Multiplying fractions using cancellation - Free Educational videos for Students in K-12

Multiplying fractions using cancellation - By tecmath

Transcript


00:0-1	Today in this video , we're going to be looking
00:01	at how to make multiplication of fractions even easier by
00:04	using this thing called cancellation . Uh it's basically a
00:07	way of simplifying as you go along . So I'm
00:10	just going to launch into this with an example ,
00:12	say for instance we were multiplying 9/10 By 5/12 .
00:19	Now without cancellation , what we would usually do is
00:22	we would just multiply straight across , we get the
00:24	enumerators here , nine times five is equal to 45
00:28	and 10 times 12 . These are the denominators and
00:31	would multiply those and get 120 . And then we
00:34	could simplify their by finding common factors that go into
00:37	both . But what we do with counseling down as
00:39	we find common factors as we go , I'll show
00:42	you what this means . So for instance , 9/10
00:47	times 5/12 we're going to look at any of the
00:51	numerator is here and compare them to the denominators .
00:54	And is there any common factors that go into both
00:56	? So we look at nine for instance here and
00:59	12 , they have a common factor that goes into
01:01	both of them . Three goes into both . So
01:03	we divide both of them by three and we reduced
01:06	down as we go , so nine divided by three
01:09	is equal to three . 12 divided by three is
01:12	equal to four . And we can do that when
01:15	comparing any of the numerator with any of the denominators
01:19	, even for different fractions , as you see .
01:21	So another example , as you can see five and
01:23	10 have a common factor of five . five divided
01:27	by five is equal to one . 10 divided by
01:30	five is equal to two . Okay , so now
01:33	what we can do is we can multiply directly across
01:36	as we did before , but with a really much
01:38	easier numbers three times one is equal to three ,
01:42	Two times four is equal to eight . And you
01:45	can check this and we can't reduce down any further
01:48	. But it's a lot easier answer than what we
01:50	had before . And so that's what multiplying fractions using
01:53	cancellation is . I'll give you another example and then
01:56	we'll move on to a harder example . Okay ,
01:58	what about four Over seven ? multiplied by 21/24 and
02:05	we'll see what that equals . But first we will
02:07	counsel down . So comparing the numerator and the denominator
02:11	is here uh we could go okay 21 7 here
02:15	they have a common factor which is seven , seven
02:18	goes into seven once and seven goes into 21 3
02:22	times comparing 4 to 24 . They have a common
02:26	factor which is 44 goes into four once and 24
02:30	divided by four is equal to six . All right
02:34	now we can directly multiply across one times three is
02:38	equal to three . One time six is equal to
02:41	six . Did you notice here ? I miss a
02:44	little common are common factor that three and six have
02:47	, which is three but I can deal with that
02:49	here . Okay , so three and six . I
02:52	can cancel this down . Three divided by three is
02:54	equal to 16 divided by three is equal to two
02:58	. So I could have done it either here or
03:00	I can do it over here but it makes life
03:02	easier as we go along . All right . What
03:05	about one last example , a final example where this
03:07	is much bigger is say 6/15 . Multiplied by 5/16
03:15	. Multiplied by 8/9 . Now , if we were
03:20	just directly multiplies across we get some big numbers either
03:23	here , which would be quite difficult to counsel down
03:25	and quite uh take quite a bit of time .
03:27	It's much faster to simplify as you go . And
03:31	so let's start off say by looking for the obvious
03:33	factors are both five and 15 . Well Five goes
03:37	into five once and five goes into 15 . 3
03:40	times 16 and eight it goes into eight ones and
03:45	16 divided by eight . It's true . We also
03:49	have six and three here . Okay , three goes
03:52	into both . Six divided by three is equal to
03:55	two and three divided by three is equal to one
03:59	. You can see here that we have a two
04:00	and a two . So two goes into both of
04:02	those , two divided by two is 12 divided by
04:05	two is one . And I think we can do
04:07	anymore . Well , no we can't . So let's
04:09	just multiply this out there one times 1 times one
04:12	is one , one times 1 times nine it's not
04:17	, There's an answer one north lot easier than getting
04:20	this big ugly answer on the other end . And
04:22	we would have got and then trying to cancel down
04:25	. So that's just the way we can do that
04:27	. So as you can see canceling down is a
04:29	pretty handy little thing to be able to do if
04:31	you like this video pleasure ever hit the like button
04:33	. And if you need more help with fractions in
04:35	the description below , you will find a link to
04:38	an entire playlist , looking at all sorts of things
04:40	to do with fractions , how to add , how
04:42	to subtract , how to multiply . And even some
04:44	little shortcuts you can type . So I do recommend
04:47	giving that a bit of a look anyway . Thank
04:49	you for watching and we'll see you next time .
04:50	Bye .

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