What are Improper Fractions & Mixed Numbers? Convert Improper Fraction to Mixed Number - [3] - Free Educational videos for Students in K-12

What are Improper Fractions & Mixed Numbers? Convert Improper Fraction to Mixed Number - [3] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called Changing improper fractions to mix numbers . This
00:05	is part one . I'm excited to teach you this
00:08	because you'd be surprised how many people find this concept
00:11	to be really difficult . But I promise you in
00:13	the beginning everything we're going to learn here is very
00:16	, very simple . Once we of course everything seems
00:18	simple once you understand it . But as we get
00:20	to the end of the lesson here you'll understand everything
00:22	And be able to solve the problem . So first
00:25	we have to talk about what is an improper fraction
00:27	anyway . So if we have something called an improper
00:31	fraction , you might also guess we have something called
00:33	a proper fraction . Let me show you what a
00:36	proper fraction is an example of a proper fraction .
00:39	The fraction 1 3rd . This is called a proper
00:45	fraction . Why is it proper ? Because the numerator
00:48	the top number is less than the denominator . So
00:50	any fraction where the top number is smaller is called
00:54	a proper fraction . Right ? That's how most fractions
00:56	are . They describe something less than one . So
00:59	we look at this example , this is the fraction
01:03	one third because you can think of a circle being
01:06	divided into this would be two thirds and this would
01:09	be three thirds . And of course this is one
01:11	circle cut into three pieces . If we only have
01:13	one of those pieces we have one third . So
01:15	this is a proper fraction . All right . What
01:18	would be for instance , another example of a proper
01:21	fraction ? Let's take a look at the fraction two
01:23	thirds . This of course is also proper why ?
01:28	Because the top number is smaller . So any fraction
01:30	where the top number is smaller is a proper fraction
01:33	. This fraction would be represented by this amount of
01:36	pizza or pie or whatever you want to talk about
01:39	. Two pieces . When the circle is cut into
01:41	three pieces , two out of three pieces . That's
01:43	what this means . This is one out of three
01:45	pieces . Now let's take a look at our first
01:47	improper fractions . And the improper fraction we're going to
01:50	use is going to be five thirds . Now notice
01:53	the difference between this and the other one's , the
01:56	top number is actually larger than the bottom . So
01:59	any fraction where you have the top number larger than
02:02	the bottom number , We call it an improper fraction
02:05	. So this one is called improper improper fraction .
02:11	And it turns out that all of these improper fractions
02:14	, we can turn them into mixed numbers , which
02:16	I know we have talked about and learned in the
02:18	past . A mixed number would be like one and
02:21	two thirds three and 3/4 5 and you know 5/7
02:26	something like that as a mixed number . So any
02:29	of those mixed numbers can be turned into improper fractions
02:31	and any of these improper fractions can be turned into
02:34	a mixed number . So what we're going to do
02:35	here is learn how to turn any improper fraction into
02:40	a mixed number . So before we actually calculate the
02:42	answer , I want to show you graphically what it
02:45	means . If this is the fraction one third ,
02:48	that means one piece out of three slices and this
02:51	is two thirds , two pieces out of three slices
02:53	. What is five thirds going to look like ?
02:55	Well we're counting in terms of thirds , so this
02:58	is one third . This is two thirds . Just
03:02	count in terms of thirds . Three thirds notice that
03:06	makes a whole pizza right there , but we still
03:07	have to go higher because three thirds , three out
03:10	of three is just one hole . But now we
03:12	have to keep going up , here's four thirds And
03:16	then finally we would have 5/3 . So look at
03:20	what we have here , we have a visually without
03:23	actually doing any math , we can see that five
03:25	thirds because the top number is bigger , it means
03:27	that we have more than one whole because remember when
03:30	the top and the bottom number are both the same
03:33	. Three out of three is 15 out of five
03:36	is 1 , 10 out of 10 is one .
03:38	So any time the top number is going to be
03:40	bigger , it means you must have more than one
03:42	whole pizza for example , so 12345 slices when they're
03:47	cut into thirds means we have one whole plus what's
03:50	left over ? What do we have here ? This
03:51	is two thirds of another pizza . So without doing
03:54	any actual math , we can see immediately that five
03:58	thirds is exactly equal to the mix number one and
04:01	two thirds . So we can kind of circle this
04:05	and we can say that these two things are exactly
04:08	the same thing . There is no difference , no
04:11	difference at all between saying that you have one and
04:14	two thirds of a pizza or saying that you have
04:17	five thirds of a pizza . They both mean the
04:19	same thing . It's just like saying it's like different
04:22	words of language , you might say something is beautiful
04:25	and you might say something is pretty . Yeah ,
04:27	there's slight differences there . So the analogy is not
04:29	perfect , but you get the idea , we have
04:32	different ways of talking about things and in math we
04:35	have the same thing . We have the uh improper
04:37	fraction way of expressing this much pizza . Five slices
04:41	when they're cut into thirds . And we also have
04:43	the mixed number way one whole pizza plus another 2/3
04:47	of a pizza . Now what we want to do
04:48	next is figure out without using any of these magnets
04:52	, how do we actually get the right answer ?
04:54	How do we calculate this here ? So what we
04:56	have to do is remember we talked in the last
04:58	lesson that fractions are all about divisions . So when
05:01	we have the fraction 5/3 , what we're saying is
05:04	this means five divided by three . Remember from the
05:07	last lesson , every fraction , every fraction can be
05:10	written as division . In this case it's five divided
05:12	by three . Now if you actually take the number
05:14	five and you actually divided by the number three ,
05:17	this is how you would write the division of this
05:19	five divided by 35 divided by three . So let's
05:22	go and do this division . Well three times something
05:26	is five , you can say three times one is
05:28	33 times two is six , that's too big .
05:30	So it has to be three times one is three
05:32	. Then we multiply three times one is three and
05:34	we subtract and we get a remainder of two .
05:37	So what we say is that the answer to this
05:39	problem is when we take five here and we divided
05:43	by three here , the answer we get is it
05:45	goes one whole time . Notice that means we have
05:47	one whole pizza here and what is left over a
05:51	remainder of two . What does it mean to have
05:53	a remainder of two ? We're talking about slices of
05:55	something , we have two slices leftover when they are
05:58	cut into thirds . So it means that when we
06:01	do this division , we have one whole pizza with
06:04	two slices left when the pizzas actually cut into thirds
06:08	, one and two thirds . So the way that
06:11	we convert a improper fraction to a mixed number is
06:15	just to do the division . That's all we have
06:17	to do for every one of them . All you
06:19	have to do is write it down and do the
06:21	division whatever remainder you get , you just stick it
06:23	over what you were dividing by , and then you
06:26	have your whole number of course here and then that
06:28	is the mixed number , because when we do this
06:30	division it goes one whole time and the leftover is
06:33	two slices when they are cut into thirds . So
06:37	for the rest of these problems , we're going to
06:39	do it both ways , we're gonna show graphically ,
06:41	and then we're also going to calculate let's go ahead
06:43	and crank through uh several more problems to get more
06:46	practice . Let's take a look at the mixed number
06:48	, three halves , three halves . Before we do
06:51	anything . Let's see if we can figure it out
06:53	without actually doing any math . We're saying we have
06:56	three slices but all of the slices are actually in
06:59	size is called halves . So for instance , here's
07:02	one half , right ? But we don't have one
07:05	half . We have three have so here's two halves
07:07	. Oops , that makes the whole right there ,
07:09	doesn't it ? And then we have this guy over
07:11	here three halves , one half to half , three
07:14	halves . What does this mean when we look at
07:16	what we have here ? What this means is that
07:18	we can see graphically that three and I'm sorry ,
07:20	three halves is the same thing as one whole ,
07:24	plus another half , 1.5 . And so of course
07:27	this is the answer graphically , but let's figure out
07:30	how to do it without using graphically . When we
07:32	say three halves were saying that this is a division
07:35	problem , three divided by 23 divided by two .
07:40	We just have to do the division . Now divide
07:43	two times one is 22 times two is four ,
07:45	that's too much . two times 1 is to multiply
07:48	subtract and we get a one , that's the remainder
07:51	. So what does this mean ? It means when
07:53	we take three and we divided by two , what
07:55	happens ? It goes one whole time one whole time
07:58	, that's why we got this and the remainder was
08:01	a one and we put it over what we were
08:03	dividing by over the same denominator of the original fraction
08:06	. In other words one and one half . So
08:09	essentially all you do is you divide you get a
08:11	whole number whatever the remainder is , you stick it
08:14	over the denominator of the original fraction because it's one
08:17	slice left over as a remainder when the slices are
08:20	called halves , so you get one and one half
08:23	. All right . Now for the next problem ,
08:25	we're going to do it a little backwards . We're
08:28	going to calculate first and then verify with our pictures
08:33	that everything is right . Let's take a look at
08:35	the improper fraction . 8/4 . Top number is bigger
08:38	, so that's an improper fraction . What does this
08:40	actually mean ? This means that I have eight and
08:44	I divide it by four because fractions are always division
08:47	eight divided by four . So let's see what happens
08:51	. Four times one is 44 times two is eight
08:54	, exactly four times two is eight . Subtract ,
08:57	get a zero , the remainder is zero , so
09:00	there is no remainder . We don't have any fractional
09:02	leftovers at all . The answer is just too .
09:05	And so we think that the improper fraction 8/4 is
09:10	exactly the same as two holes . But that seems
09:12	weird . How can these things be equal ? Let's
09:15	see . We're saying in our original problem , we
09:17	have eight slices in terms of force or 8/4 .
09:20	That's what we have here is 1/4/2/4 . There's 3/4
09:26	. There is 4/4 but we don't have 4/4 .
09:29	4 . Force would be one hole . We have
09:31	8/4 5/4 there's 6/4 . There is 7/4 and there
09:38	is 8/4 . Notice we have two whole pizzas and
09:41	that's why we got an answer of two . So
09:44	we can see from the magnets that 1234567 8/4 is
09:49	exactly equal to two holes . So when you convert
09:53	these um improper fractions , sometimes you get a whole
09:57	number and you won't even have a fractional piece to
10:00	it . All right , let's take a look at
10:02	the problem . Improper fraction 7 6th 76 Let's go
10:07	and calculate that . What does this actually mean ?
10:09	This means division . It means seven divided by six
10:12	. So this means that I take the number seven
10:15	and I divided by the number six . Let's crank
10:18	through this six times one is 66 times two is
10:21	12 . That's too big . So it has to
10:23	be six times one is six multiply and subtract seven
10:27	minus six is one and this is the remainder one
10:30	slice left over . So what it means is that
10:32	when I do this division here , seven divided by
10:34	six . The answer I get is it only goes
10:36	one whole time , but I have a remainder of
10:39	one . And I put it over When I what
10:42	my original denominator was when I'm dividing by 16 The
10:45	one piece out of six left over . The answer
10:47	is one in 16 Whatever remainder you get . You
10:50	just put it over the same denominator over there .
10:53	Now let's see if we can convince ourselves that this
10:56	is actually correct . How many six do we actually
10:58	have ? We have 76 Now think about it for
11:02	a minute . 66 or six out of six would
11:05	just be one hole . We have a little more
11:07	than that . So we expect it to be a
11:08	little bit more than one . Let's take a look
11:11	. We have Here is 1/6 here's to sixth ,
11:14	here's 36 here's 4/6 here's 56 and here is six
11:21	. Sixth . Of course we have more than that
11:23	. We have 76 Which means we have this leftover
11:26	. So altogether it means we have one whole pizza
11:29	plus 1/6 of another pizza one and +16 And that's
11:33	why that works out . So I kind of just
11:35	move this over here and stick it over there and
11:37	we just keep it there . All right . So
11:39	once you get the hang of this , it's actually
11:41	not very hard . So let's crank through more problems
11:44	to make sure we understand . Let's take a look
11:46	at the improper fraction . 9/5 . Top members big
11:49	or so . Of course it's improper . And what
11:51	does this actually mean ? Well , in terms of
11:54	division , we take the number nine divided by five
11:57	, nine divided by five . All right . So
12:01	what do we have ? Five times one is 55
12:04	times two is 10 . So it can't be too
12:06	It has to be 15 times one is five .
12:09	And then subtract nine minus five is four . So
12:12	what we're saying is when we divide this thing ,
12:14	it goes one whole time , one whole time with
12:16	a remainder of four , and we just put it
12:18	over the same denominator 1.4/5 . So this improper fraction
12:24	of 9/5 is exactly the same thing as one and
12:27	4/5 . Let's make sure and see if we agree
12:30	that this is the case . We said we had
12:32	9/5 so we're gonna count by 50 . Here's 1/5
12:36	here's to fifth , here's 3/5 here's 4/5 here's 5/5
12:41	. That makes a hole right there but we have
12:43	9/5 . We have to keep going . 6 57
12:47	58 5th in here is 9/5 . So that's what
12:52	we have 12345678 9/5 . We have one whole pizza
12:57	+123 4/5 of another pizza . And that's why the
13:02	answer that we got there makes sense . Yeah .
13:06	Alright , cranking right along . Let's get a little
13:09	more practice . Let's take a look at the improper
13:11	fraction 86 . We treat it as a division problem
13:16	. Eight divided by 68 divided by 66 times one
13:20	is 66 times two is 12 . That's too big
13:23	. Has to be six times one is six .
13:25	Subtract 8 -6 is to the remainder is too .
13:29	So what we figured out is that when we do
13:31	this it goes one whole time with a remainder of
13:33	two left over and we put it over the same
13:35	denominator 2 6 . Now we have to think a
13:39	little bit here because this is the right answer .
13:42	However , We can look at this to 6th .
13:45	It is correct but to six can be simplified further
13:48	because they're both even numbers . See we didn't have
13:51	to simplify this . This was already simplest . This
13:53	was already simple . We couldn't divide top and bottom
13:57	of any of these other fractions . Buy anything to
13:59	make them simpler , but we know that we can
14:01	simplify fractions by dividing the top and the bottom by
14:05	any number . We want to make it simpler ,
14:06	we can divide these by two so we can say
14:09	one and 2/6 . What I'll do is I'll say
14:14	well I'll just divide the top by two and I'll
14:16	divide the bottom by two and that gives us an
14:18	answer of one and two divided by two is one
14:21	and six divided by two is three . And so
14:23	the answer we get is one third . Now let's
14:26	really take our time making sure that we understand this
14:28	. We had 8/6 here We had 86 so let's
14:33	go and do it over here . Here's 1 6th
14:35	263646 . If I can get my magnets right here's
14:42	5/6 and here is 66 like the 66 but we
14:47	don't have 66 we have 86 So here is after
14:51	66 years . 76 here is 8/6 . So notice
14:55	what we got . We got an answer of one
14:57	whole plus 2 +62 out of six pieces . That's
15:01	exactly what we initially calculated . One in +26 is
15:05	the correct amount of pizza . But we can simplify
15:07	this because we can say this is a whole and
15:10	then we can also say well wait a minute .
15:12	126 . Like this is exactly the same amount of
15:16	Pizza as 1/3 . Notice how they line up exactly
15:19	. So one whole and to six which is this
15:23	fraction is the same as one whole and one third
15:27	. They're just different ways of writing the same amount
15:29	of pizza . So that's why we say this is
15:31	the simplest one and that's the one we're going to
15:33	like the best . Yeah . All right we just
15:36	have a few more problems and then we will be
15:38	done . We'll crank up to probably the speed just
15:41	a little bit . What about 23/10 ? Well ,
15:48	we can treat it as a division problem . Just
15:49	like all of these guys . We can say 23
15:53	divided by 10 . All right . Well , 10
15:57	times one is 10 . 10 times two is 20
16:00	. That's as close as I can go . So
16:01	I can put it to hear . Multiply get a
16:03	20 subtract , get a three and the remainder is
16:07	three . So what does this mean ? It means
16:08	that when I divide this I get a whole number
16:10	of two with a remainder of three and I put
16:14	it over the same denominator over 10 . So it's
16:17	three slices leftover when they're cut into tents . So
16:20	the answer is two and 3/10 . I cannot simplify
16:23	3/10 anymore because I can't divide top and bottom by
16:26	the same number and make it any simpler . So
16:28	let's see if this actually makes any sense . So
16:31	, I actually have tents here and I have 23
16:34	of these tents . So let's take a look .
16:35	Here's uh here's 1/10 . There's 2/10 345 6/10 .
16:42	So I'm gonna squish them together . Here , there's
16:44	6/10 right there , and then there's 7/10 8 10th
16:48	, 9/10 . And then here's 20th . I know
16:52	it looks a little ugly , but I'll push them
16:53	together . There's 20th . Well , let's keep going
16:56	because we actually have 23 of these things called 10th
16:58	. There's 11 10th , 12 , 10 , 13
17:01	, 10 , 14 10th . 15 10th . 16
17:04	10th , 17 10th , 18 10th , 19 10th
17:11	. 30th . Okay . 20 tents , but I'm
17:13	still not done at 23 . So there's 30th ,
17:16	here's 21 Here's 22 . Here's 23 10 , 23
17:22	10th . What do I get as an answer ?
17:23	One whole pizza , two whole pizzas , 3/10 1
17:28	, 10 to 10 , 3 tensors , two holes
17:30	, plus 3/10 . And that's why this is exactly
17:34	the same amount of pizza is what's represented there ,
17:37	two and 3/10 , and we can circle that to
17:41	be our final answer . Yeah . All right ,
17:43	well , we have a couple more and then we
17:45	are done . Let's take a look at 26/5 .
17:48	I think at this point we can probably stop using
17:51	the magnets . We understand the concept here . And
17:53	now we can just crank through the division and get
17:55	the answers . We take 26 and we just divide
17:57	it by five , divided by five . And then
18:00	, what do we say ? Well five times four
18:04	is 25 times five is 25 . Uh , and
18:08	then five times six is 30 But that's too big
18:11	. So it has to be five times five .
18:12	That's gonna multiply give me 25 subtract and I'll get
18:16	a one left over as the remainder . So what
18:18	this means is that in the end of the day
18:20	when I divide this , I have a whole number
18:23	of five , it goes five whole times and the
18:25	remainder I have left over is just one out of
18:28	five or 1/5 because it's one slice left over .
18:31	But they're cut into fifth . So the answer is
18:33	five and 1/5 . And of course if I had
18:37	You know 5th , a bunch of fifth slices of
18:39	Pizza did 26 of them . I would find out
18:41	that it would make five holes and I would have
18:42	a little bit left over . Alright . Almost done
18:46	. I promised only two more . Mhm . And
18:49	the answer or the question here is is 24/8 .
18:53	Okay . 24/8 . So 24 divided by eight .
18:59	divided by eight . All right . What do we
19:02	do ? Eight times three is exactly 24 . 8
19:06	times 3 . 24 . And then of course the
19:09	remainder is zero . So when I do this division
19:11	, it goes three whole times No remainder at all
19:15	. So , there's nothing , there's no fraction two
19:17	right here because there's no remainder . I've done the
19:18	division , it divides exactly . And so if I
19:21	had a it's like this and put 24 of them
19:23	together , I would find that it would make three
19:25	whole pizzas with nothing left over . And now I
19:30	have our very last problem . Let's take a look
19:33	at 13 fourths And of course , as always ,
19:37	will write this in terms of division , this is
19:39	13 divided by four . Four times three is 12
19:45	. That's as close as I can get when I
19:46	multiply get 12 subtracting it a one . So what
19:50	this means is that when I divide it goes three
19:53	whole times with a remainder of one slice left over
19:56	, but they're cut into fourths . So the answer
19:58	is three and 1/4 and that is the final answer
20:02	. So I really hope that by using the pictures
20:04	, the models that we have along with doing the
20:06	math , you can understand that any improper fraction you
20:09	have must represent something bigger than one . How do
20:13	we know that ? Because any time you have 3/3
20:17	for instance , that's just one hole . 5/5 is
20:20	one whole six out of six is one whole 10
20:23	out of 10 is one whole . So anytime the
20:25	top number is bigger than the bottom number it must
20:27	be larger than one . And so to get the
20:29	answer , we just do the division the remainder that
20:32	we have just gets expressed as a fractional left over
20:35	and then we call it a mixed number , that's
20:37	all it is . So I'd like you to solve
20:38	every one of these problems and then follow me on
20:41	the part two . We'll get a little more practice
20:43	with converting improper fractions to mixed numbers .

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