01 - What is a Fraction? - Definition & Meaning - Part 1 - Numerator, Denominator & More. - Free Educational videos for Students in K-12

01 - What is a Fraction? - Definition & Meaning - Part 1 - Numerator, Denominator & More. - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called what is a fraction also called parts of
00:06	a whole . So we could call it parts of
00:07	a whole , we can call it what is a
00:09	fraction . I'm really excited to teach this lesson because
00:12	a lot of students have problems with fractions and it
00:15	actually fractions is one of the most important things you
00:18	will ever ever learn in math and we can take
00:20	and break it apart and make it understandable so that
00:23	everyone watching this will understand exactly how to work with
00:26	a fraction exactly what a fraction is . And so
00:29	there's never any confusion about anything because the little secret
00:32	is fractions are actually really , really easy to understand
00:35	, we just have to talk about it a little
00:36	bit . So what is a fraction anyway , why
00:40	do we care ? And by the way you'll be
00:41	using fractions from now all the way until the end
00:44	of your education many , many , many years from
00:46	now you will still be using fractions , so it's
00:48	that important . So what is a fraction ? Alright
00:51	basically let's go back and reverse a little bit for
00:54	a second . We all know how to count numbers
00:56	. Let's say we have three oranges . There's orange
00:59	number one orange number two Orange number three . We
01:02	know how to count objects . 123456 You know 10
01:07	987654321 for instance , fractions . Let us talk about
01:13	when we have less than one of an object .
01:15	So let's say we have four oranges , we take
01:17	one away , we have three oranges , we take
01:19	another one away , we have two oranges , we
01:22	take another one away , we have one orange .
01:23	Or let's just talk about pins . We have one
01:25	pen left . But what happens if I don't even
01:27	have a whole pen or a whole orange ? What
01:30	if I only have half of an orange ? I
01:32	mean you all have dealt with fractions your whole life
01:33	. What if you cut a sandwich in half ?
01:36	Then you don't have an entire sandwich , You have
01:39	less than a sandwich , you have a half of
01:41	a sandwich or a half of a pizza . Or
01:44	if I cut this marker in half you would have
01:46	half of a marker . So what we need to
01:48	do is understand what fractions are and also how to
01:51	write them down so that we understand exactly what they
01:53	are . But in the big picture a fraction .
01:56	Let's us talk about when we have less than one
01:59	entire objects . What if I cut this marker into
02:02	two pieces ? I have a half of a marker
02:04	. Right ? What if I cut it into three
02:06	pieces ? I'll have some other fraction . What if
02:08	I cut it into seven pieces and I only have
02:10	one little piece of the marker . What if I
02:12	only have this little piece ? This little cap then
02:15	that's less than one marker . But how much less
02:18	? How do we talk about something when it's less
02:20	than one ? So that's what we want to do
02:22	and then we have a bunch of problems . But
02:24	before we get into the problems we want to talk
02:26	about exactly what this fraction stuff is . So this
02:28	is one has one in the middle . It means
02:31	there's one whole object if you want to think about
02:34	the circle as being a pizza . Great that I
02:36	actually like talking about pizza . So we can think
02:38	of it as being a pizza or we can think
02:40	about it as being you know a pie or we
02:42	can think about it as being a cupcake or whatever
02:44	you want it to be . But it's it's a
02:46	circular thing , right ? But fractions can be used
02:49	to cut any shape you want ? But in this
02:51	lesson we're gonna use mostly circles and rectangles because they're
02:53	easy . But you can use any shape you want
02:56	and slice it up and talk about the fractions that
02:59	are inside . So in this case we have one
03:01	whole pizza . What happens if we cut this pizza
03:04	in half ? Then we all know cutting in half
03:06	means you divide it into two pieces . So let's
03:09	take a look at that . This is exactly the
03:12	same size as the pizza we started with , but
03:14	now we actually have broken it into two pieces .
03:18	All right , How many pieces of the pizza do
03:21	we have ? We have two pieces piece number one
03:23	piece , number two . We put them together .
03:25	It makes an entire pizza . So if we put
03:28	one half and add to it another half , then
03:31	we have the entire pizza . But if we cut
03:34	it in half and throw this half away , let's
03:36	say . So this is all we have left ,
03:38	we only have half of the pizza , right ?
03:40	So what does this mean ? Here ? The one
03:42	slash the one and then the line and then the
03:45	two . What's going on here is first of all
03:48	you have to when you cut the pizza in half
03:50	, how many pieces do you have ? You only
03:53	have two pieces of that pizza , right ? So
03:56	let's put it to their uh total . When you
03:58	cut it in half , you cut it into two
04:00	pieces . So we have a two there . But
04:02	if I give this piece to my friend and it's
04:04	gone . Now all I have is one piece out
04:07	of two . So we put a line here and
04:09	we put a one on there and we say that
04:11	this fraction here , this much of the pizza is
04:14	one half . So when you cut a pizza in
04:17	half or when you cut a sandwich in half or
04:20	when you cut a marker in half you're cutting it
04:22	into two pieces . The whole object is now two
04:26	pieces but I gave one piece away . This is
04:29	all I have , so I only have one out
04:31	of two pieces . So any time you see a
04:34	fraction I want you to think in your mind the
04:36	top number and the bottom number . You read it
04:38	like this , I have one out of two pieces
04:41	. All I did was cut the original pizza into
04:43	two pieces but I don't have both pieces . Let's
04:46	say I gave it to someone else . Let's say
04:48	I ate one of those pieces . I only have
04:50	one piece left . So it's called one out of
04:52	two pieces . This is called one half . The
04:55	two means it's a half , but I only have
04:57	one of those halves . So it's called one half
05:00	. That's what we say when we call it one
05:02	half . All right . Obviously this is one half
05:05	and this guy is another half . One half .
05:08	One out of two pieces . If I were to
05:10	put them together the one half and the plus another
05:12	one half would make the entire pizza whole . Again
05:15	, we're gonna be talking about that a whole lot
05:17	more later . But right now we're just going to
05:19	be labeling what the fractions are . Now let's say
05:23	you're having a party and you uh you don't have
05:26	to people that you're trying to share the pizza with
05:28	, but you have three people . That means you
05:30	need to cut the pizza into three pieces instead of
05:34	two pieces . So how do you do that ?
05:36	Well what you would do is you would say here
05:40	is a pizza that I've cut to three pieces .
05:42	Notice that this pizza is the same size as the
05:44	original pizza , but I cut it here to the
05:46	center like this and then I cut it to the
05:49	edge here and cut it to the edge here .
05:51	So this amount of the pizza is the same exact
05:54	amount as what's on the other part here and that's
05:57	exactly the same amount as what is over here .
06:00	So this is one out of three pieces . This
06:04	is another one out of three pieces . This is
06:06	another one out of three pieces . But notice that
06:09	we did not cut the pizza into two pieces .
06:12	We cut it into three pieces . But if you
06:14	talk about what one of these pieces are , it's
06:17	only one out of three pieces . So you label
06:20	this piece one out of three pieces again , if
06:24	I take one out of three pieces and I add
06:26	to another one out of three pieces and I add
06:29	to another one out of three pieces . Then you
06:31	get your whole pizza back . Just know that we
06:34	are going to be able to add these things together
06:36	, We're going to do that a long time ,
06:38	you know , down the road , but I just
06:39	want to mostly label everything for you now , just
06:42	keep in your mind that you are going to be
06:44	able to add these guys a little bit later .
06:46	So here we have one whole pizza . This portion
06:49	of a pizza is one out of two pieces .
06:52	This portion of a pizza is one out of three
06:55	pieces . So what do you think would happen if
06:57	I have four people over for pizza instead of two
07:01	or three ? Well I'm gonna have I'm going to
07:03	have to cut that pizza into four pieces and so
07:06	it's going to look something like this , I'm going
07:09	to cut this pizza notice that if I put them
07:11	all together , it's exactly the same size as the
07:14	as this pizza right above , it's exactly the same
07:17	size , but now I just cut it diagonal two
07:20	times . I guess I can put it like this
07:22	maybe , and then you can see now how many
07:25	pieces have I cut the pizza into 1234 pieces .
07:29	So the pizza is only cut into now four pieces
07:33	. But if I give all of these pieces away
07:35	and I'm only talking about this one or let's do
07:38	it like this , I give the other pieces away
07:39	and I'm only gonna talk about this piece , I
07:41	only have one out of four pieces , that's this
07:44	one . So this is one out of four pieces
07:47	. This is another one out of four pieces .
07:49	This is another one out of four pieces . This
07:51	is another one out of four pieces . All right
07:54	, So this is the fraction 1/4 this is the
07:57	fraction one third , this is the fraction one half
08:01	, right ? So you might talk about or listen
08:03	to . You know , some teachers talk about fractions
08:06	are part of the whole , that's exactly what they
08:08	are . When I have one third of a pizza
08:11	, I have one part out of the hole which
08:14	is three pieces . If I have half of a
08:16	pizza I have one part out of the hole which
08:18	is two pieces of the pizza . If I have
08:20	1/4 of the pizza , I have one part out
08:23	of the hole , which is actually four pieces .
08:25	So part out of whole part out of whole It's
08:28	the same thing as what I'm saying when I tell
08:30	you it's one out of three pieces , one out
08:32	of two pieces and so on . So we can
08:34	have fun with the next to , we're just gonna
08:36	crank through them a little bit a little bit faster
08:38	. What if we have more people over and we
08:40	actually cut the pizza into five pieces ? What do
08:42	you think is going to happen ? I'm gonna give
08:44	myself a little room down here . So here is
08:46	a pizza that's cut exactly into five pieces . Okay
08:50	of course I can push them all together and I
08:52	can see that this makes an entire pizza but also
08:55	I can pull them apart a little bit to make
08:57	it a little bit easier . What if I only
08:59	actually have one of those pieces ? Well I have
09:01	cut the pizza into 12345 pieces . There is a
09:06	total of five pieces . But let's just say I
09:08	only have one of those because I give my friends
09:11	the other pieces . Then I have one out of
09:13	five pieces or 1/5 . And then lastly where this
09:17	is the last one we'll do here . What if
09:19	I cut the pizza ? You might guess into six
09:23	pieces , six pieces . So let's push them together
09:26	and let's make sure the pizza is the same size
09:28	, everything looks to be about the same . So
09:30	let me kind of separate as we can see a
09:32	little bit better here . Now let's say I take
09:34	only one out of those six pieces . One out
09:37	of six pieces . That's this amount . So the
09:40	fraction one half you can see is bigger than the
09:43	fraction one third which is bigger than the fraction 1/4
09:48	which is bigger than the fraction 1/5 which is bigger
09:51	than the fraction 1/6 . So the bottom number of
09:54	the fraction is what ? How many pieces you cut
09:57	the pizza into ? And the top number is telling
10:00	me how many pieces I have . One slice out
10:02	of 61 slice out of 51 slice out of 41
10:06	slice out of 31 slice out of two . And
10:09	then here's the whole pizza , of course , all
10:10	by itself . So now what we need to do
10:13	is we need to switch gears to working some problems
10:16	. I'm going to we're going to draw we're gonna
10:18	have a drawing on the board that's going to be
10:20	a fraction . And we're gonna write down what the
10:22	fraction is . So let's go and work on that
10:24	right now . All right , welcome back . Here
10:27	is our shape . Now , for our first problem
10:29	, it is a kind of rectangular or square object
10:32	like this , and it's cut into four pieces .
10:34	So notice with fractions it doesn't have to be circles
10:37	that you're cutting up . You can cut squares up
10:39	, you can cut anything up to make a fraction
10:41	. So here the object that we have is a
10:43	large square type object here And we cut it into
10:46	how many pieces . four pieces . But the shaded
10:49	area is how many pieces I have for myself .
10:51	So I want to write down what is that fraction
10:53	? So how many pieces do I have altogether when
10:56	I cut it ? 1234 So what that means is
11:00	that there are four pieces total . How many pieces
11:03	do I have ? I only have one out of
11:05	those four pieces , so that is 1/4 . So
11:09	, this shaded region is 1/4 . Notice that this
11:13	1/4 right ? It represents one out of four pieces
11:17	of the whole object . It represents the same fraction
11:20	as this , which is one out of four pieces
11:22	of this circle object . So no matter if the
11:25	object is big or small , the fraction is telling
11:27	you how many , how much of it do you
11:30	have ? We're counting in all of these cases less
11:33	than one . Notice that this is less than a
11:35	whole pizza . This is less than a whole pizza
11:37	. All of these are less than a whole pizza
11:39	, and this is less than a whole square thing
11:41	. The whole square object like this . One out
11:44	of four pieces . All right . We can also
11:47	talk about we're not gonna do everyone like this ,
11:49	but we can put this one in terms of this
11:52	leasable object here , one whole square . There's 1
11:55	4th . There's another fourth , 1/4 1 out of
12:00	four pieces . Here's another one out of four pieces
12:03	. Here's another one out of four pieces . If
12:05	we push them all together , then what we get
12:07	is the whole object . But if I pull this
12:09	one aside and say I only have this much ,
12:11	then I only have one out of four pieces ,
12:14	one out of four pieces . So the top number
12:17	is how many pieces I have , and the bottom
12:21	number is how many pieces I've cut the object into
12:24	. So one out of four pieces . All right
12:26	, so let's crank on through and start to solve
12:28	some more problems . What about something like this ?
12:32	So the first thing you have to say is what
12:33	fraction is the shaded region . First thing you have
12:36	to do is say , how many pieces have I
12:38	cut this thing into 123456 I've only cut it into
12:45	six pieces , so six goes on the bottom ,
12:48	because that's how

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