Math Antics - Long Division with 2-Digit Divisors - Free Educational videos for Students in K-12

Math Antics - Long Division with 2-Digit Divisors - By

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00:03	Uh huh . Hi , welcome to Math . Antics
00:07	in our video called long division , we learned how
00:10	to do division problems that had long multi digit dividends
00:14	. The key was to break up big division problem
00:17	into a series of smaller and easier division steps .
00:20	And that involved trying to divide the dividend , one
00:23	digit at a time digit by digit . And in
00:26	the examples we saw going digit by digit was pretty
00:29	easy because we only had one digit divisor . But
00:33	what if you need to use that division method for
00:35	problems that have bigger divisor ? Like if you're dividing
00:38	by a two or three digit number in this lesson
00:41	, we're going to learn how you handle problems like
00:43	that . The good news is that you kind of
00:46	already know what to do . You just may not
00:48	realize it yet to see what I mean . Have
00:50	a look at these two division problems . They both
00:53	have the same dividend and both have a one digit
00:56	divisor . But these Divisor are different numbers and as
00:59	you'll see that's going to affect our digit by digit
01:02	division process . To solve this first problem , we
01:05	start by asking how many two's does it take to
01:08	make five or almost five or you can think of
01:11	it as how many twos will fit into five .
01:14	And it's easy to see that the answer is to
01:17	so we put it to as the first digit of
01:19	our answer . Then we multiply two times two which
01:22	is four and we subtract that four from the five
01:26	which leaves us a remainder of one . Now we
01:28	move to our next digit and we need to bring
01:30	down a copy of it to combine with the remainder
01:33	from the first digit . Then we ask how many
01:36	twos will make 12 . That's easy . six .
01:39	So we put six as the next digit of our
01:42	answer , two times 6 equals 12 and 12 -12
01:46	leaves no remainder . And finally for our last digit
01:49	, even though there was no remainder , we can
01:51	bring a copy down and ask how many twos will
01:54	make eight and the answer is exactly four , four
01:58	times two equals eight , which again leaves no remainder
02:01	there we went digit by digit and broke our problem
02:04	up into three division steps , one for each digit
02:07	, and we got our answer 264 . Now let's
02:11	solve the next example . And right at the start
02:14	you'll see we have a bit of a problem when
02:16	we asked , how many aides does it take to
02:18	make five or almost five ? The answer is none
02:21	. And that's because the first digit taken by itself
02:24	is less than the Divisor eight is too big to
02:27	divide into five . So what do we do ?
02:30	Well , instead of just trying to divide the first
02:32	digit all by itself , let's group the first two
02:35	digits together . If we group the five and the
02:38	two together , then our first step will be to
02:40	ask how many eights will make 52 That's better .
02:44	eight will divide into 50 to about six times .
02:47	So we'll put a six and our answer line right
02:49	above the two . Why does it go there ?
02:52	Because we had to skip the first digit and group
02:54	it with the two . If we wanted to ,
02:57	we could have put a zero above that first digit
02:59	since the eight wouldn't divide into it any times .
03:02	And if that helps you keep track of which answer
03:04	digit you're on , then that's a good idea ,
03:06	but it's not required . So six times eight equals
03:10	48 then 50 to minus 48 gives us a remainder
03:14	of four . Now we only have one digit left
03:17	to divide , so we bring down a copy of
03:19	it to combine with the remainder and ask how many
03:21	eighths will make ? 48 ? We know the answer
03:24	to that is six . Also six times 8 is
03:27	48 , which leaves no remainder There are answer is
03:31	66 . Did you notice the difference between these two
03:34	problems ? We wanted to go digit by digit in
03:37	both problems , but in the second problem , the
03:40	divisor was bigger than the first digit of the dividend
03:43	. So we had to start out by going to
03:45	digits at a time in that case and that helps
03:48	us see something really important about this traditional long division
03:51	method . You don't always have to go one digit
03:54	at a time . You can break the dividend up
03:56	into bigger chunks of digits if you want . And
03:59	apply the same procedure to those bigger chunks , you
04:02	could go two or three digits at a time or
04:05	even try to divide the entire dividend all in one
04:08	step and taking bigger chunks of the dividend usually results
04:12	in fewer division steps . I noticed that there were
04:15	three steps in the first problem , but only two
04:17	steps in the second problem , fewer steps . I
04:20	like the sound of that . That seems like a
04:22	lot less work . Yes , fewer division steps does
04:26	sound better but it's really not . That's because the
04:30	more digits you group together , the harder that division
04:33	step will be . I thought it sounded too good
04:36	to be true . It's kind of like climbing stairs
04:40	when you have a lot of small steps . Each
04:42	one is easy to climb but with only a few
04:45	big steps , each one can be a challenge of
04:47	its own . That's why we always try to go
04:51	just one digit at a time . If you only
04:53	have to divide into one or two digits of the
04:55	dividend at a time , it's much easier because all
04:59	of the answers to those smaller division steps can be
05:01	found on the multiplication table which you have memorized ,
05:04	right ? But when we have to go three or
05:07	four digits at a time , it's a lot harder
05:10	to figure out the answer of each step . Okay
05:13	, but how does that relate to two digit divisor
05:16	? Ah As you'll see two digit Divisor force us
05:20	to take bigger steps to see what I mean .
05:22	Let's try solving two new division problems that have the
05:25	same dividend as before . But two new divisor and
05:29	both of these are two digit Divisor in this first
05:32	problem , we could start by asking How many 24s
05:36	will fit into five . But since our divisor now
05:39	has two digits , we already know that no one
05:42	digit chunk of the dividend will be big enough for
05:45	that to divide into . So because we have a
05:48	two digit divisor , we automatically need to group the
05:51	first two digits and ask how many 24s will make
05:55	52 . This is trickier because multiples of 24 are
05:59	not on our multiplication table . Instead we have to
06:02	figure it out by estimating or good guessing Because we
06:06	know that two times 25 would be 50 two is
06:10	a really good estimate for the first digit of our
06:12	answer . Two times 24 is 48 . And then
06:16	when we subtract 48 from 52 we get a remainder
06:20	of four . Okay , so far so good .
06:24	We've already dealt with the first two digits of the
06:26	dividend , so now we bring down the last digit
06:29	to join the remainder and ask how many 24s will
06:32	make 48 ? That's easy . It's too again Because
06:36	we just saw that two times 24 is 48 so
06:40	that will leave no remainder . So the answer to
06:43	this first two digit divisor problem is 22 . Now
06:46	let's have a look at the next problem . It's
06:48	also got a two digit divisor . So we'll start
06:51	the same way , we'll start with a two digit
06:53	chunk of our dividend and ask how many 80 eight's
06:56	will it take to make 52 or almost 52 ?
07:00	Oh , I see the problem , even though both
07:03	are two digits , this won't work because 88 is
07:06	already greater than 52 and that means we're gonna have
07:10	to take an even bigger chunk of this dividend .
07:12	We need to group the first three digits together ,
07:14	but that's just like doing the whole problem at once
07:18	without breaking it into any steps , yep . And
07:21	that's why division problems with Big Divisor is can get
07:24	difficult when you have a two or three digit divisor
07:27	. Each step might be as big as the whole
07:29	long division problems and it can take a lot of
07:32	trial and error to figure it out . In fact
07:34	, if we had our way here at math antics
07:36	when division problems get that complicated , we just let
07:39	students use calculators to solve them , what do we
07:42	want calculators ? When do we want them ? Whenever
07:45	we have long division with two or more digital advisors
07:49	? Okay . But what if we don't get our
07:50	way and you need to solve this problem without a
07:53	calculator ? What's the best strategy ? Well , a
07:56	little estimating will help us make much better guesses at
07:59	her answer . The numbers 88 and 528 are kind
08:04	of hard to work with . But if we made
08:06	estimates of those numbers , like if we change them
08:08	to 90 and 500 , that would make it easier
08:11	to estimate the answer . Since 100 would divide into
08:14	500 exactly five times . That means that 90 will
08:18	divide into 500 at least that many times . So
08:22	let's make five our first estimate for the answer .
08:25	To check to see how good that estimate is .
08:27	We multiply five x 88 and then subtract that from
08:31	528 to see what the remainder is . Now .
08:35	five times 88 is kind of tricking on its own
08:37	. So you may want to use scratch paper to
08:39	work it out . Five times 88 is 440 .
08:43	And when we subtract 440 from 528 we get a
08:47	remainder of 88 . Hm . Looks like her estimate
08:51	was too low . Whenever the remainder is greater than
08:55	or equal to the divisor , it means we underestimated
08:58	the answer . In fact , since our remainder is
09:01	equal to the device er it means we could have
09:03	divided exactly one more 88 into 528 so we should
09:08	have picked six . And if you multiply six times
09:12	88 you'll see that it's 528 . So as you
09:16	can see even though the division procedure is basically the
09:19	same in all these cases , the value of the
09:22	divisor makes a big difference on our division steps .
09:26	Whenever the divisor is bigger than the part of the
09:28	dividend that we're trying to divide , it means that
09:31	we need to group more digits and take bigger division
09:34	steps . Let's try one more much longer two digit
09:38	Divisor problem . 817,152 divided by 38 . I'm going
09:44	to work through this kind of fast so you may
09:47	want to re watch it a couple times if you
09:49	have trouble following it . Since we have a two
09:51	digit Divisor , we start with the first two digits
09:54	of the dividend and ask how many 30 eight's will
09:57	it take to make 81 again ? We're going to
10:00	use Rounding to help us estimate the answer . 38
10:04	is close to 40 and 81 is really close to
10:06	80 And since 80 is two times 40 , my
10:10	estimate for the first answer digit will be too Two
10:14	times 38 equals 76 and 81 -76 leaves a remainder
10:20	of five . We know our estimate was just right
10:23	because five is less than our divisor of 38 .
10:26	Now we move on to the next digit , we
10:28	bring a copy of it down and combine it with
10:31	our five and ask how many 38s will it take
10:34	to make 57 ? That one's easier to estimate just
10:38	one because it's easy to see that to 38s would
10:41	be too big . One times 38 equals 38 and
10:44	57 -38 leaves a remainder of 19 On to the
10:49	next digit . We bring down a copy of the
10:51	one and now we ask how many 38s will it
10:54	take to make 191 ? That's a bit tougher to
10:58	estimate around those numbers . To 40 and 200 I
11:02	know that five forties makes 200 . So five is
11:05	my estimate for the next answer digit . Five times
11:08	38 equals 190 And 191 -1 90 leaves a remainder
11:14	of one . Moving on , we bring down a
11:17	copy of our next digit and ask how many 30
11:20	eight's will it take to make 15 ? Oh 15
11:23	isn't big enough to be divided by 38 . But
11:26	don't worry , we already know what to do .
11:28	When this happens . Whenever we're trying to divide a
11:30	bigger number into a smaller number , we just put
11:33	a zero in the answer line and move on to
11:35	the next digit , We bring down a copy of
11:38	the two and combine it with our remainder of 15
11:41	. Now we ask how many 38s will it take
11:44	to make 152 To estimate this one ? I'm going
11:48	around those numbers to 40 and 160 And since four
11:52	times 40 equals 160 , I'll put four in the
11:55	answer line . As my estimate four times 38 equals
11:59	152 and 150 to minus 152 leaves no remainder .
12:05	And we're done , wow , that was a lot
12:08	of work . But did you see how much rounding
12:10	helped us out ? We made good estimates each time
12:13	by rounding the numbers we were working with . All
12:16	right now , you know that the long division procedure
12:19	works the same for two digit divisor . It's just
12:22	that each division step will involve two or three digits
12:25	of the dividend . And since each of those bigger
12:28	steps is harder to figure out , you want to
12:30	use estimating to help you find the answers . And
12:33	while it's good to know how to do complex division
12:36	problems like this , we still think that complex division
12:39	problems are a job for your calculator , so try
12:42	a few practice problems but don't wear yourself out doing
12:45	really long division like this after all , the reason
12:48	we study math is to become good problem solvers and
12:51	to be able to understand all sorts of important math
12:54	ideas . And there's a lot more to math in
12:56	division as always . Thanks for watching Math Antics and
12:59	I'll see you next time learn more at Math Antics
13:02	dot com .

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