How to check math multiplication - cast out nines trick - Free Educational videos for Students in K-12

How to check math multiplication - cast out nines trick - By tecmath

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00:0-1	Good day . Welcome to take Math Channel . What
00:01	we're gonna be having a look at in this video
00:03	is a way of checking out multiplication answers through this
00:06	method of called Casting Out Nines . It's a fairly
00:08	simple method . Uh Hope you like . It's a
00:11	really , really good one . And it's a very
00:12	fast method for checking out my application much faster than
00:16	uh re multiplying things out or something like this .
00:19	Okay , so let's have a look how this works
00:21	. So say we had 100 and 32 we multiply
00:25	this by 434 and we wanted to check the answer
00:30	that we got which was 57,288 was indeed most likely
00:36	the right answer . So we do this as follows
00:39	. We do this through this method called Casting out
00:42	nines . We're looking at this with addition for an
00:45	earlier video and now we're looking at it for this
00:47	and it's a fairly similar method . What this means
00:50	is we're gonna be adding our digits for each of
00:53	our numbers here . But anyway we see at nine
00:55	we can cast our numbers away cast at nine away
00:59	. Okay . So what we do for this is
01:01	we're reducing it to a single digit number . One
01:04	plus three is four plus 26 Um We have four
01:12	. None of these numbers here are 4400 and 34
01:14	hours nine . So we're just going to add them
01:16	together . Four and three is seven plus four is
01:19	11 . But this is a double digit numbers are
01:23	going to reduce to a single digit number by going
01:25	one plus one which is to okay . Um Then
01:31	what we can do because we're multiplying here , we're
01:34	gonna multiply our answers here six times two is 12
01:37	. And then we reduce this also so one times
01:40	21 plus two is three . Okay , We only
01:49	multiply in this part here . Okay . So what
01:52	we're gonna be doing is now we're gonna be casting
01:55	out any nine that we can do in here .
01:56	So what it means by this is seven and to
01:59	add up to nine so we can just chuck it
02:00	away and ignore that . And what we're going to
02:03	be doing is adding these numbers we have left here
02:05	, so five and eight is 13 plus eight is
02:09	21 reduce this down two plus one , which is
02:14	three . You notice that these numbers here match .
02:18	If they match , you can assume that the answer
02:20	is correct . Again , this method does not provide
02:22	100% proof but it's if you get a difference in
02:26	these numbers , it means that you definitely have an
02:28	error . So this means that we've probably got the
02:30	right answer here and indeed it is the right answer
02:34	. Okay , so what about we give ? We
02:37	have another go here . Say we do something like
02:45	um 36 And we multiply this by 313 . Mhm
02:54	. And we get the answer of 11,268 . Now
02:58	, what casting out nines would mean is first off
03:02	this three and six at up to nine , we're
03:04	gonna chuck it away , so it's gonna be a
03:05	zero . Okay , we're gonna be multiplying this by
03:09	number . We're gonna actually gonna realize that our answer
03:11	here is going to be zero because we're gonna be
03:12	multiplying a number by zero . But let's go through
03:14	it anyway . Three plus one plus three is 70
03:19	times seven zero . I almost right seven down .
03:25	You wouldn't believe it . All right . Okay .
03:28	So we're gonna have a look at Anthony and see
03:30	if this matches up . So uh one and eight
03:33	. Well , they cancel each other , and well
03:35	that's as up the night we can throw that away
03:37	, but also does six and two and one add
03:40	up to nine . So we're left with nothing ,
03:43	nothing and nothing match up together . So our answer
03:46	is most likely correct . Okay , so let's have
03:51	a look at one last example of this this great
03:53	method of casting out nines and where it really comes
03:56	into like where it's really great is when you get
03:58	some question like this 14,600 oh man , I can't
04:04	write a number down . 613 And or modify this
04:09	boy , say 6130 . And now I'm going to
04:17	check my answer here , which is eight million ,
04:22	actually 89 million . 577,690 , Wow . Let's check
04:32	to see if we got the right answer here .
04:33	So let's use casting out Nines . Now , we
04:36	could either remote file that out , wow . That
04:38	would take a while , wouldn't it ? We just
04:40	cast out Nines . Let's do that . Okay ,
04:43	so say we have six and three at the moment
04:46	, they add up to nine , we can get
04:48	rid of those . So we're left with 14 and
04:50	one which is six . Okay ? We can cast
04:54	out the six and the three because they add up
04:56	to nine , we're left with one . So six
04:58	times one is six . Happy Happy Joy Joy .
05:02	Now on our answer here we can now cast out
05:05	nights here , we can get into that night and
05:06	that nine nice and easy straight away . And I
05:10	don't see any of these other numbers which we can
05:11	definitely earning up to nine . Right ? So let's
05:15	just add them as we go . Eight and five
05:17	is 13 plus seven is 20 plus seven is 27
05:22	plus six is 33 33 . So 3-plus 3 is
05:27	six . These guys match . It's a good indication
05:31	it's the right answer . When I say it's a
05:33	good indication it's not necessarily the right answer . Because
05:36	pretend , for example , instead of what I've had
05:40	is this had been are you annoyed And not 90
05:45	? It would still add up to the same amount
05:47	, wouldn't it ? So it's only an indication that
05:49	it is a correct answer . Okay , So just
05:53	be aware of that . It's not 100% proof .
05:56	It's a good 90% sort of proof answer . Okay
05:59	, So anyway , that's a method of casting out
06:01	nines . It's a great method for quickly working out
06:04	whether your multiplication is likely to be correct . Anyway
06:08	, we're gonna have a look at this in the
06:09	next video where we're gonna be looking at applying this
06:12	to division . Especially long division . Okay . Anyway
06:16	, see you next time . Bye .

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