Math Antics - Long Division - Free Educational videos for Students in K-12

Math Antics - Long Division - By mathantics

Transcript


00:03	Uh huh Hi , welcome to Math Antics . In
00:08	this lesson , we're going to learn about long division
00:10	. If you haven't already watched our video about basic
00:13	division , then be sure to go back and watch
00:14	that first . It'll make learning long division a lot
00:17	easier . Long division is just a way of breaking
00:21	up a bigger division problem into a series of short
00:24	division steps , like the ones that we did in
00:26	the basic division video . The nice thing about long
00:29	division is that once you know the procedure , you
00:31	can divide up all kinds of numbers . Even if
00:33	they're really big , the key to long division is
00:37	to think about our division problem , digit by digit
00:40	. If our dividend , the number we're dividing up
00:43	has a lot of digits , then that means that
00:45	there'll be a lot of division steps to do .
00:47	When we learned basic one step division , all of
00:50	the dividends were small enough that we could just use
00:53	the multiplication table to help us find the answer .
00:55	But what if we have a division problem like this
00:57	? 936 divided by four , 936 is definitely not
01:02	on our multiplication table . In fact , there's not
01:05	anything even close to 936 . So what do we
01:08	do ? Well , instead of trying to divide the
01:11	entire 936 by four all at once , let's break
01:15	this problem up into smaller steps by just trying to
01:18	divide each digit by 41 digit at a time digit
01:22	by digit . Do you remember how with multi digit
01:25	multiplication and addition ? We always start with the smallest
01:28	digit , the ones place digit and we work from
01:30	right to left . Well division is backwards , we
01:33	still go digit by digit . But the other way
01:36	we start by trying to divide up the digit in
01:38	the biggest number . Place first and we work our
01:41	way from left to right . So the first step
01:44	in this problem is to divide the first digit of
01:46	our dividend by four will just ignore the other digits
01:49	for now That makes it look like we had the
01:51	vision problem . nine divided by four . Great .
01:55	That's easy . It's just a basic division problem like
01:58	in the last video so we ask how many fours
02:01	will it take to make nine or almost nine ?
02:03	Well to force would be eight and that's almost nine
02:07	. So just like before we put the two and
02:10	our answer spot on top of the line . But
02:12	wait a minute . There's a lot of room up
02:14	there . Where exactly do we put it ? Well
02:16	, the answer digit should always go directly above the
02:19	digit we're dividing since we're dividing the digit , nine
02:22	are too should go right above the nine . Okay
02:26	now we multiply two times four is eight and the
02:29	eight goes below the nine so that we can subtract
02:31	to get our remainder 9 -8 is one . So
02:34	our remainder is one . Now at this point in
02:37	our basic one step division problems we would rewrite our
02:41	remainder up in our answer with a little our next
02:43	to it , but we aren't going to do that
02:45	yet because this is long division and we still have
02:47	more digits to divide the ones we've been ignoring since
02:51	we're going digit by digit , let's stop ignoring the
02:54	next digit in our dividend the three . Now you
02:57	might think that our next division step is to divide
02:59	that three by the four but it's not quite that
03:02	simple . We had a remainder from our last division
03:05	step and we can't just forget about that . We
03:07	need to combine that remainder with our next digit and
03:10	divide them both together . We do that by bringing
03:13	down a copy of the next digit the three And
03:16	put it right beside the remainder which is one .
03:19	When we do that it looks like our remainder is
03:22	13 . It's kind of like our remainder is teaming
03:25	up with the next digit over . And if you
03:27	think about it , that makes sense because the digits
03:30	that we were ignoring during our first division step really
03:33	are part of the remainder because we still need to
03:35	divide them . Okay so bringing down that next digit
03:39	makes our remainder bigger and that's good because before the
03:42	remainder was so small that four couldn't divide into it
03:45	, but now it's 13 and four will divide into
03:48	13 . So we ask how many fours will it
03:51	take to make 13 ? Well three fours would be
03:55	12 and that's really close without being too big .
03:58	So let's put three in our answer line , yep
04:00	it goes right over the three because that's the next
04:02	digit we were dividing in this digit by digit process
04:06	And then three times four is 12 which we put
04:08	right below the 13 so that we can subtract to
04:11	get the next remainder which will also be one .
04:13	See how we're just repeating the Basic Division procedure ,
04:16	but we're going further down the screen as we do
04:19	. All right now that we have a new remainder
04:21	, it's time for our next division step . Let's
04:24	stop ignoring the last digit in the dividend , the
04:26	six and bring down a copy of it to team
04:28	up with our new remainder Together they form a remainder
04:31	of 16 . Ha ha . That's good because it's
04:35	going to be easy to divide 4 to 16 because
04:37	16 is a multiple of four Takes exactly 4/4 to
04:41	make 16 . So we put a four in the
04:43	last place of our answer line and then we write
04:46	the 16 below our new remainder . Now if we
04:49	subtract 16 from 16 we see that our last remainder
04:53	will be zero , which means there's no remainder left
04:55	. That's great . We solve the whole division problem
04:58	digit by digit by breaking it up into three basic
05:01	division steps . And now we know that 936 divided
05:05	by four equals 234 . And we also know why
05:09	they call it long division . In fact I was
05:12	so long . I think I need a coffee break
05:16	. Oh man that was some long division . Who
05:23	see mhm mm . Okay , so that problem had
05:34	a three digit dividend and it also had three division
05:36	steps but the number of steps isn't always the same
05:40	as the number of digits we have and that's because
05:42	the number of steps also depends on how big our
05:44	divisor is to see what I mean . Let's work
05:48	to division problems side by side . These both look
05:51	like the basic one step division problems that you did
05:53	in the last video , don't they ? But as
05:55	you'll see one of them is actually a two step
05:57	problem . Let's start with the first problem , 72
06:00	divided by eight . We just ask , how many
06:03	eights does it take to make 72 or almost 72
06:06	? Well , that's easy on our multiplication table .
06:08	You can see that 72 is a multiple of 88
06:11	times nine equals 72 . So we put nine in
06:14	our answer line And we write 72 below and we
06:16	see that we have no remainder . Now , let's
06:19	try the next problem , 72 , divided by three
06:22	. If we ask , how many threes will it
06:24	take to make 72 or almost 72 , We can
06:27	see that the answer is not on our multiplication chart
06:29	. The biggest multiple of three listed there is 30
06:32	, which isn't even close . The reason is that
06:35	this should really be a two step problem . Let's
06:37	try using the new digit by digit method , we
06:39	just learned . Instead of asking how many threes make
06:42	72 let's just focus on the first digit and ask
06:45	how many threes does it take to make seven ?
06:48	Ah that's easy to threes would give us six ,
06:51	which is very close . So let's put a two
06:53	in the answer line right above the seven . And
06:56	then we multiply two times three and that makes six
06:59	And we subtract six from 7 to get a remainder
07:01	of one . Now for the second step we bring
07:04	down a copy of the next digit the two and
07:07	we combine it with the one to get a new
07:09	remainder of 12 . Then we ask , how many
07:11	threes does it take to make 12 ? And the
07:14	answer to that is exactly for . So we write
07:18	a four in the answer line and three times four
07:20	equals 12 , 12 minus 12 equals zero . So
07:23	we have no remainder were done , 72 divided by
07:27	three is 24 . Now , here's the interesting thing
07:30	about these examples . The first problem could have been
07:33	a two step problem . Also , if we had
07:35	taken it digit by digit , we would have first
07:38	asked how many eights does it take to make seven
07:40	or almost seven ? But the answer would have been
07:42	zero since eight is too big to divide into seven
07:46	, we would have put zero in our answer line
07:48	and the remainder would have just been seven . So
07:51	basically we just skip that step and that will happen
07:54	with digit by digit division . Sometimes if the number
07:57	is too small to divide into and just put a
07:59	zero in the answer line and you move on to
08:01	the next digit . Okay . Now that you know
08:04	the procedure for long division , are you ready to
08:06	see a really long problem ? Good . I thought
08:09	so let's divide 315,000 , 270 by five . Now
08:15	. Don't worry . It's really not that hard .
08:17	If you just go digit by digit , I'm gonna
08:20	work the problem pretty fast . So don't worry .
08:22	If you don't follow all the math , just focus
08:25	on the repeating division process as we go along .
08:27	Are you ready ? The first digit is three .
08:31	How many times will five divide into 3 05 is
08:34	too big . So let's just skip that step and
08:36	combine our first digit with our next digit . So
08:40	how many times does five divided into 31 ? Six
08:43	? Six times five is 30 and 31 minus 30
08:46	gives us a remainder of one . Now on to
08:49	the 3rd digit . We bring a copy of it
08:51	down to join with the remainder and we ask how
08:54	many times will five divide into 15 , three ,
08:57	three times 5 is 15 and 15 -15 is zero
09:02	on to the next digit . Now , even though
09:04	our previous remainder was zero , we still bring down
09:07	a copy of the next digit . Now we ask
09:10	how many times will five divide into 205 is too
09:14	big , so we need to move on to the
09:15	next digit and bring a copy of it down also
09:19	There . That's better . Now we ask how many
09:22	times will five divide into 27 five , five times
09:26	5 is 25 and 27 -25 gives us a remainder
09:30	of two now , for that last digit , which
09:32	is a zero . And you might wonder why do
09:35	we even have to bring a copy of a zero
09:37	down ? Isn't that nothing ? But the zero is
09:40	an important place holder , and when we bring a
09:42	copy of it down , it changes our remainder of
09:44	two into a remainder of 20 . Now , that's
09:47	a big difference . Now , we ask , how
09:50	many times will five divide into 20 4 ? four
09:54	times 5 is 20 and 20-20 is zero . Yes
09:58	, we're done . There's no more digits to divide
10:00	, and you can see that our final answer is
10:02	63,054 . All right . That's a procedure for long
10:08	division . As you can see , it's kind of
10:10	complicated . So don't get discouraged if you're confused at
10:13	first . Like almost everything , it just takes practice
10:16	. So as you get ready to practice some long
10:19	division problems on your own . Here's a few tips
10:21	that will help you out first . If you haven't
10:24	already done it . Memorizing your multiplication table will really
10:27	help with division second when you're working problems . It's
10:31	really important to write neatly and stay organized . If
10:34	you're writing is messy , it might be hard to
10:36	keep your columns lined up and that could lead to
10:38	mistakes . And if that's the case , try using
10:41	graph paper to help keep things lined up . Third
10:44	start with some smaller two or three digit dividends .
10:47	So you only have a few division steps to do
10:50	, then work up to the longer problems . And
10:52	last of all , after each practice problem . You
10:55	do check your answer with a calculator that will let
10:58	you know right away if you've made any mistakes so
11:00	you can correct them and most importantly , learn from
11:02	them . And it will give you practice with a
11:05	calculator , which is also important . All right ,
11:08	that's all for this lesson . Thanks for watching Math
11:11	Antics and I'll see you next time learn more at
11:15	Math Antics dot com .

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