Learn to Divide Decimals (Long Division with Decimals) - [19] - Free Educational videos for Students in K-12

Learn to Divide Decimals (Long Division with Decimals) - [19] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called dividing decimals . This is part one .
00:04	It's a long lesson . We have a lot of
00:06	problems here but it's a very , very important skill
00:09	to master . So we're going to get a lot
00:10	of practice now before you have before you conquer this
00:14	, I really would like you to do two things
00:15	first . I'd like you to watch the previous lessons
00:18	on understanding what a decimal division is using pictures .
00:21	So in the back of your mind I want you
00:23	to have the picture a picture of what's going on
00:25	as we do our problems . Second of all ,
00:27	you really need to be pretty good at long division
00:30	already . Long division of whole numbers . We've done
00:32	that many , many times in the past . Many
00:34	, many , many problems . If you are fuzzy
00:35	on how to do long division , please stop and
00:38	go do that right now . So once we have
00:41	those two things out of the way , what we
00:42	want to do is divide a decimal by another decimal
00:45	. So for instance , let's say we have the
00:47	decimal 20.4 , we have 20 whole sandwiches and .4
00:52	of another , which is a little bit less than
00:54	half of another sandwich . And we want to divide
00:56	it by 1.7 . So we have a decimal divided
01:01	by another decimal . Now in the picture model that
01:03	we had in the last lesson we could draw a
01:05	picture of 20 whole things and then .4 of a
01:09	of a fraction of another thing . And then we
01:11	can divide by 1.7 , we could draw a picture
01:13	of that and we could see how many times 1.7
01:16	is going to fit in there . How many times
01:18	will it fit in To 20.4 ? That would work
01:21	. But that's not going to be a great way
01:23	to solve a lot of problems . So what I
01:25	want to do is I'm gonna show you how to
01:26	do this , you will have some questions the first
01:28	time you'll be like why ? Why can we do
01:30	that ? How do we do that ? Why is
01:31	that ? Okay ? I want you to kind of
01:33	keep your questions but let me cycle through the first
01:36	couple of problems so I can cycle through all of
01:38	your questions and then at the end you'll understand everything
01:41	. Now , dividing by 1.7 in long form is
01:45	difficult to do . So what we're actually going to
01:47	do is we're going to change this problem a little
01:50	bit . What we want to divide by on the
01:53	outside , we always wanted to be a whole number
01:56	. It just makes the math easier . So what
01:58	we want to do is take this nasty little decimal
02:00	point and we want to move it over here .
02:02	But if we move the decimal spot , one position
02:05	over this way then we must also move what is
02:08	under the the the division symbol ? Uh one spot
02:13	as well . So we move the decimal one spot
02:15	this way and then one spot that way you might
02:17	say why are you allowed to move decimals ? Just
02:19	hold your questions . I will explain why we are
02:21	allowed to move decimals in just a second But for
02:24	now just know that we want a whole number out
02:26	here . So we move at one spot and if
02:28	we move at one spot out here then we must
02:30	also move this one spot as well . So then
02:33	what happens is we're not going to solve this problem
02:36	. What we really will do is solve a very
02:38	closely-related problem which is 20 , I'm sorry 204 Divided
02:43	by 17 . You see the original decimal was here
02:47	and we moved it one spot to the right ,
02:49	so now we have 17 , the original decimal was
02:51	here and we moved it also one spot to the
02:54	right , which means we have a decimal point here
02:56	and now a decimal point here exactly as we've shown
02:58	here . So what we're saying is now we're going
03:01	to solve the problem . 204 divided by 17 .
03:05	We already know how to solve that problem . You
03:07	already know how to do that right ? Um the
03:11	only trick is knowing that we're not trick , but
03:13	the only thing we have to know is that we
03:15	have we want a whole number on the outside of
03:17	the division symbol . So we have one spot .
03:20	One spot . Now let's solve this problem . The
03:22	answer that we get to this problem , whatever we
03:24	get is the answer is the same answer as what
03:28	we would get . If we just drew a picture
03:29	and divided this , it just so happens that this
03:32	is much easier to do and it gives us the
03:34	same answer again . I will explain why we're moving
03:36	the decimal in just a minute . Let me finish
03:38	the problem . All right . How do we do
03:41	? Long Division 17 divided into two . It can't
03:44	go it's it's not too is not big enough .
03:46	So consider 17 , dividing into 20 . It can
03:49	only go one time 17 is very close to 20
03:52	. So we'll put anyone right here and we put
03:54	it over the zero because we're dividing into the 20
03:58	. The next step is one time 17 . We
04:00	just put the 17 here and subtract . Now .
04:02	You can do the borrowing and all that to subtract
04:05	or you can just think that you're subtracting 20-17 .
04:09	You can start at 17 and count up to 20
04:12	to do the subtraction . If you want to go
04:14	subtract 2019 , 17 on the side , that's fine
04:16	. Or you can count up from 17 18 1920
04:20	. There's only three units between 17 and 20 .
04:24	So we can just put a three down here to
04:28	do it long form we have to borrow here and
04:30	all this stuff and that will make it cluttered .
04:31	So we know the answer is three After we subtract
04:35	, grab the next digit , bring it down .
04:38	Now what do we do ? We have to figure
04:40	out 17 times something is 34 . We know that
04:43	17 times one is 17 . What is 17 times
04:46	two , 17 times to seven times 2 is 14
04:51	and two times one is two plus one is 3
04:54	, 17 times two is exactly 34 . So this
04:57	has to be a 22 times 17 is 34 .
05:00	Subtract 34 minutes , 34 0 . And so we
05:05	grabbed the next digit but there is no next digit
05:07	, so we're basically done and the remainder is zero
05:10	. So what have we figured out here ? We
05:12	figured out that if we take 204 and divided by
05:16	17 we get 12 times it fits in there exactly
05:20	12 times . So the answer to this problem is
05:24	12 . The answer is this problem as 12 and
05:28	that is exactly the same answer As we get when
05:31	we take 20.4 and divide by 1.7 we convert it
05:35	to this because when we don't have nasty decimals here
05:38	on the outside , it makes doing the long division
05:41	process easier . So what we're going to do every
05:44	single time is when we're dividing by a decimal ,
05:47	we're going to move the decimal as many spots as
05:50	it takes , so that we only have a whole
05:52	number out here and however many spots we move it
05:55	, we must also move the inner decimal the same
05:58	number of spots because if you Move one but not
06:02	the other than you've changed the problem , but if
06:05	you move one of them and then also move another
06:07	one then they're the same . Let me give you
06:10	a couple of a couple of reasons why it's okay
06:13	to do this picture , you have a teeter totter
06:16	or a seesaw right , and you have , it's
06:19	balanced in the middle , you have one person on
06:21	this side and one person on this side and it's
06:23	perfectly balanced , it's not moving , it's perfectly flat
06:27	. Now if I put a bag of sand on
06:29	one side of course it's going to do this ,
06:31	but I can keep it balanced by also putting another
06:34	bag of sand on the other side , and then
06:36	I can keep the exact balancing the same of the
06:39	seesaw . If I take one bag of sand off
06:42	its course is gonna move , but if I take
06:44	both sands off at the same time , then the
06:47	Children are still there and the seesaw is still exactly
06:50	balanced . If we move one of these decimals by
06:53	itself , then we've unbalanced everything and changed everything ,
06:56	but if we move both of these decimals the same
06:59	, then the problem looks different , but actually gives
07:02	exactly the same answer as if we do this .
07:05	So that's one way of thinking about it . Let
07:08	me tell you another way , a better way of
07:09	thinking about it when we do division like this ,
07:12	you really need to start thinking about division as being
07:16	kind of like a fraction , it is a fraction
07:17	fractions and divisions are basically the same thing . So
07:20	, what we have here is the fraction uh to
07:25	let me do it , yeah , I'll do it
07:26	here 20.4 Divided by 1.7 . 20.4 , divided by
07:33	1.7 . I know that you may not be thinking
07:37	of fractions in terms of division yet , because we
07:40	talk about fractions as parts of a whole , but
07:43	as we go more and more into fractions , you
07:45	need to start thinking about fractions as being division .
07:47	The fraction bar is basically a division symbol actually the
07:51	bar here with something on top and something on the
07:53	bottom doesn't look a whole lot like this . A
07:55	bar with something on the top and something on the
07:57	bottom . A bar with something on the top and
07:59	something on the bottom . So a fraction is division
08:02	. It's the top thing , divided by the bottom
08:05	thing . Now we're dividing taking this and dividing by
08:08	this . Now remember we said that when we deal
08:11	with fractions we can multiply or divide the top and
08:15	the bottom by the fraction Of the fraction by any
08:17	number we want . That's how we simplify fractions .
08:20	Remember we can divide the top by two and the
08:22	bottom by two . We can divide the top by
08:24	four in the bottom by four . I can divide
08:26	the top by 10 and the bottom by 10 .
08:29	As long as I do it to the to both
08:31	the top and the bottom . I have not changed
08:33	the fraction . The same thing is true of multiplication
08:36	. I can multiply a fraction by two or three
08:38	or four as long as I do it to the
08:40	top and the bottom at the same time . So
08:43	let's see what happens since I can do whatever I
08:46	want . What would happen if let me extend this
08:49	fraction bar here . What would happen if I multiply
08:52	the top of this fraction and the bottom of this
08:54	fraction by 10 Multiply the top and the bottom of
08:58	the fraction by 10 multiplying by the same number does
09:01	not change the fraction . It just changed the way
09:03	the fraction looks . And then what would we have
09:07	, Remember we talked about what happens when you multiply
09:10	by 10 ? All that happens is you move the
09:12	decimal Right ? So when you multiply by 10 ,
09:15	you move the decimal to the right , making it
09:18	10 times bigger . And when you divide by 10
09:20	you move the decimal . The other way we talked
09:22	about that before , so 20.4 times 10 is 204
09:27	and 1.7 times 10 is 17 . So what we're
09:30	saying here is that this fraction , 204 over 17
09:35	looks different than 20.4 divided by over 1.7 . But
09:39	it's the same fraction because we multiplied the fraction top
09:43	and bottom by 10 and all that does is move
09:45	the decimal . So this is why I can take
09:47	204 and divide by 17 . And it gives me
09:50	the same answer because this thing is the same exact
09:55	thing as this thing . It means the same thing
09:58	. We multiply top and bottom by 10 . When
10:01	I tell you to move the decimal , all you're
10:03	doing is multiplying this one by 10 and multiplying this
10:05	one by 10 which you already know that you can
10:08	do that for fractions . But most of the time
10:10	in , in in learning division , the teacher doesn't
10:13	tell you what you're doing . They just tell you
10:15	move the decimal , move the decimal on the inside
10:18	and on the outside and you don't know why it's
10:20	because this is really a fraction and multiplying top and
10:24	bottom by the same thing is okay , and so
10:26	when you move that decimal here and here in lockstep
10:29	at the same time , it's just doing this ,
10:32	so this is exactly the same thing as doing this
10:36	. So for the future problems we're not going to
10:38	do so much thinking about it , I wanted to
10:40	just tell you what you're doing but what we are
10:43	in practice going to do is move the outside uh
10:46	decimal point to the right to give us a whole
10:49	number and then we'll move the inside decimal point ,
10:51	the same amount of places that is going to give
10:54	us the right answer in all situations . Mhm .
10:58	Now , with all that talking out of the way
11:00	, we can finally work more problems , let's say
11:04	that we have the problem . Uh we're going to
11:06	divide the number 1.85 and we'll divide it by 0.5
11:13	. Now what we want to do is we want
11:14	to move the outside decimal point one spot to the
11:19	right and then one spot to the right , that
11:21	is like multiplying this by 10 and then multiplying this
11:24	by 10 . And so you haven't changed the problem
11:26	. But really we're going to kind of work a
11:28	related problem which since we move the decimal here ,
11:31	it'll be 18.5 and we'll divide that by move the
11:36	decimal over here , it's just going to be five
11:38	. The zero won't matter at all . 05 you
11:41	don't need the zero there . So what we're doing
11:42	really is we're going to be solving this division problem
11:45	, We want a whole number on the outside .
11:48	Just like we wanted to get to a whole number
11:50	on the outside here . Now when we do it
11:52	, get it here , we ended up with a
11:54	whole number on the inside to hear . We ended
11:57	up with a still a decimal on the inside .
11:59	That's okay . The very first thing you want to
12:02	do when you do these division problems , if you
12:04	still have a decimal on the inside the decimal point
12:06	and the answer , it just floats right above .
12:09	You don't have to count positions , you don't have
12:11	to to do it like we did for multiplication or
12:14	anything . All you have to do is look at
12:16	where the decimal is in the final decimal is there
12:19	? Look here the decimal point invisible was here .
12:22	Now we have an invisible decimal directly . Can kind
12:24	of put a little dot there if you want right
12:25	there . So the same rule is happening here .
12:28	So the decimal we already have now , we can
12:31	just solve the rest of the problem . Normally five
12:34	divided by going into one , doesn't work five going
12:38	into 18 , 5 times three is 15 , 5
12:40	times four is 20 . That's too big . So
12:42	it has to be five times 3 15 . What
12:46	is 18 minus 15 ? Or you can think of
12:48	eight minus five is 30 minus 00 After we subtract
12:53	, Grab the next digit down , we have 35
12:56	Now , five times what is 35 ? five times
12:59	7 is 35 . So multiply subtracting zero , grabbed
13:04	the next digit , there is no next digit ,
13:06	so we're done the remainder here . When we get
13:08	down to a zero here , we're done and the
13:10	answer that we get is 3.7 . So the answer
13:13	to the whole problem that we're doing here Is we'll
13:15	just say the answer is 3.7 , this is the
13:19	final answer . So in the first problem we did
13:22	the division and we got an answer of 12 .
13:24	A whole number . That just means that if we
13:26	drew this out and divided it into 20.4 , it
13:29	would go 12 whole times , exact amount of division
13:33	going in there . When we do 185 divided by
13:36	five or the same one , divided by five .
13:40	When you draw it out , what's going to happen
13:42	is it's going to fit three whole times , but
13:45	it's not going to fit a four time , it's
13:48	only going to fit a portion passed that it's not
13:50	gonna fit quite four times . You'll have some left
13:53	over , it will be able to go in a
13:55	little bit more , but not all the way four
13:57	times , it's only going to go 3.7 Because remember
14:00	if we get to 3.8 and 3.9 we'll get closer
14:03	and closer then we'll roll over to 4.0 so when
14:06	we get an answer of 3.7 it means it divides
14:09	in three whole times in almost four but not quite
14:13	. So it wasn't able to go another full time
14:15	in . All right . I know it's a little
14:19	weird in the beginning but I promise it will become
14:21	clearer as we work more problems . We're gonna move
14:24	that decimal point every single time on the outside .
14:27	Let's take the next problem . Let's say that we
14:30	really want to divide 16.72 and divide that by 3.8
14:38	. Yeah , so the very first step is to
14:39	look on the outside , we have a decimal point
14:41	here , we do not want decimals on the outside
14:43	, we want whole numbers , we move one position
14:46	there . Therefore we must move one position there which
14:49	is keeping it balanced . But also this is like
14:51	multiplying by 10 and multiplying by 10 . So we
14:53	keep everything balanced . So the related problem that we're
14:57	actually going to solve , We'll move the decimal one
15:00	position over is 167.2 and we'll divide that by 38
15:08	. 38 . All right . 38 . So what
15:12	we want to do is we want to figure out
15:16	this problem here is going to give us an answer
15:19	which will be the exact same answer as what we
15:21	have started with here . Now , question for you
15:25	, How many times can 38 go into one ?
15:27	Actually one thing 1st . Before you do anything else
15:30	, the decimal point of the answer just floats right
15:33	above . You can even do that is the first
15:34	step . All right . 38 goes into um one
15:40	. How many times ? Well , zero times because
15:43	one is too small . How many times can you
15:45	go into 16 ? Well , doesn't really go at
15:48	all because 16 is too small . So we have
15:49	to consider 167 . I'm not sure how many times
15:53	it can go in . So I may have to
15:54	go off to the side and start multiplying . Let
15:56	me start multiplying 38 times four . eight times 4
16:00	is 32 , Three times four is 12 . Then
16:04	we go up 13 , And we get an answer
16:07	of 152 . 152 is as close as I'm going
16:11	to get to 1 67 . If I multiply by
16:14	five , I'm confident I'm gonna blow it because I'm
16:17	already very , very close . So it goes four
16:20	times . So put a four here . It goes
16:22	four times into 1 67 . When I multiply that
16:25	I get 152 . We just did that . And
16:28	so now I can subtract 7 -2 is five .
16:31	6 -5 is 1 . -1 is zero . But
16:35	I don't have to put leading Zeros . And then
16:38	finally after I do the subtraction , I grabbed the
16:40	next digit which is a two and a two goes
16:42	down there . Now How many times do I go
16:46	into this ? 38 times something is 152 but we
16:49	already know it's exactly four . So 38 times four
16:53	when we multiply is 152 and we subtract we get
16:57	zero and there are no more digits to bring down
17:00	. So the process is done and the answer that
17:03	we got was 4.4 . The decimal just come straight
17:06	. It floats right above there . And so the
17:09	answer that we get for this problem is 4.4 .
17:12	So what does this actually mean ? It means if
17:15	I have $16.72 and $3.80 I can float another zero
17:21	there if I want and I divide in there ,
17:23	then what's going to happen is this can go into
17:25	16.7 to 4 whole times , But it can't go
17:30	five times . It goes a little bit more than
17:32	four . I'll have some leftover that it can go
17:35	a little bit more , but not a whole time
17:37	. Not even a half of if it were 4.5
17:39	, it would go exactly 4.5 times . It's a
17:43	little less than that . So it's a little less
17:44	than 4.5 is what that division is . All right
17:50	. I know it's a lot . I do .
17:51	But really when you get the hang of it you
17:53	realize there's really only one more step in the beginning
17:56	and that is moving the decimal point . Let's take
17:58	a look at the problem . 28 .86 . And
18:03	we'll divide that by 7.4 . Yeah . All right
18:08	. So we want a whole number on the outside
18:10	. So we move the decimal one position here and
18:13	in order to keep it balanced , we move one
18:15	position there . In other words , multiplying by 10
18:18	and multiplying by 10 keeps everything balanced . So we
18:21	want to rewrite the problem and do the related problem
18:24	. It's going to be 288 point six And we'll
18:29	then divide that by 74 . That's what we actually
18:34	have to do . Yeah . All right . So
18:37	first step we take a look at what we have
18:39	, we have a decimal point here in the decimal
18:41	point . In the answer will float directly above .
18:44	Alright , next 74 can't go into two is too
18:48	small , 74 . Can't go into 28 . That's
18:50	too small , 74 can go into 2 88 .
18:53	How many times ? I don't really know . So
18:56	let's try multiplying by three . Three times four is
19:01	12 carry seven times three is 21 . 1 more
19:04	is 22 . So when I multiply by three I
19:08	get 222 and I'm trying to get as close as
19:11	I can to to 88 . I can multiply by
19:14	four . You can multiply by four if you want
19:16	but you're definitely going to blow past 288 . It's
19:19	not gonna work . It's gonna be too high .
19:21	The 222 if you add 74 more is going to
19:24	be too high . In fact we can just do
19:25	it real quick , 74 times four . Four times
19:29	four is 16 , 7 times four is 28 .
19:32	1 more is 29 . So 296 is too big
19:35	, so that's too big . So it has to
19:37	go only three times . So the three goes here
19:39	and we just said three times that is 222 .
19:43	And so we then subtract 8 -2 is six .
19:49	8 -2 again is six and 2 -2 is zero
19:52	. I don't really need to put that . After
19:54	I subtract I dragged the next digit down and so
19:57	I have 666 down there . All right . Now
20:01	, the next question is 74 times what is 666
20:04	? Now , I know that 74 times 10 is
20:08	just 740 . When you multiply by 10 , you're
20:10	just adding a zero So that's too big . So
20:13	let's try multiplying times nine instead Will do 74 times
20:18	nine nine times four is 36 carry the three and
20:23	then nine times 7 63 64 65 66 . Oh
20:27	, look at exactly is equal to 6666 . So
20:31	it can go nine times nine times 74 is 666
20:36	which gives me a leftover of zero . And so
20:39	the answer that we get is 3.9 . So I
20:42	can either just circle this or I could just write
20:45	the answer down anywhere else . I guess I'll just
20:46	circle it up here Just so you can kind of
20:48	see that this is the final answer is 3.9 .
20:51	So if I were to take 28.86 of something and
20:56	divided by 7.4 and see how many times it can
20:59	fit in . It's telling me that it can fit
21:02	three whole times And not quite four times but very
21:06	close to four times . Because the .9 is telling
21:08	me it almost goes four times but not quite it's
21:11	not quite enough extra to go 1/4 time . But
21:15	it's very close because it's at 3.9 . Yeah .
21:19	All right . Making good progress . Let's take a
21:23	look at problem number five , we want to divide
21:26	the following numbers 8.47 Want to divide it by 0.2
21:33	to 0.22 Now here we have a decimal here and
21:37	we have two digits . We do not want any
21:39	whole numbers whereas before we only have to move one
21:42	position here , we actually have to move the outside
21:45	digit decimal .2 positions . And if we do it
21:49	to positions on the outside then we must move the
21:52	inside decimal two positions also . So you might say
21:55	what would be happening here ? If we multiply by
21:58	10 , it would move at one position . If
22:00	we multiply by 10 again it moves it another position
22:03	. So it's like multiplying this by 100 to move
22:06	the decimal point . But we also move this one
22:09	, multiplying by 100 . So it moves the decimal
22:11	, the same amount , putting bags of sand on
22:13	the seesaw , multiplied by 10 , multiplied by 10
22:16	. As long as I'm doing it to both ,
22:19	uh the inside and the outside or the top and
22:22	the bottom of the fraction . I'm not changing anything
22:25	. So what I really want to do is solve
22:28	the related problem . The related problem is 847 because
22:32	we move the decimal two times divided by 22 and
22:37	it doesn't even look like there's any real decimal points
22:39	on the problem . But if you remember there's an
22:41	invisible decimal after the whole number . So there's like
22:44	an invisible decimal right there . We don't usually write
22:46	it but we can still put it there . All
22:49	right , 22 cannot go into 82 small , 22
22:54	can go into 84 . How many times ? I'm
22:56	not sure . So let me try to go over
22:58	here and say 22 . Let's start by multiplying by
23:01	32 times three is 62 times three is six .
23:04	Alright , that's pretty close . Let's try to go
23:06	a little higher . 22 times four , two times
23:10	four is 82 times four is eight . This is
23:12	actually too high . So it only actually can go
23:15	three times three times and three times 22 we just
23:19	said was 66 we subtract now here is where you
23:24	know we have to do a little thinking because what
23:26	we have to do is 84 minus 66 . It's
23:29	difficult to do that in our head and we have
23:31	to do borrowing here but the four minus six it's
23:35	going to look ugly if we do it under here
23:36	. So what I'd really rather you do is come
23:38	over to the side . What we wanna do is
23:40	84 minus 66 And we cannot do 4 -6 so
23:47	we'll change this to a 14 and we'll borrow making
23:49	that seven . Mhm . 14 going down by six
23:54	is 13 12 11 10 98 14 minus six is
23:59	eight and seven minus six is one . So the
24:01	answer is 18 84 minus 66 is 18 . After
24:06	we subtract we pull the next digit down . We
24:09	have 187 there . 187 . I'm not really sure
24:13	. Um Exactly 22 times something has to be 187
24:17	. I'm not totally sure . But I know that
24:20	it's going to be times six times seven times eight
24:23	or whatever . I'm not really totally sure . So
24:24	you have to kind of play with a little bit
24:26	. So let's go over here and see what 22
24:29	times eight is 22 times 88 times two is 16
24:33	, carry the 18 times two is 16 . 1
24:35	more is 17 . So that's 176 . If I
24:39	go times nine I'm going to blow it , I'm
24:42	going to go past 187 . So it has to
24:45	be times eight . And if you want to go
24:48	times nine and prove it to yourself and of course
24:50	you can do that . So we're going to say
24:52	it goes eight times so it goes eight times here
24:54	in eight times 22 . We just said is 1
24:56	76 And we subtract 7 -6 is 1 8 -7
25:02	is also 1 1 -1 . I don't have to
25:05	write now . Here is the point where I turn
25:08	around and I have to teach you something really important
25:10	. When we're dividing decimals , our goal is to
25:13	get down to where the remainder is zero , notice
25:15	how the remainder was zero . So we knew we
25:17	were done here , the remainder was zero . So
25:20	we knew we were done here , the remainder was
25:21	zero . So we knew we were done . I
25:23	can keep going back to the other problems . The
25:25	remainder was always zero . So we knew we were
25:26	done . But now when we subtract it looks like
25:30	there's no other digit here so it looks like we
25:32	have a remainder of 11 and you think you're gonna
25:34	put remainder 11 Our 11 . We don't do that
25:37	with decimals . We do that for the other division
25:40	. The whole number division that we have learned in
25:42	the beginning but when we have decimal division we really
25:45	want the remainder to be zero down here if possible
25:47	. Hear the remainder is 11 so we need to
25:50	keep going in the process but we don't have any
25:52	more digits . So what we have to do is
25:54	add some digits Right ? Because what's going on here
25:58	is even though we're dividing 847 divided by this ,
26:01	there's an invisible decimal here . And as you know
26:04	we can add Zeros after a decimal point . As
26:07	many as we need to add to make the process
26:10	work out . So since I was able to add
26:13	a zero there now the the the I do have
26:18	another digit to drag down which is a zero .
26:21	Remember what we did was we subtracted , we get
26:24	an 11 and we always try to grab the next
26:26	digit but we didn't have another digit so we had
26:28	to add after the decimal zero . So we would
26:31	have something to grab to come down . Now we
26:35	have 110 down here , two times what is 110
26:40	? I'm not sure . So we're going to try
26:42	to go 22 times five and let's see what we
26:46	get two times five is 10 , carry the 12
26:48	times five is 10 plus one is 11 , so
26:51	22 times five is 110 . 22 times five multiply
26:57	Is 110 Subtract now we get a remainder of zero
27:01	. Now we know we can stop . So the
27:03	answer to this problem is 38.5 . So when we
27:08	take this number and divided by .22 it can go
27:12	in and fit inside 38 whole times plus another half
27:16	. It can't go another whole time , it can
27:17	go a half . I need a Kind of talk
27:20	about this a little bit before we go on .
27:22	The process works . The same for this problem is
27:24	for the other problems but in the other problems we
27:26	got a remainder of zero . So we stopped ,
27:28	we got a remainder of zero , so we stopped
27:29	, we got a remainder of zero so we stop
27:31	. But here we had a remainder of 11 and
27:35	we thought we should stop but when we divide decimals
27:37	we always want to get to a remainder of zero
27:40	. And so we had to add and put the
27:43	decimal point that we know is there and add a
27:45	zero . Which does not change the number . It
27:47	doesn't change anything but it allows us to continue the
27:50	process to get down to a remainder of zero .
27:52	So we have to keep an eye out for that
27:54	. Sometimes we will have to do that . All
27:57	right , Moving right along problem # six , Let's
28:02	say we have the problem 3.36 . And we want
28:07	to divide that by 2.1 , 2.1 . So on
28:13	the outside we have a decimal here . We don't
28:15	want any decimal . So we move one position so
28:18	we move this decimal one position also . So that
28:21	means really we're going to solve the related problem over
28:24	here of 333.6 and we'll divide it by 21 .
28:31	Move the decimal one position one position in this problem
28:34	will be the same as the previous problem . So
28:37	now we then look at the decimal point , we
28:39	can float the decimal up into the final answer and
28:42	now we say , how many times can 21 go
28:44	into three ? We can't go into three . How
28:47	many times can 21 go into 33 ? It can
28:49	only go once because we know that you know ,
28:51	you can kind of think of it as being close
28:53	to 20 times to would be 40 that would be
28:56	too much . So it really can only go one
28:58	time . one times . 21 is 21 . subtract
29:03	three minus one is two and three minus two is
29:06	one . After subtract . The next step is to
29:08	grab the next digit which is a six and remember
29:11	we're looking for a remainder of zero before we stop
29:14	this process , So we have 126 down here .
29:18	And what do we do next ? 21 times something
29:21	is 126 . I'm not sure uh what to pick
29:25	. I know it's not gonna be it's gonna be
29:26	kind of a big number , but I'm not sure
29:28	. So let's go off to the side 21 times
29:30	six . Six times 166 times two is 12 .
29:35	And I get 126 . I kind of guessed here
29:37	. You might start with five or seven . Eventually
29:40	you'll figure out the closest you can get is six
29:42	. So , it can go six times For 126
29:46	, subtracting at zero . Now the remainder is zero
29:49	and there are no more digits to drag down .
29:51	Now . We know the process can be stopped and
29:54	the answer to this is 1.6 16 Final answer .
30:01	All right , we're almost done actually . I know
30:04	these are kind of long , but we just need
30:06	to really get a lot of good practice to make
30:08	sure that we're on the same page . Let's take
30:10	a look at the problem 6.56 . And we'll divide
30:15	it by 0.02 . So on the outside I have
30:22	two digits after the decimal . I want to move
30:24	this decimal one position to positions to get a whole
30:27	number . That means to keep it balanced , I
30:29	have to move one position to positions to keep it
30:31	balanced on the inside . So really I'm going to
30:34	then solve the related problem of 656 and I'll divide
30:39	that by Once . I move the decimal , I
30:41	only have two on the outside the leading Zeros .
30:44	You can throw away once you move the decimal .
30:46	This is what I want to solve . 656x2 .
30:50	Now , I know there's an invisible decimal here so
30:53	there's basically an invisible decimal that floats right above .
30:55	I don't have to put that but you know I
30:57	can . Alright next , what do we have ?
31:01	Two times what is six ? Two times three is
31:03	six ? So multiply and subtract , I get a
31:06	zero drag the next digit down which is then five
31:10	. Two times what is five ? Two times two
31:13	is four . That's as close as I can get
31:15	two times to being four . Subtract , I get
31:17	a one and I then after subtraction , dragged the
31:20	next digit down . Now I have 16 . two
31:23	times what is 16 ? two times 8 is exactly
31:26	16 and I get a zero now I have a
31:29	remainder of zero . I don't have any more digits
31:32	. Of course I can keep adding zeros but I
31:33	don't need to because I already got to a remainder
31:35	of zero . So the answer we get this 328
31:39	the . really doesn't doesn't really do much because you
31:42	can put a decimal zero after if you like .
31:45	So what I'm going to do is just say that
31:47	the answer is 328 . That was a whole number
31:50	answer . Alright , next problem . Let's go ahead
31:55	and give ourselves some room . We're gonna solve the
31:57	next problem down here . Let's say we're solving the
32:00	problem . 0.91 and one divide that by 0.65 .
32:08	All right . First thing we look on the outside
32:10	, we have to move this decimal one position to
32:12	positions . That means we have to move this 11
32:14	position to positions also to keep it balanced . So
32:18	we're really going to solve a related problem . We
32:21	move the decimal , it'll be 91 on the inside
32:24	and we'll divide it by 65 on the outside ,
32:28	65 on the outside . Alright , next thing we
32:32	want to notice is that just as always we have
32:35	an invisible decimal right here . Let me get rid
32:37	of this real quick . We have an invisible decimal
32:39	here . So the answer will have an invisible decimal
32:41	right there as well . Give myself a little bit
32:43	more room here . I just kind of come more
32:46	like over here . All right . Um and so
32:50	then we want to start by looking at saying alright
32:52	65 can go how many times into nine ? Well
32:55	it can't go at all into nine . Too small
32:58	. How many times can you go into 91 ?
33:00	Well I know it can go one time and I
33:02	know that it cannot go to times because if you
33:04	think about this is being pretty close to 66 times
33:07	two is 12 , So 60 times two is 120
33:10	. If you multiply this you're going to get something
33:12	way bigger than 91 . So it has to go
33:15	only one time right here . So put it one
33:17	right here and then multiply get 65 And then we
33:21	need to subtract . Now unfortunately you have to do
33:23	a little borrowing so let's go over here and do
33:25	91 -65 . Now we know that we can't do
33:32	one minus five so make it 11 and borrow and
33:34	that becomes 8 11 minus five . Go down 10
33:38	9876 11 minus five or 68 minus six it's two
33:43	. So the answer here is 26 . So we
33:45	put a 26 down here Now we don't have any
33:48	more digits in our problem but we also do not
33:51	have a remainder of zero so we have to keep
33:53	going even though you you think oh I don't have
33:55	any more digits really . You need to be looking
33:57	at the remains the remainder that you kind of have
33:59	and you want to get it down to the point
34:01	where it's essentially zero if you can . And so
34:05	we have to continue the process . So we look
34:07	up here and we say well We have 91 ,
34:09	we have a decimal , we can easily add another
34:11	zero here without changing the problem at all . So
34:14	we're going to insert that and add that zero .
34:17	Then after we did the subtraction we just drag that
34:19	zero down and now we have 260 down there .
34:23	So the question then is 65 times what is 260
34:29	? I'm not sure the answer . So let's go
34:30	here and do 65 times four . You can try
34:32	times three or times five five times four is 20
34:36	carry the 26 times four is 24 25 26 .
34:39	I didn't know that ahead of time but you know
34:42	, I also know what the answer is . So
34:43	but you might try times three times five or whatever
34:45	. Eventually you're gonna figure this out , Times four
34:48	is the answer . So you put a four here
34:50	, four times 65 is 260 Then you subtract and
34:55	get a remainder of zero and now we don't have
34:57	any more digits . We could continue adding zeros but
35:00	it doesn't help us do anything because the remainder is
35:02	already at zero . So the answer to this is
35:04	1.4 . So I guess I'll just kind of box
35:07	this the answer is 1.4 . Sorry , this is
35:09	kind of crowded here . The answer is 1.4 for
35:13	this problem . So if we take 0.91 and we
35:16	divide it by 0.65 it can go one whole time
35:19	. Almost 1.5 times a little bit less than 1.5
35:23	times . All right . I think we have room
35:27	for one more problem . I think that would be
35:31	a good place to stop it over here . So
35:34	, let's take a look at the next problem .
35:38	I guess . Let's go up like this . Give
35:40	me a little space . Let's take a look at
35:41	the final problem . 2.52 . And we're going to
35:45	divide that by 0.08 . So on the outside we
35:54	don't want any decimal . So we move to spots
35:56	to the right ? That means we move to spots
35:58	to the right here . All right . So that
36:01	means we're actually going to be solving the related problem
36:04	. I'll write it over here of 252 and we'll
36:09	divide that by zero point . I'm sorry eight because
36:12	we moved it to , its gonna be eight on
36:14	the outside . Eight now we can put the decimal
36:18	here because we know that there's a decimal after every
36:20	whole number . And so the decimal and the answer
36:22	has to be above there as well . So let's
36:24	see how this shakes out . Alright eight can go
36:29	, cannot go into too , it's too small .
36:31	Let's try going into 25 . 8 times two is
36:33	16 . 8 times three is 24 . So it
36:36	can go three times into 25 . 8 times three
36:39	is 24 . We subtract and we know that the
36:42	answer is one After we subtract , grab the next
36:45	digit which is a two now eight times one is
36:48	88 times two is 16 . That's too big .
36:50	So it has to go only one time eight times
36:53	1 is eight subtract now we can you know borrow
36:58	and all that . But really you know that if
36:59	you go start from eight and count up to 12
37:02	9 10 11 12 is four so 12 minus eight
37:06	is four and then you look for another digit ,
37:09	you don't have another digit and you think oh I
37:10	guess I'm done but you say wait a minute we're
37:12	always trying to get to a remainder of zero in
37:15	here , I don't have a remainder of zero .
37:16	So in decimal problems I need to keep going I
37:19	can insert zeros after the decimal it doesn't change anything
37:23	and then that allows me to drag because I just
37:25	subtracted to drag the next digit down Which is zero
37:29	and I have now 40 . So now eight times
37:32	what is 48 times five is 40 . Multiply you
37:36	get the 40 subtract , you get a zero And
37:40	so now I do have a remainder of zero .
37:41	I don't have any more digit . I could keep
37:43	adding zeros but I don't need to because I've already
37:46	gotten to a point where my remainder is zero .
37:49	So the answer to this is 31 .5 . All
37:57	right . That is a long lesson . A lot
38:00	of writing . A lot of you have to go
38:02	off to the side and your side work to make
38:04	sure you can subtract or multiply to figure out what
38:07	to do . I don't want you to lose sight
38:08	of the big picture . The big picture is you
38:11	have to do this division but the decimal on the
38:14	outside , you don't want decimals here . So you
38:16	move the decimal over in the same member of positions
38:19	. You have to move the the what's under here
38:21	? The decimal , the same number of places and
38:24	then you do the division as normal . Sometimes you
38:26	will end up where after you move the decimal you
38:29	still have a decimal on the inside . It just
38:31	floats up above . See here after we moved it
38:34	we still had one inside . It just floats up
38:35	above . But sometimes you do it and you'll end
38:38	up with a whole number on the inside but you
38:40	still have a decimal there , it still floats up
38:42	above . It just it's there , it's just 12
38:44	has an invisible decimal there and then you go through
38:46	the process is normal . Always looking to make sure
38:49	that you have a remainder of zero . Then you
38:51	stop when you have a remainder , then you stop
38:54	here . We got to a point where the remainder
38:56	what's for but we didn't have any more digits and
38:59	so you're thinking you should stop but you need to
39:00	keep going . And the way that you keep going
39:03	is you have to add zeros after the decimal point
39:06	as many times as it takes until you get to
39:08	remainder of zero uh there . And then Then when
39:12	you finally do get to the point where the remainder
39:14	is zero down under there , then you can stop
39:16	and the answer , you've calculated up above . I
39:18	know it's a little weird , a little hard the
39:20	first time we do it . But I think with
39:22	practice you'll get the hang of it . I'd like
39:24	you to solve every one of these problems yourself .
39:27	Start dusting over right down the problem and do it
39:30	yourself . Even if you just saw me do it
39:32	then I'd like you to follow me on the part
39:34	two . We'll get a little more practice with the
39:36	concept of dividing decimals .

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