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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