Math division - cast out nines trick - Free Educational videos for Students in K-12 | Lumos Learning

Math division - cast out nines trick - Free Educational videos for Students in k-12


Math division - cast out nines trick - By tecmath



Transcript
00:0-1 Good day . Welcome to take Mouth channel . What
00:01 we're gonna be having a look at in this video
00:03 is a method for checking your division questions . Especially
00:06 long division . Just checking you got the right answer
00:08 . It's using this method call casting out nines ,
00:10 which we've been having to look at in terms of
00:12 multiplication and addition , especially where it also comes in
00:16 really , really handy . So let's have a look
00:18 at it right now . So , say you've done
00:20 this particular question . Um you had uh divided 28
00:26 into Uh 15,158,060 . And when you've done this ,
00:34 you've got the answer of Put this in a different
00:37 answer , a different colour . 5645 . Now ,
00:43 do you notice with this ? Keep your head about
00:44 what's going on here when you do this ? Not
00:46 everyone does division exactly like this . And so you
00:49 might want to modify . But what we're doing is
00:51 this number times this number should be equal to this
00:54 number . All right . I'm almost I'm actually going
00:57 to write this down . So this year we might
01:01 even want to call a . This one we call
01:03 what call be this ? We might call B .
01:05 C . And we're going to just remember that A
01:07 times B . Here is going to be equal to
01:09 our answer . C . Just really handy just to
01:12 keep your head around what's going on there . Casting
01:15 out Nines is a special method where what we're doing
01:18 is for each part of our answer . A .
01:20 B . And C . Here , what we're going
01:21 to be doing is adding the digits of our answer
01:24 . So in this for this part here we're gonna
01:26 be adding to and ate together to get and we're
01:29 gonna be eventually trying to reduce it down to single
01:32 digits . But you can also as you go along
01:34 , throw out uh numbers that are rather nine or
01:38 add up to nine to make life easier . So
01:40 I reckon watch this as it goes along and I'll
01:42 show you what I mean . So first off let's
01:44 start with this . So we're going to reduce this
01:46 answer down two plus side . So I'm going to
01:50 add these digits together . Two plus eight is 10
01:54 10 . We can we wanted to reduce it down
01:57 to a single digits so we just add these further
01:59 so 1.0 is one . Tell me I'm gonna put
02:02 a one there at the moment . Be over here
02:06 , this one over here . Uh We're looking for
02:09 any numbers that add up to nine that we can
02:11 get rid of because that's what it's called casting at
02:13 the nines this particular method . And we do we
02:15 have a four or five years so we can ignore
02:17 those were left with just five plus six which is
02:21 11 , add these together weekend too . So this
02:27 over here is to Yeah , okay . Now what
02:32 we're gonna do is we're answer part this this big
02:35 party here , this last part this was a bit
02:37 weird , dividing into we're going to be adding digits
02:41 but we can cast at any nine nines or numbers
02:43 that add up to nine before we start , we
02:45 have one at eight here , they add up to
02:47 nine , we can get rid of those . So
02:49 we're just left with five and six , which is
02:53 11 , one plus one equals two . So This
03:00 equals to this number times . This number should equal
03:03 this number and if it does , it's a fairly
03:05 good indication that you have the right answer . Okay
03:09 , it's pretty cool . Right ? So we're and
03:11 it is indeed the right answer . It's a fairly
03:13 good indication that we are on the right track .
03:16 It's not 100% proof positive , But it's a good
03:19 90% chance . Okay , So that's the way Casting
03:22 out Nines works with division . But the big thing
03:25 is to keep your head about what's actually going on
03:29 Okay , because especially we're going to get a stage
03:32 where we're going to be having things like remainder is
03:34 in there . So what about we had to say
03:36 something like 17 ? And that was going into a
03:39 number like 316,000 UB 873 . And we got this
03:47 answer of 18,000 639 reminder 10 . You're going to
03:55 see there's a couple of parts of this and usually
03:58 what would actually be doing is we should be able
04:00 to , in reality multiply these two numbers together and
04:04 add a remainder , and we'd get this answer here
04:06 correct . So this is what we're going to be
04:08 looking to be happening when we cast that no one's
04:11 because that same thing should happen , we should be
04:13 able to add this number and this number add this
04:17 Stuart and get this answer here . Okay , Because
04:21 that's what we do in reality to everyone to check
04:23 our answer . Using multiplication and a calculator , but
04:27 we're not going to use a calculator . We're gonna
04:28 use this method called casting . And so we're gonna
04:30 start with this part . First one plus seven is
04:34 I'd Okay , so and it's gonna put this debate
04:41 over here . Um What we're gonna be doing now
04:46 is we're gonna be casting out nines over here .
04:49 So we're gonna get rid of that one first at
04:51 nine there , we can get rid of that nine
04:52 there , we can get rid of that nine there
04:54 . In fact , we're left with a zero here
04:56 . Nice and easy . We have a remainder of
04:58 10 which we could add on but we can cast
05:02 out no one's gonna do that . The reducing this
05:04 to which would make that into a 11 plus zero
05:06 is one . So what we're left with is this
05:11 times this eight times zero , which is zero plus
05:16 one . Okay , This number times this number plus
05:20 this number which is equal to one and it should
05:25 be equal to our number here . Okay , So
05:28 let's check it out . three and 6 is knowing
05:32 one in eight is 90 with Castro's away . We're
05:35 left with seven and three . We've got 10 ,
05:37 one and 0 is one . These numbers here matching
05:41 up . It's a good indication we're on the right
05:44 track . We've got the right answer . Okay ,
05:46 So just be very , very aware that's what I'm
05:48 saying with this . You need to keep your head
05:49 about what you're doing , okay ? That you would
05:51 be multiplying these two numbers and adding this one to
05:54 do that same process . Okay ? Otherwise , you
05:57 will get in a pickle . Alright , get yourself
06:00 in a pickle . All right . Um I'm gonna
06:05 do one last one of these . So , we're
06:07 going to have a look at 40 for going into
06:11 Uh this really big number . 563,753 . Now ,
06:17 if you do this off the top of your head
06:18 , hopefully you will be able to get instantly .
06:21 I do have methods of work this out , by
06:23 the way . Check out some videos you haven't seen
06:25 these . Um but you should get 12,812 remained uh
06:31 25 bike . I let's check our answer again .
06:36 This time . This pluses . Should we call this
06:38 ? So we're going to do the same thing again
06:40 . Okay , this plus this is I This one
06:44 here . We can cast out the one of the
06:46 eight and we're gonna left with one plus two plus
06:49 two , which is five . So we're gonna be
06:52 multiplying these and adding our answer here . So ,
06:55 First off , what is this one in which is
06:58 7 ? So eight times five , which is 40
07:03 plus seven . So all right , the same here
07:05 actually , eight times five , which is 40 plus
07:07 seven . You would get the answer of 47 .
07:10 4 and seven . We're going to reduce down we
07:13 add +24 and seven . We get 11 . We're
07:15 gonna reduce those down . We get it too .
07:17 Okay . Happy . Happy . Right ? Okay .
07:20 Hopefully we cast that knowledge . We should get to
07:22 hear then correct ? So , let's try that .
07:25 six and 3 . Cast that away . Okay .
07:28 So what we're gonna be doing is we're gonna be
07:29 adding the rest of our numbers here . Five and
07:32 seven is 12 plus five is 17 plus three is
07:37 20 two and 0 is too these two I match
07:44 . We've got a small if ice happy , it
07:48 all works out . So that's the way you can
07:50 check your answers in division by casting out nines .
07:53 And it's really , really a great method and if
07:56 you haven't seen them once for multiplication addition and also
07:58 on my way working at subtraction and checking our answers
08:01 and that really check it out . It's a really
08:03 handy little method anyway , hopefully that was of some
08:06 help to you . We'll see you next time .
08:08 Bye .
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