Dividing Fractions - Free Educational videos for Students in K-12

Dividing Fractions - By Anywhere Math

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00:0-1	oh you have six delicious chocolate bars And naturally your
00:04	friends all want some your friends say a half a
00:07	bar is not enough . You think a full bar
00:09	is too much ? So you guys settle on two
00:12	thirds . So the question is , how many 2/3
00:16	are in six . Welcome to anywhere Math . I'm
00:36	Jeff , Jacobson , and today we're going to talk
00:39	about dividing fractions . Okay , so the question was
00:44	, how many two thirds are in six ? You're
00:46	gonna break these chocolate bars into two thirds of a
00:49	bar uh to give your friends . So let's see
00:53	. Well we know the first bar , I can
00:56	break it into two thirds there , So that's 1/2/3
01:03	. Well then if that's two thirds that means this
01:06	is one third . So I just need one third
01:09	from this and that will make the red that together
01:16	with this chunk , that one third will make 22
01:20	3rd . This is two thirds left here , that's
01:23	another one , that's three . Make 2/3 out of
01:27	here as four . If that's two thirds , that
01:32	means that's one third left in there . So that
01:35	means Over here I need another 1/3 . So there's
01:40	the 1/3 from here . So that 1/3 plus .
01:45	This would be all right . Here would be five
01:50	. Yeah , two thirds . Here's another one and
01:54	six . That would be seven . We just need
02:00	a 1/3 here . So this part in that part
02:07	becomes eight . And we've got finally , there is
02:12	our ninth To 3rd chunk of a candy bar .
02:18	Sorry chocolate bar . So the question , how many
02:21	2/3 are in sex ? And the answer is nine
02:26	. Now , Yeah , we've got to think what
02:30	did we actually do here ? We had six candy
02:34	bars and we broke them into Groups of 2/3 .
02:40	Well , we know when we're grouping things , when
02:42	we have a whole bunch of stuff and we break
02:44	them into groups . we're dividing . So this problem
02:49	we can write as six , Starting with 6 ,
02:54	6 chocolate bars , dividing them into groups of 2/3
03:00	. And we just found But that is equal to
03:03	nine . Let's look at some more examples and figure
03:07	out why that is all right . Let's see if
03:10	we can explain dividing with fractions a little a little
03:13	bit more . Uh We've got division on this side
03:17	in this column , and we've got multiplication in this
03:19	side , notice we always start with an eight on
03:21	both columns . Uh And also notice the difference here
03:26	were divided by four . We're multiplying by 1/4 divided
03:28	by two , multiplied by a half , one and
03:31	11 half and two . So you can notice that
03:34	from here to here . Uh It gets switched ,
03:38	it gets flipped upside down . Uh Well let's go
03:41	through it and see what we get . Well eight
03:42	divided by four . We know that's too Uh eight
03:46	divided by two is 4 . eight divided by one
03:49	is 8 . Now this is the tricky part ,
03:52	we're not sure here dividing . Uh If I wanted
03:56	to do it , just like we did the chocolate
03:59	bars , maybe I've got eight chocolate bars and this
04:02	time I'm putting them in groups of a half .
04:06	Okay , how many has would you get ? Well
04:09	in the first chocolate bar , you'd have two halves
04:11	in the second , you had another to the third
04:14	, another two and so on and so on and
04:15	so on . So you would end up getting 16
04:21	. Same thing here . Well what if we divided
04:22	to make groups of 1/4 ? The first bar would
04:26	have four groups of 1/4 the second bar , another
04:28	four and then another four and another four . You
04:31	end up having 32 groups of 1/4 . Uh Now
04:37	let's go here . The multiplication eight times 1/4 .
04:40	Well , if you watched the previous video , you
04:42	know , multiplying fractions , I can simplify this .
04:47	That would become one . That would become too ,
04:49	so it's just two times one is two . Eight
04:52	times one half same thing . One , that would
04:55	become four is 48 time one is just eight times
04:59	to 16 . 8 times four is 32 . Okay
05:05	, so do you notice something interesting ? All the
05:09	answers are exactly the same . And if we want
05:13	to , if you're thinking yourself . Okay , well
05:16	let's see why is that ? Uh If you notice
05:20	dividing by four is the same thing as multiplying by
05:25	1/4 , divided by two . Same thing is multiplying
05:29	by one half divided by one . Same thing is
05:31	multiplied by one , divided by one half . Same
05:34	thing is multiplying by two . Okay , so dividing
05:39	by a fraction . Okay let's write this down mm
05:44	dividing by a fraction is the same as multiplying by
06:04	its reciprocal ? Yeah . Okay now we haven't talked
06:14	about what a reciprocal is and we'll get to that
06:17	in a second but make sure you have this written
06:19	down . Let's talk about reciprocal real quick . Uh
06:23	two numbers are reciprocal if their product is one .
06:26	So for example if you are thinking well what's one
06:29	half of to one half of two ? You know
06:34	that that's just one Which means 1/2 and two are
06:38	reciprocal . Yeah one way to find a number is
06:43	reciprocal is to just flip it , make sure .
06:46	So if you're wondering well what's the reciprocal of ?
06:49	3/4 ? You just switch it , you just flip
06:53	it over and that would be 4/3 . And we
06:57	could check by multiplying well for And 4 3 and
07:03	three those would all simplify and you would just get
07:05	one . So 3/4 and 4/3 are reciprocal . If
07:10	you have a whole number , make sure You write
07:14	it as a fraction . That's gonna help . So
07:16	for example if you're talking about five uh and you're
07:22	wondering what it's reciprocal is Make that over one ,
07:26	make it look like a fraction and then you know
07:29	. Okay I just flip it So five times 1
07:33	5th those fires would simplify and you would get one
07:38	so five and 1/5 are reciprocal . Okay let's do
07:42	an example . Alright , example # one right ?
07:45	The reciprocal of the number . So what is the
07:48	reciprocal of 3/5 ? Well like I said all you
07:51	have to do if it's written as a fraction you
07:53	just flip it . So the reciprocal of three fist
07:57	is five parents . Okay . And if we wanted
08:01	to check if we multiply those together , our product
08:05	would be one which means they are reciprocal . If
08:08	you want to try the other two on your own
08:09	, go for it positive video and try them on
08:12	your own . Ah What's the reciprocal of nine fists
08:17	? Same thing . Just flip it . That would
08:19	be five overnight . Now let us see the reciprocal
08:25	of to what we want to do when we have
08:27	whole numbers is to write it as a fraction first
08:31	. So I'm gonna put that over one to over
08:34	one is the same thing as too . We haven't
08:35	changed anything and then it's much easier . The reciprocal
08:39	if you flip it is just one half . Okay
08:43	here's some to try on your own . Alright example
08:52	number to find 16 divided by 2/3 . So if
08:57	you remember at the beginning of the video we said
09:00	dividing by a fraction is the same thing as multiplying
09:05	by it's reciprocal or one way to simplify that is
09:10	keep change flip . So 1 6 doesn't change .
09:15	I keep it Divided by a fraction same thing as
09:20	multiplying by its reciprocal . What's the reciprocal of 2/3
09:25	? Well , that's three halves . Okay , we
09:30	can't keep change flip , Keep change flip . Uh
09:37	Now this is just a simple multiple multiplying fractions problem
09:41	. Always , always , always try to simplify .
09:43	1st three and six have a common factor of three
09:47	. So that becomes one That becomes to multiply straight
09:52	across and I get one fourth . Let's try another
09:57	example . All right , here's our last example aboard
10:01	is 15 ft long . How many ? 3/4 of
10:05	a foot pieces can you cut from the board ?
10:08	Uh This is very similar to the chocolate bar problem
10:13	. Um hopefully you recognize that . This is division
10:17	. I have 15 ft of a 15 ft long
10:20	board . I'm putting in groups of 3/4 . How
10:24	many groups can I make ? That's essentially what we're
10:26	asking . Uh so that's division . Right ? I'm
10:29	starting with 15 . I'm going to divide that by
10:33	3/4 , Putting it in groups of 3/4 . So
10:39	here we go , Divided by a fraction is the
10:41	same thing as multiplying by its reciprocal . What is
10:47	the reciprocal of 3 ? Force 4/3 . And remember
10:53	keep change foot . Okay , now with this ,
11:02	I want to write this as a fraction . That's
11:04	going to help kind of keep things a little more
11:06	organized I think so I'm gonna put that over one
11:09	and always , always , always try to simplify before
11:13	you multiply . Hopefully you notice 15 and three have
11:17	a common factor of three , That becomes one that
11:21	becomes five . And now it's very simple , multiply
11:24	straight across and I get 20/1 , which is the
11:29	same thing as 20 . So my answer , how
11:33	many pieces can I make ? I can make 20
11:36	pieces . Now you'll notice that the value increased ,
11:45	Right ? We started with 15 divided by 3/4 and
11:48	we ended up with 20 . That's a little confusing
11:52	at the start because when you think division you think
11:56	you start with a bunch of things , you divide
11:58	them into groups and you get a number that's less
12:00	than what you started with . But now you've got
12:02	to think I'm dividing by a proper fraction . This
12:06	is less than one . So instead of groups of
12:10	whole numbers now my group is so small . I
12:14	get many groups . Okay ? Um So don't worry
12:18	about that . Um Here's some more to try on
12:21	your own . Thank you for watching . And as
12:29	always if you like the video , please subscribe .

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