07 - Writing & Comparing Fractions - (Equivalent Fractions & More) - Part 1 - Free Educational videos for Students in K-12

07 - Writing & Comparing Fractions - (Equivalent Fractions & More) - Part 1 - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called writing and comparing fractions . This is part
00:05	one . It's exactly the same concept that we've learned
00:08	in the last two lessons . But in this lesson
00:10	we have to first write the fraction down before comparing
00:13	the fractions . And so it's just one little extra
00:16	step there . But the basic skill is essentially the
00:18	same . So let's get started with our first example
00:20	. We want to compare this fraction whatever it is
00:23	, to this fraction , whatever it is . So
00:25	the very first step is to write down what the
00:27	fraction is . So here we have 12345678 and we
00:33	have 10 pieces , 9 10 total . So we
00:35	have eight out of 10 pieces . So this fraction
00:37	is eight out of 10 , that's what I'm putting
00:40	here above the blank here . Eight out of 10
00:42	, 8 , 8/10 . And this one is 1234
00:46	out of five pieces . Those five pieces total ,
00:48	but I only have four of them . So this
00:50	is 4/5 . The fraction 4/5 . Now , the
00:54	question is , is a tense bigger or smaller than
00:57	4/5 . And so you look at your drawing because
00:59	we have it all here . This shaded area turns
01:02	out to be exactly the same area as this one
01:05	here . This shaded amount is exactly the same as
01:07	this . If I could grab this and flip it
01:09	over , everything would line up perfectly . So actually
01:13	these fractions , even though they look different , are
01:15	exactly equal to one another . And the reason it's
01:18	kind of like , it kind of makes sense when
01:20	you think about it here . I have 4/5 .
01:23	So I I cut this pizza into five pieces ,
01:27	but I only take four . So in the other
01:29	pizza , what have I actually done ? I've doubled
01:32	the amount of slices , I've cut the pizza into
01:34	five , going to 10 , I've doubled it ,
01:36	multiplied by two . Right ? Five times two is
01:39	10 . But at the same exact time I've doubled
01:42	the amount of slices I took . So in one
01:44	pizza had smaller slices , a smaller number of slices
01:48	in another pizza . I had double the amount of
01:51	slices , but I also took double the amount of
01:53	slices . So I have twice as many slices total
01:56	. But I took twice as many slices . So
01:58	actually I have exactly the same amount of pizza .
02:01	Right ? And you can see from from the drawings
02:03	here that these are two of these pieces will fit
02:06	inside of here because I've doubled the amount of slices
02:09	total . The thing I really want you to understand
02:12	as I've been saying over and over again , is
02:14	that fractions can look different , but they actually can
02:17	be the same exact thing , even though they look
02:19	different . All right , let's take a look at
02:21	our next problem . What is our first fraction ?
02:24	We have 123456 total slices , but we only have
02:28	five . So actually the fraction here is five out
02:32	of 656 What is the fraction here ? 12345 out
02:37	of 6789 10 . So here we actually have five
02:41	out of 10 slices . So 5/10 compared to 56
02:45	? Which one is bigger ? This one is bigger
02:48	, This one is smaller . So the arrow always
02:51	points to the smaller uh number there . So we
02:54	say that 56 is greater than 5/10 . And the
02:58	way we would write that down , you know ,
03:00	without any pictures is we would just say 56 is
03:03	greater than 5/10 . Now , I cannot figure out
03:07	just by looking at these numbers which one's bigger than
03:09	which one smaller ? I can't do it . I'm
03:10	serious . So , you have to draw a picture
03:12	. There's also other ways I can show you later
03:14	, but by the picture you can see that this
03:16	one is bigger than that one . All right .
03:18	Let's take a look at the next one , first
03:21	of all . What fractions do we have ? We
03:22	have 123456789 10 slices total , but I only have
03:28	nine of them . So here the fraction is 9/10
03:32	. That's the fraction . What's the fraction here ?
03:35	It is 1234 pieces . But I only have three
03:38	. So it's three Out of four pieces . So
03:40	I'm comparing nine Tense as compared to 3/4 . Which
03:45	one's bigger . What you can see here that the
03:49	amount of material here is actually way bigger than what
03:52	I have over here . So , this is the
03:53	smaller amounts of the arrow goes to the smaller number
03:57	like that . All right . So the way that
03:59	we would write that down without any pictures , we
04:02	would say 9/10 is greater than that's the greater than
04:05	3/4 . And it always points to the smaller amount
04:09	, which is what we have right here . So
04:11	, what I want you to do is is as
04:13	we go along here , even after you watch me
04:15	work them , I'd like you to work them yourself
04:16	. Let me take these down and put up our
04:18	next batch to get more practice . All right .
04:22	Here's our next fraction what we have here is a
04:25	fraction here is compared to a fraction here , what
04:27	is this ? 1123456 total . Uh And I only
04:32	have 44 out of six essentially . So the fraction
04:35	is four out of 646 Okay , for this one
04:40	. And here we have 12345678 And I only have
04:44	seven out of eight . So I have seven out
04:46	of eight for this fraction . So which fraction is
04:49	bigger ? Well , if you look at it ,
04:51	this one has way more shading than this one ,
04:54	so this one has to be smaller and the arrow
04:56	goes to the smaller points towards the smaller uh fraction
05:00	. So we say that 46 is less than 7/8
05:05	4 , 6th is less than 7/8 . All right
05:10	, moving right along right here , what do we
05:11	have for the next one down here ? We have
05:15	this fraction as compared to this one , we have
05:17	12345 pieces total , but we actually only have three
05:21	of them . So we actually have a fraction of
05:24	3/5 for this 13 out of five pieces here we
05:28	have 123456 pieces . We only have five out of
05:32	those , so five out of a total of six
05:35	pieces . So we're comparing 3/5 to 56 Which one
05:39	has less ? This one has less . This one
05:41	has more . So this fraction is smaller in the
05:44	arrow always points to the smaller fraction . So we
05:47	say 3/5 is less than 5/6 , 3/5 is less
05:53	than 56 All right , let's take a look at
05:56	the next one . What do we have ? So
05:59	we have this fraction compared to this one ? Well
06:01	, this one is really easy , it's just one
06:02	half . It's one out of two pieces . So
06:04	let's write that down . And this one is 123456789
06:09	10 . It's four out of 10 pieces , So
06:12	four out of 10 pieces , so which one has
06:15	a few ? A less amount ? A smaller amount
06:17	. Is this one right here ? So the arrow
06:19	points towards the 4/10 and we say that 4/10 is
06:24	a smaller fraction or is less than one half 4/10
06:28	of a pizza is definitely going to be less than
06:31	one half of a pizza . All right , here's
06:36	our last one for dispatch . We have this fraction
06:38	compared to this one . What do we have ?
06:40	12 345 ? We have one piece out of five
06:44	. So we have 1/5 for this fraction , we
06:47	have 123456789 10 . We have two pieces out of
06:52	10 . The fraction of 2/10 compared to the fraction
06:57	of 1/5 . So you try to think which one
07:00	is bigger and they start to look like they're the
07:01	same . So you can even get like something to
07:04	measure it if you want to and just look at
07:05	at this and see how much of it is there
07:07	. And then I can put this right over here
07:09	and see that basically it's exactly the same amount .
07:12	So 2/10 which is this amount is exactly the same
07:16	as 1/5 . These guys are actually equal . So
07:19	we say that 1/5 is exactly the same fraction is
07:23	too tense now before we go on it's important to
07:26	kind of see why is that the case if we
07:28	start with one out of five pieces right ? And
07:32	compared to two out of 10 pieces , what happened
07:34	as we move from here to here ? Well I
07:36	double the amount of pieces . I went from five
07:38	pieces total to cutting the thing into 10 pieces ,
07:41	but at the same time I'm not holding one piece
07:44	, I'm holding two pieces . So I double the
07:46	amount of pieces but also double the amount of pieces
07:49	I kept . But I double the total amount of
07:52	slices , double the amount that I actually kept .
07:55	So actually I have exactly the same amount because I
07:57	did two things , I doubled the total amount of
07:59	pieces but I kept double the amount . So these
08:02	pieces just happened to be smaller but they add up
08:04	to be the same thing . So we have three
08:06	more problems gonna take these down and get you more
08:08	practice with writing and comparing fractions . Alright for our
08:13	next problem here's a fraction 12345678 out of 9 ,
08:18	10 pieces . So we say that this is the
08:21	fraction 8/10 8 out of 10 pieces and this is
08:26	12 out of four pieces . So to fourth 2/4
08:31	2 out of four pieces , which one seems to
08:33	be bigger to you ? This is a whole lot
08:35	more material than this one . So this one is
08:37	smaller and the arrow always points to the smaller number
08:41	. So we say 8/10 Is greater than 2/4 ,
08:46	which is exactly what it is . eight out of
08:47	10 pieces of something is way more than two out
08:50	of . Why shouldn't they weigh more ? But it
08:52	is significantly more than two out of four pieces .
08:56	All right . What about the next one ? Here
08:57	we have two fractions . How do we go ahead
08:59	and count the first one ? We have 123456 and
09:04	we have two out of six pieces . So we
09:06	write this is a fraction to sixth like this and
09:10	this is 12 out of three pieces , two out
09:14	of three pieces . Which one's smaller , This one
09:18	smaller than this one . So the arrow is going
09:23	to point towards this one like this because it's a
09:26	smaller number and we say the fraction to six is
09:29	less than the fraction , two thirds to sixth is
09:32	less than two thirds now for our last one it's
09:38	not like a tricky question or anything like that .
09:40	But what fraction do we really have here we have
09:43	123 out of four pieces . So we have three
09:47	out of four pieces total . And here we have
09:50	12 out of 345 So we have two out of
09:54	five pieces total , Which one seems to be the
09:57	smaller amount , this is the smaller amount . So
09:59	the arrow always points to the smaller amount like this
10:02	. And so we say that 3/4 Is greater than
10:07	2/5 , is greater than 2/5 which is exactly the
10:11	case . So in these lessons we've learned not only
10:14	how to compare the fractions , but first we have
10:16	to write the fractions down . That's the difference between
10:19	this lesson and the last lesson . So we're combining
10:21	skills were riding down what the attraction is , then
10:24	we're also comparing them . I cannot tell from looking
10:27	at this which one is bigger , I cannot tell
10:29	from looking at this which which one is bigger at
10:32	this stage of the game . We have to be
10:33	drawing pictures to tell which fraction is bigger . And
10:36	that's what gives a lot of students problems because I
10:38	can't look at two fractions , you just know which
10:40	one is bigger usually , but by drawing pictures we
10:42	can always find out . So solve these yourself .
10:45	I want you to practice and make sure you're getting
10:46	all of these questions correct . And follow me on
10:48	to Part two . We're getting more practice , wrapping
10:51	up the concept of writing and comparing fractions .

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