Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31] - Free Educational videos for Students in K-12

Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title here is called
00:02	fractions as multiples . This is part one . The
00:05	driving purpose of this section is for you to understand
00:08	that the fractions that we have been working with ,
00:10	all of the fractions that we've been working with ,
00:12	you can think of them as you can break apart
00:15	the fractions and express them as multiples of a of
00:18	a smaller fraction , and that's a little hard to
00:21	understand by words , but it'll be really simple once
00:23	they get it on the board . Actually , I've
00:25	been emphasizing this whole concept from the very first fraction
00:29	lesson we've done . So when you look at this
00:31	, you might think you already know that . Well
00:32	, that's because I've been emphasizing it from the beginning
00:35	to try to make it easier to understand . Let's
00:37	just jump right in . Let's take the fraction 2/8
00:41	. I've been telling you since we started that what
00:44	this means is two pieces out of eight of a
00:46	pizza . Cut a pizza into eight slices . That
00:50	means every slice would be 1/8 but you don't have
00:52	1/8 you have 2/8 . So I've been teaching you
00:56	to think of these slices of the pizza like this
00:58	is a slice of the pizza . To think of
01:00	these slices as things that you count , you count
01:03	them as you go around . This is 1/8 .
01:05	If you have two of them it's to eight and
01:07	then 3/8 and then 48 So you've been counting uh
01:10	these slices of the pizza , counting in eighth the
01:12	whole time . So what I want to do to
01:14	to illustrate the point here is I want us to
01:17	write this fraction two eights . I want us to
01:19	write it two different ways . The first way I
01:21	want to write it as a multiplication equation or something
01:25	involving multiplication . And then the second way we're going
01:28	to write it in terms of addition . So we're
01:30	gonna write two different ways . We're going to write
01:32	an equation with multiplication and an equation with addition .
01:36	It's going to be very very simple . Let me
01:38	ask you to 8th . It's going to be easier
01:41	for us to get to the punch line and then
01:43	go from there for this one for our multiplication equation
01:46	we can say that 2/8 is equal to what ?
01:50	1/8 but times two , that's what 1/8 is times
01:56	two you get to eight . So you can kind
01:58	of like rip this apart and the two can go
02:01	over as a whole number and the 1/8 can come
02:03	over here because remember there's like an invisible being this
02:07	over one . I can write this as to over
02:09	one times 18 and when I multiply one times two
02:13	is 21 times eight is eight . So it makes
02:16	perfect sense that I can say that this fraction is
02:19	equal to the fraction 18 times two . That's why
02:22	it's called multiples . I want you to think of
02:25	28 and 3/8 and 4/8 is just like multiplying 1/8
02:30	times two or multiplying diffraction 18 times three or whatever
02:34	this is called a multiple . And so I can
02:37	show you that with a uh with a fraction or
02:40	with a with a model we can say this is
02:43	the fraction two eights . That's what this is .
02:45	This is the fraction to AIDS . But I can
02:46	write that as the fraction 1/8 times to write .
02:52	And that's another way of of of writing that 18
02:55	the fraction 18 times . To the other way we
02:57	want to write it is in terms of addition ,
02:59	we can say that 2/8 is equal to just like
03:02	two times 1/8 . We can write it as 1/8
03:04	plus 1/8 because remember all multiplication can be written as
03:09	addition . So these are the two answers I'm going
03:11	to give you a fraction . And our goal is
03:14	to write it as the multiplication of something and then
03:16	also to write it as the addition of something .
03:18	And every problem will be the same . This two
03:21	eights means the fraction 1/8 times to just like this
03:25	. And then we can also think of these as
03:26	being just added together . 1/8 plus 1/8 gives you
03:29	2/8 . Because if you add these you keep the
03:32	same denominator , add enumerators , you get the 2/8
03:35	. If you multiply this , you multiply the tops
03:38	, multiply the bottoms . Of course the bottom of
03:39	the one here and so you get the same thing
03:41	back . All right now that all of that talking
03:44	is out of the way , It's gonna be much
03:47	, much easier for us to just jump in and
03:49	understand the rest . Let's write the fraction . 4
03:53	5th . We're gonna write it two different ways .
03:56	We're gonna write it first . It's multiplication , And
03:59	then we're gonna write it as edition . So ,
04:01	4/5 . What does this mean ? It means we
04:03	have four pieces out of five . It means we
04:06	have four slices , each of which is 1/5 .
04:09	It means that we can take the fraction 1/5 which
04:12	is a small fraction . And we can multiply it
04:14	times four , Right ? Four times 1/5 . Because
04:18	that's what we're doing . We're basically going and saying
04:20	we have a fraction is 1/5 and we replicate it
04:22	. And we multiply it times four and that's what
04:24	4/5 is . So , let's take this . We
04:28	have uh here we have the fraction 4/5 there's 1/5
04:33	there's 2/5 there's 3/5 There's 4/5 , there's a fraction
04:37	4/5 . But that's the same thing as just taking
04:40	the fraction 1/5 and multiplying it times four . I
04:44	guess I can flip this over like this 1/5 times
04:47	for the representing it . This way , it's the
04:49	same amount of pizza as uh when you when you
04:54	kind of wrap it around like this , it's the
04:55	same . Exactly the same thing , whether you spread
04:57	it out or you put it into a circle is
04:59	the same thing . This front , 4/5 is the
05:01	fraction 1/5 times four . That's what 4/5 is actually
05:05	equal to . And we can also then write it
05:08	. In terms of edition , we can say that
05:10	4/5 is going to be equal . What ? Thinking
05:12	about this , we can say 1/5 plus 1/5 plus
05:17	1/5 plus 1/5 +1234 times . Because multiplication is the
05:24	same thing as adding the thing that many times .
05:27	So this whole fraction which is 4/5 can be thought
05:30	of as 1/5 plus 1/5 plus 1/5 plus 1/5 .
05:33	That's all we're saying . It can also be thought
05:36	of as 1/5 times . four , same thing .
05:39	So , we circle all of these . All right
05:43	, Let's take a look at problem # three .
05:47	What about the fraction 56 ? How do we write
05:49	that as multiplication . And how do we write it
05:52	as edition ? Well , what we're saying here is
05:55	that we have the fraction 56 can be written as
05:58	five times the fraction 1/6 . And if you can
06:02	think about it , if you think about five being
06:04	5/1 , then five times one is five and the
06:08	one that's down here , one time six is six
06:10	. So this equation is true and we can also
06:13	write that 56 is equal to 1/6 plus 1/6 plus
06:18	1/6 plus 1/6 plus 1/6 +12345 times . So we're
06:25	just adding them together . So let's see if that
06:28	makes sense in terms of six , let's put the
06:31	fraction on the board . There's 1/6 there's +26 we'll
06:34	add that , there's 3/6 there's 46 and then of
06:39	course we have 56 All we're saying here is whether
06:43	or not I keep it tucked into a circle like
06:45	this , or if I spread it out , if
06:48	I add all of these sixes together , it equals
06:51	the 56 Or if I take 16 times five It
06:55	equals what we already know 56 to be . So
06:57	I want you to start thinking of fractions As yes
07:01	it's five out of six slices but it's also like
07:03	taking 1/6 and just adding it to itself that many
07:07	times . Or multiplying times that many numbers there .
07:11	So that's all we're trying to do in this lesson
07:15	. Let's take a look At the fraction . 5/12
07:20	. Let's write it as a multiplication first . Well
07:23	we can say 5/12 is the same thing as 1/12
07:29	Right ? Multiplied by five . Right ? Because if
07:32	I put it put this over one it would be
07:34	five times one is five and then one down here
07:36	times 12 is 12 . So this is how to
07:38	write it as a multiplication . But also we can
07:41	write it as what ? 1/12 plus 1/12 plus 1
07:48	12 Plus 1 12th . That's four times plus 1
07:54	12 . So we're basically doing the multiplication , we're
07:56	representing it as addition . And if you add these
07:59	fractions together , the denominator will be the same and
08:02	you'll add all the ones and you'll get 5/12 .
08:05	So we can do the same thing . Here's 1/12
08:09	. 2 12 , 3 12 , 4 12 5/12
08:13	. That's what we It's five out of 12 pieces
08:16	, but we can also represent it as being 1
08:18	12 , just just multiplied by five . It's a
08:22	multiple This fraction 5 12 is a multiple of the
08:25	fraction . 1 12 . It's just a smaller fraction
08:28	. 1/12 replicated and multiplied times five . So ,
08:31	it's a multiple of the smaller fraction . It's like
08:34	the smaller fractions the core fraction . And then we
08:38	make it a multiple of this by multiplying by five
08:42	and it becomes then 5 12 . Or you can
08:43	think of it as addition . 1 12 plus 1
08:45	12 plus 1 12 plus 1 12 plus 1 12
08:51	. All right . How many more do we have
08:53	? Only two more ? How do we write the
08:56	fraction ? 2/4 . In terms of multiplication ? We
09:02	can write that as the fraction 1 4th times two
09:07	or two times 1/4 . However , you want to
09:08	write it because this too is really to over one
09:11	and then two times one is two and then the
09:13	one times four is four . So it's like taking
09:16	the smaller fraction 1/4 and just multiplying by two .
09:19	That's what the larger fraction is . And we can
09:22	also represent that as simple . In addition we can
09:26	say its 1/4 plus 1/4 . We do it two
09:31	times and adam together . So the fraction 2/4 is
09:34	this this is the fraction to fourth , two out
09:37	of four pieces . It's the same thing as saying
09:40	, here's the fraction 1/4 times to that equals to
09:44	fourth or the fraction 1/4 plus 1/4 That equals the
09:48	2/4 . So this concept should be pretty familiar now
09:54	because as we've been going through this , I've been
09:55	kind of emphasizing this without really saying it . Last
09:59	problem . 4/10 . Let's write it as a multiplication
10:04	. Well , we can say that that's 1/10 times
10:07	four , because if this were 4/1 , 4 times
10:11	one is 41 times 10 is 10 . We can
10:13	also represent 4/10 as 1/10 since it's times 4 .
10:18	1/10 we'll just add it four times plus 1/10 plus
10:22	1/10 plus one 10th . Let's see if that makes
10:28	sense . What I'm saying here is that we have
10:30	1/10 from here , 1/10 from here and 1/10 from
10:33	here and 1/10 from here . And if we add
10:36	all of these together we get the fraction 4/10 that's
10:39	all we're saying . Same thing is thinking about it
10:42	in multiplication . This larger fraction 4/10 is just equal
10:45	to one of these small ones and multiplying it times
10:49	the top number times for so it's not 1/10 it's
10:53	4/10 because we've multiplied the small fraction times four .
10:57	So here in this lesson we're just trying to get
10:59	you to think about fractions in different ways . Yes
11:01	it is four out of 10 slices of a pizza
11:04	but it can also be thought of as 1/10 multiplied
11:08	by four or 1/10 plus 1 10 plus 1 10
11:11	plus 1/10 . We can think about fractions in different
11:13	ways and sometimes the different ways we think about them
11:16	are helpful in different in different problems . So I'd
11:19	like you to practices yourself when you feel like you
11:22	understand it . Follow me on to the next lesson
11:23	. We're gonna give you a little bit more practice
11:25	with this concept

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