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

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



Transcript
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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