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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