multiplying top and bottom by the same thing is okay and so when you move that decimal here and here in lock step at the same time it's just doing this so this is exactly the same thing as doing this so for the future problems we're not going to do so much thinking about it i wanted to just tell you what you're doing but what we are in practice going to do is move the outside decimal point to the right to give us a whole number and then we'll move the inside decimal point the same amount of places that is going to give us the right answer in all situations now with all that talking out of the way we can finally work more problems let's say that we have the problem uh we're going to divide the number 1.85 and we'll divide it by 0.5 now what we want to do is we want to move the outside decimal point one spot to the right and then one spot to the right that is like multiplying this by 10 and then multiplying this by 10. and so you haven't changed the problem but really we're going to kind of work a related problem which since we move the decimal here it'll be 18.5 and we'll divide that by move the decimal over here it's just going to be 5. the zero won't matter at all 0 five you don't need the zero there so what we're doing really is we're going to be solving this division problem we want a whole number on the outside just like we wanted to get to a whole number on the outside here now when we do it did it here we ended up with a whole number on the inside too here we ended up with a still a decimal on the inside that's okay the very first thing you want to do when you do these division problems if you still have a decimal on the inside the decimal point in the answer it just floats right above you don't have to count positions you don't have to to do it like we did for multiplication or anything all you have to do is look at where the decimal is and the final decimal is there look here the decimal point invisible was here now we have an invisible decimal directly you can kind of put a little dot there if you want right there so the same rule is happening here so the decimal we already have now we just we can just solve the rest of the problem normally 5 divided by going into 1 doesn't work 5 going into 18. 5 times 3 is 15 5 times 4 is 20. that's too big so it has to be 5 times 3 15. what is 18 minus 15 or you can think of 8 minus 5 is 3 0 minus zero zero after we subtract grab the next digit down we have thirty five now five times what is thirty five five times seven is thirty five so multiply subtract and get a zero grab the next digit there is no next digit so we're done the remainder here when we get down to a 0 here we're done and the answer that we get is 3.7 so the answer to the whole problem that we're doing here is we'll just say the answer is 3.7 this is the final answer so in the first problem we did the division and we got an answer of 12 a whole number that just means that if we drew this out and divided it into 20.4 it would go 12 whole times exact amount of division going in there when we do 18.5 divided by 5 or the same 1.85 divided by 0.5 when you draw it out what's gonna happen is it's going to fit three whole times but it's not going to fit a fourth time it's only going to fit a portion past that it's not going to fit quite four times you'll have some left over it'll be able to go in a little bit more but not all the way four times it's only going to go 3.7 because remember if we get to 3.8 and 3.9 we'll get closer and closer then we'll roll over to 4.0 so when we get an answer of 3.7 it means it divides in three whole times and almost four but not quite so it wasn't able to go another full time in all right i know it's a little weird in the beginning but i promise it will become clearer as we work more problems we're going to move that decimal point every single time on the outside let's take the next problem let's say that we really want to divide 16.72 and we'll divide that by 3.8 so the very first step is to look on the outside we have a decimal point here we do not want decimals on the outside we want whole numbers we move one position there therefore we must move one position there which is keeping it balanced but also this is like multiplying by 10 and multiplying by 10. so we keep everything balanced so the related problem that we're actually going to solve we'll move the decimal 1 position over is 167.2 and we'll divide that by 38. 38. all right 38. so what we want to do is we want to figure out th this problem here is going to give us an answer which will be the exact same answer as what we have started with here now question for you how many times can 38 go into one actually one thing first before you do anything else the decimal point in the answer just floats right above you can even do that as the first step all right 38 goes into 1 how many times well 0 times because 1 is too small how many times can it go into 16 well it doesn't really go at all because 16 is too small so we have to consider 167. i'm not sure how many times it can go in so i may have to go off to the side and start multiplying let me start multiplying 38 times 4. 8 times 4 is 32 3 times 4 is 12 then we go up 13 14 15 and we get an answer of 152. 152 is as close as i'm going to get to 167. if i multiply by 5 i'm confident i'm going to blow it because i'm already very very close so it goes four times so put a 4 here it goes 4 times into 167 when i multiply that i get 152. we just did that and so now i can subtract 7 minus 2 is 5. 6 minus 5 is 1. 1 minus 1 is 0 but i don't have to put leading zeros and then finally after i do the subtraction i grab the next digit which is a 2 and a 2 goes down there now how many times do i go into this 38 times something is 152 but we already know it's exactly four so 38 times four when we multiply is 152 and we subtract we get zero and there are no more digits to bring down so the process is done and the answer that we got was 4.4 the decimal just comes straight it floats right above there and so the answer that we get for this problem is 4.4 so what does this actually mean it means if i and seventy have cents and three dollars and eighty cents i can float another zero there if i want and i divide in there then what's going to happen is this can go into sixteen point seven two four whole times but it can't go five times i it goes a little bit more than four i'll have some left over that it can go a little bit more but not a whole time not even a half of if it were 4.5 it would go exactly four and a half times it's a little less than that so it's a little less than four and a half is what that division is all right i know it's a lot i do but really when you get the hang of it you realize there's really only one more step in the beginning and that is moving the decimal point let's take a look at the problem 28.86 and we'll divide that by 7.4 all right so we want a whole number on the outside so we move the decimal one position here and in order to keep it balanced we move one position there in other words multiplying by 10 and multiplying by 10 keeps everything balanced so we want to rewrite the problem and do the related problem it's going to be 2 8 8 and we'll then divide that by 74. that's what we actually have to do all right so first step we take a look at what we have we have a decimal point here and the decimal point in the answer will float directly above all right next 74 can't go into two it's too small 74 can't go into 28 that's too small 74 can it can go into 288 how many times i don't really know so let's try multiplying by three three times four is twelve carry seven times three is twenty one one more is twenty two so when i multiply by three i get 222 and i'm trying to get as close as i can to 288 i can multiply by four you can multiply by four if you want but you're definitely going to blow past 288 it's it's not going to work it's going to be too high the 222 if you add 74 more is going to be too high in fact we can just do it real quick 74 times 4 4 times 4 is 16 7 times 4 is 28 one more is 29 so 296 is too big so that's too big so it has to go only three times so the three goes here and we just said three times that is 222 and so we then subtract eight minus two is six eight minus two again is six and 2 minus 2 is 0. i don't really need to put that after i subtract i drag the next digit down and so i have 666 down there all right now the next question is 74 times what is 666. now i know that 74 times 10 is just 740. when you multiply by 10 you're just adding a zero so that's too big so let's try multiplying times nine instead we'll do 74 times nine nine times four is 36 carry the three and then nine times seven 63 64 65 66 oh look it exactly is equal to 60 666 so it can go nine times nine times 74 is 666 which gives me a leftover of zero and so the answer that we get is 3.9 so i can either just circle this or i can just write the answer down anywhere else i guess i'll just circle it up here just so you can kind of see that this is the final answer is 3.9 so if i were to take 28.86 of something and divide it by 7.4 and see how many times it can fit in it's telling me that it can fit three whole times and not quite four times but very close to four times because the point nine is telling me it almost goes four times but not quite it's not quite enough extra to go a fourth time but it's very close because it's at 3.9 all right making good progress let's take a look at problem number five we want to divide the following numbers eight point four seven we want to divide it by zero point two two zero point two two now here we have a decimal here and we have two digits we do not want any whole numbers whereas before we only had to move one position here we actually have to move the outside digit decimal point two positions and if we do it two positions on the outside then we must move the inside decimal two positions also so you might say what would be happening here if we multiply by 10 it would move at one position if we multiply by 10 again it moves it another position so it's like multiplying this by a hundred to move the decimal point but we also move this one multiplying by a hundred so it moves the decimal the same amount putting bags of sand on the seesaw multiply by 10 multiply by 10 as long as i'm doing it to both the inside and the outside or the top and the bottom of the fraction i'm not changing anything so what i really want to do is solve the related problem the related problem is 847 because we move the decimal two times divided by 22 and it doesn't even look like there's any real decimal points in the problem but if you remember there's an invisible decimal after the whole number so there's like an invisible decimal right there we don't usually write it but we can still put it there all right 22 cannot go into 8 too small 22 can go into 84 how many times i'm not sure so let me try to go over here and say 22 let's start by multiplying by 3. 2 times 3 is 6. 2 times 3 is 6. all right that's pretty close let's try to go a little higher 22 times four two times four is eight two times four is eight this is actually too high so it only actually can go three times three times and three times 22 we just said was 66 and we subtract now here's where you know we have to do a little thinking because what we have to do is 84 minus 66. it's difficult to do that in our head and we have to do borrowing here but the 4 minus 6. it's it's going to look ugly if we do it under here so what i really rather you do is come over to the side what we want to do is 84 minus 66 and we cannot do 4 minus 6. so we'll change this to a 14 and we'll borrow making that a seven fourteen going down by six is thirteen twelve eleven ten nine eight fourteen minus six is eight and seven minus six is one so the answer is eighteen 84 minus 66 is 18. after we subtract we pull the next digit down we have 187 there 187 i'm not really sure um exactly 22 times something has to be 187 i'm not totally sure but i i know that it's going to be times 6 or times 7 or times 8 or whatever i'm not really totally sure so you have to kind of play with it a little bit so let's go over here and see what 22 times 8 is 22 times 8. 8 times 2 is 16 carry the 1. 8 times 2 is 16 one more is 17. so that's 176. if i go times 9 i'm going to blow it i'm going to go past 187 so it has to be times eight and if you want to go times nine and prove it to yourself then you of course you can do that so we're going to say it goes eight times so it goes eight times here and eight times 22 we just said is 176 and we subtract seven minus six is one eight minus seven is also one one minus one i don't have to write now here is the point where i turn around and i have to teach you something really important when we're dividing decimals our goal is to get down to where the remainder is zero notice how the remainder was zero so we knew we were done here the remainder was zero so we knew we were done here the remainder was zero so we knew we were done i can keep going back to the other problems the remainder was always zero so we knew we were done but now when we subtract it looks like there's no other digit here so it looks like we have a remainder of 11 and you think you're going to put remainder 11 r11 we don't do that with decimals we do that for the other division you know the whole number division that we have learned in the beginning but when we have decimal division we really want the remainder to be 0 down here if possible here the remainder is 11. so we need to keep going in the process but we don't have any more digits so what we have to do is add some digits right because what's going on here is even though we're dividing 847 divided by this there's an invisible decimal here and as you know we can add zeros after a decimal point as many as we need to add to make the process work out so since i was able to add a zero there now the um the the uh i do have another digit to drag down which is a zero remember what we did was we subtracted we get an 11 and we always try to grab the next digit but we didn't have an another digit so we had to add after the decimal point a zero so we would have something to grab to come down now we have 110 down here 2 times what is 110 i'm not sure so we're going to try to go 22 times 5 and let's see what we get 2 times 5 is 10 carry the 1. 2 times 5 is 10 plus 1 is 11. so 22 times 5 is 110 22 times 5 multiply is 110 subtract now we get a remainder of 0 now we know we can stop so the answer to this problem is 38.5 so when we take this number and divide it by 0.22 it can go in and fit inside 38 whole times plus another half it can't go another whole time it can go a half i need to kind of talk about this a little bit before we go on the process works the same for this problem as for the other problems but in the other problems we got a remainder of zero so we stopped we got a remainder of zero so we stopped we got a remainder of zero so we stopped but here we had a remainder of 11 and we thought we should stop but when we divide decimals we always want to get to a remainder of zero and so we had to add and put the decimal point that we know is there and add a zero which does not change the number it doesn't change anything but it allows us to continue the process to get down to a remainder of zero so we have to keep an eye out for that sometimes we will have to do that all right move them right along problem number six let's say we have the problem uh 3.36 and we want to divide that by 2.1 2.1 so on the outside we have a decimal here we don't want any decimals we move one position so we move this decimal one position also so that means really we're going to solve the related problem over here of 33.6 and we'll divide it by 21 move the decimal one position one position and this problem will be the same as the previous problem so now we then look at the decimal point we can float the decimal up into the final answer and now we say how many times can 21 go into three we can't go into three how many times can 21 go into 33 it can only go once because we know that you know if you can kind of think of it as being close to 20 times 2 would be 40 that would be too much so it really can only go one time 1 times 21 is 21 subtract 3 minus 1 is 2 and 3 minus 2 is 1. after subtract the next step is to grab the next digit which is a 6 and remember we're looking for a remainder of zero before we stop this process so we have 126 down here and what do we do next 21 times something is 126. i'm not sure what to pick i know it's not going to be it's going to be kind of a big number but i'm not sure so let's go off to the side 21 times 6. 6 times 1 is 6. 6 times 2 is 12. and i get 126. i kind of guessed here you might start with five or seven eventually you'll figure out the closest you can get is six so it can go six times for 126 subtracting it zero now the remainder is zero and there are no more digits to drag down now we know the process can be stopped and the answer to this is 1.6 1.6 final answer all right we're almost done actually i know these are kind of long but we just need to really get a lot of good practice to make sure that we're on the same page let's take a look at the problem 6.56 and we'll divide it by 0.02 so on the outside i have two digits after the decimal i want to move this decimal one position two positions to get a whole number that means to keep it balanced i have to move one position two positions to keep it balanced on the inside so really i'm going to then solve the related problem of 656 and i'll divide that by one i move the decimal i only have two on the outside the leading zeros you can throw away once you move the decimal this is what i want to solve 656 by 2. now i know there's an invisible decimal here so there's basically an invisible decimal that floats right above i don't have to put that but you know i can all right next what do we have 2 times what is 6. 2 times three is six so multiply and subtract i get a zero drag the next digit down which is then five two times what is five two times two is four that's as close as i can get two times two being four subtract i get a 1 and i then after subtraction drag the next digit down now i have 16. 2 times what is 16. 2 times 8 is exactly 16 and i get a 0 now i have a remainder of 0. i don't have any more digits of course i can keep adding zeros but i don't need to because i already got to a remainder of zero so the answer we get is 328. the dot here really doesn't doesn't really do much because you can put a decimal zero after if you like so what i'm going to do is just say that the answer is 328 that was a whole number answer all right next problem let's go ahead and give ourselves some room we're going to solve the next problem down here let's say we're solving the problem zero point nine one and one divide that by zero point six five all right first thing we look on the outside we have to move this decimal one position two positions that means we have to move this one one position two positions also to keep it balanced so we're really going to solve a related problem we move the decimal it'll be 91 on the inside and we'll divide it by 65 on the outside 65 on the outside all right next thing we want to notice is that just as always we have an invisible decimal right here let me get rid of this real quick we have an invisible decimal here so the answer will have an invisible decimal right there as well and give myself a little bit more room here i'll just kind of come more like over here all right um and so then we want to start by looking at saying all right 65 can go how many times into nine well it can't go at all into nine too small how many times can it go into 91 well i know it can go one time and i know that it cannot go two times because if you think about this is being pretty close to 60 6 times 2 is 12 so 60 times 2 is 120. if you multiply this you're going to get something way bigger than 91 so it has to go only one time right here so put a 1 right here and then multiply get 65 and then we need to subtract now unfortunately you have to do a little borrowing so let's go over here and do 91 minus 65. now we know that we can't do 1 minus 5. so make it 11 and borrow and that becomes 8. 11 minus five go down ten nine eight seven six eleven minus five is six eight minus six is two so the answer here is 26 so we put a 26 down here now we don't have any more digits in our problem but we also do not have a remainder of zero so we have to keep going even though you you think oh i don't have any more digits really you need to be looking at the remain the remainder that you kind of have and you want to get it down to the point where it's essentially zero if you can and so we have to continue the process so we look up here and we say well we have 91 we have a decimal we can easily add another zero here without changing the problem at all so we're going to insert that and add that zero then after we did the subtraction we just dragged that 0 down and now we have 260 down there so the question then is 65 times what is 260 i'm not sure the answer so let's go here and do 65 times 4. you could try times three or times five five times four is twenty carry the two six times four is 24 25 26 i didn't know that ahead of time but you know i also know what the answer is so but you might try times three or times five or whatever eventually you're going to figure this out times 4 is the answer so you put a 4 here 4 times 65 is 260 then you subtract and get a remainder of 0 and now we don't have any more digits we could continue adding zeros but it doesn't help us do anything because the remainder is already at zero so the answer to this is 1.4 so i guess i'll just kind of box this the answer is 1.4 sorry this is kind of crowded here the answer is 1.4 for this problem so if we take 0.91 and we divide it by 0.65 it can go one whole time almost one and a half times a little bit less than one and a half times all right i think we have room for one more problem and i think that would be a good place to stop it over here so let's take a look at the next problem i guess let's go up like this just give me a little space let's take a look at the final problem 2.52 and we're going to divide that by 0.08 0.08 so on the outside we don't want any decimals so we move two spots to the right that means we move two spots to the right here all right so that means we're actually going to be solving the related problem i'll write it over here of 252 and we'll divide that by zero point i'm sorry eight because we moved it two it's going to be eight on the outside eight now we can put the decimal here because we know that there's a decimal after every whole number and so the decimal and the answer has to be above there as well so let's see how this shakes out all right eight can go cannot go into two it's too small let's try going into twenty-five eight times two is sixteen eight times three is twenty-four so it can go three times into twenty-five 8 times 3 is 24 we subtract and we know that the answer is 1. after we subtract grab the next digit which is a 2. now 8 times 1 is 8 8 times 2 is 16 that's too big so it has to go only one time 8 times 1 is 8. subtract now we can you know borrow and all that but really you know that if you go start from 8 and count up to 12 9 10 11 12 is 4. so 12 minus 8 is 4. and then you look for another digit you don't have another digit and you think i guess i'm done but you say wait a minute we're always trying to get to a remainder of zero and here i don't have a remainder of zero so in decimal problems i need to keep going i can insert zeros after the decimal it doesn't change anything and then that allows me to drag because i just subtracted to drag the next digit down which is a zero and i have now 40. so now eight times what is 40. eight times five is forty multiply you get the forty subtract you get a zero and so now i do have a remainder of zero i don't have any more digits i could keep adding zeros but i don't need to because i've already gotten to a point where my remainder is 0. so the answer to this is 31.5 31.5 all right that is a long lesson a lot of writing a lot of you have to go off to the side and do your side work to make sure you can subtract or multiply to figure out what to do i don't want you to lose sight of the big picture the big picture is you have to do this division but the decimal on the outside you don't want decimals here so you move the decimal over in the same number of positions you have to move the the what's under here the decimal the same number of places and then you do the division as normal sometimes you will end up where after you move the decimal you still have a decimal on the inside it just floats up above see here after we moved it we still had one inside it just floats up above but sometimes you do it and you'll end up with a whole number on the inside but you still have a decimal there it still floats up above it just it's there it's just 12 has an invisible decimal there and then you go through the process as normal always looking to make sure that you have a remainder of 0 then you stop when you have a remainder then you stop here we got to a point where the remainder was 4 but we didn't have any more digits and so you're thinking you should stop but you need to keep going and the way that you keep going is you have to add zeros after the decimal point as many times as it takes until you get to a remainder of zero uh there and then you then when you finally do get to the point where the remainder is zero down under there then you can stop and the answer you've calculated up above i know it's a little weird a little hard the first time we do it but i think with practice you will get the hang of it i'd like you to solve every one of these problems yourself start the lesson over write down the problem and do it yourself even if you just saw me do it then i'd like you to follow me on to part two we'll get a little more practice with the concept of dividing decimals

Channel: Math and Science

Views: 28,781

Rating: 4.8724489 out of 5

Keywords: dividing decimals, decimal division, long division, dividing decimals by whole numbers, dividing decimals with remainders, long division with remainders, long division with decimals, how to divide decimals by decimals, how to divide decimals by whole numbers, divide decimals, how to divide decimals, decimals divided by decimals, divide decimals by decimals, divide decimals by whole numbers, remainder, decimal remainders, math, algebra, divisor, 5th grade math, 6th grade math

Id: kbdFByISdwk

Length: 39min 40sec (2380 seconds)

Published: Tue Mar 16 2021