Understand & Calculate Equivalent Fractions - [11] - Free Educational videos for Students in K-12

Understand & Calculate Equivalent Fractions - [11] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called finding equivalent fractions . This is part one
00:05	here in this lesson . The main thing I want
00:07	you to remember as we jump in is that we
00:10	can take a fraction and multiply it by anything we
00:13	want . As long as we do it to the
00:14	top and to the bottom of the fraction at the
00:16	same time when we multiply a fraction like that where
00:20	we multiply the numerator and the denominator by the same
00:23	number , then we change what the fraction looks like
00:26	but we don't change the meaning of the fraction .
00:28	What happens when we multiply like that is we we
00:31	find what we call an equivalent fraction . So this
00:34	lesson is all going to be about finding equivalent fractions
00:37	. I think it's a little easier if I just
00:39	give you the first problem and we jump right in
00:41	. Let's take a look at the following thing .
00:43	What if I tell you that the fraction , one
00:44	third is equal to some fraction with the number six
00:48	on the bottom , and your job is to tell
00:51	me what goes up here , you see this is
00:53	an equivalent fraction . Once we get the answer ,
00:55	like , let's say the answer is a nine up
00:57	here , or two up here , or six up
00:59	here , whatever the answer is , once we get
01:01	the answer , what we're saying is that these two
01:03	things are equivalent . That's what an equal sign means
01:05	. So when we say finding equivalent fractions , what
01:08	it means is we're going to have an equal sign
01:10	between two fractions and then we have to provide the
01:13	answer that goes into the missing blank . That makes
01:16	these two fractions equal . Let me say that again
01:19	. We have to figure out what goes in the
01:20	blank that makes them equal . We can't put anything
01:23	there , we have to figure out the right thing
01:25	to put there . Now , before we actually do
01:27	it and and and do it with math , I
01:29	would like to do it graphically . So this fraction
01:33	is called one third , right ? Because if we
01:35	think about a circle and we can cut a circle
01:38	into three equal pieces , that's what the denominator is
01:40	. And if we only have one of those pieces
01:42	, we have one third of a pizza . Now
01:45	, what we're asking ourselves over here is what fraction
01:49	is the same meaning and the same amount of pizza
01:52	as this one , Except has a six on the
01:53	bottom ? Well , if it has a six on
01:56	the bottom , that means the pizza is divided into
01:58	six . Because if you think about this , this
02:01	is a circle divided into six pieces , that's what
02:04	1/6 is , Right , You divide a circle into
02:06	six equal slices 162636465666 So the question is what is
02:14	the correct amount of six ? That is exactly equal
02:17	to this ? Well , if I take one slice
02:19	away , is this equal to this ? Not quite
02:21	. If I take another one away , is this
02:23	equal to this ? Not quite . If I take
02:25	this one away , Is this equal to this ?
02:26	Not quite if I take this one , are these
02:29	two equal ? I think you can agree with me
02:31	that these two are exactly equal . So without doing
02:34	any math , we actually figured out that the answer
02:37	has to be what is the fraction here ? 1/6
02:40	. There's the second slice to sixth , so the
02:43	answer is to six . So what we have figured
02:46	out Graphically is that the fraction 1/3 ? We can
02:51	find an equivalent fraction to that , that has a
02:54	six in the bottom . And this fraction , even
02:56	though it looks different than one third , the numbers
02:58	are all different , but it actually represents the same
03:01	amount of stuff because if I have a pizza sliced
03:04	into six equal slices , but I have two of
03:06	those slices , it's exactly the same amount of food
03:09	. If I have a pizza divided into three pieces
03:11	and I only have one slice . So you need
03:14	to get used to the idea of seeing fractions with
03:16	different numbers . But yet they can mean the same
03:19	thing and none of us , by the way are
03:21	going to be able to look at this and understand
03:23	that they're the same . Like in our mind ,
03:25	not even me , I can't do that . Okay
03:27	. But what we do with the magnets here is
03:29	we prove to ourselves that this is the case .
03:32	And then also here I want to show you how
03:33	to calculate it . So let's say for a second
03:36	that we didn't have this magnet at all . And
03:38	we wanted to calculate the answer . 1 3rd is
03:43	equal to 26 What's not to six ? Let's say
03:46	we don't know . The answer is to six ,
03:47	so we don't know what's on the top Like this
03:49	. We know that there's a six on the bottom
03:52	. So here's how you solve this problem . Remember
03:55	every fraction in this case the one third . You
03:57	can multiply it by any number you want , as
03:59	long as you do it to the top and the
04:01	bottom . But we know that if these are equal
04:03	, how do I make this into a six ?
04:06	I can multiply the top in the bottom of this
04:08	fraction by anything I want . If I multiply by
04:10	two down here two times three is six . But
04:14	if I multiply by two here then I also must
04:16	multiply the top of the fraction by two in order
04:19	to keep the fraction balanced in order to keep it
04:22	balanced . And so that it means the same thing
04:23	. We have to multiply the top and the bottom
04:25	by the same number . So let's say for a
04:28	second we take the one third and we say all
04:30	right , I'm gonna multiply the bottom by two .
04:33	And then because to keep the balance , I have
04:34	to multiply the top by two . Then on the
04:37	top one times two is two and on the bottom
04:40	three times two is six . And so the answer
04:42	to the problem is to six which we already figured
04:44	out just by using magnets . But on a test
04:47	you're not going to have magnets , you're not gonna
04:49	be able to do it like that . So we
04:50	have to use our math . So all you have
04:53	to do is say , well these two things are
04:56	the same . I can multiply this fraction by anything
04:58	I want and I know the bottom number has to
05:00	be a six . So I have to multiply the
05:03	bottom by two because I'm multiplying the bottom by two
05:06	, I must also multiply the top by two .
05:08	In order to keep the fraction uh equivalent to find
05:11	an equivalent fraction . You have to multiply top and
05:14	bottom by the same number . So , when we
05:17	multiply top and bottom by two , this is the
05:19	answer that we get . All right . It's going
05:22	to become I think a lot easier as we jump
05:25	into a bunch more problems we can talk about this
05:26	forever . But ultimately , I think I want to
05:29	do this problem next . All right . So ,
05:33	the next problem is , let's say we have the
05:35	fraction for fifth , and we're going to say that
05:38	we're going to find an equivalent fraction to that that
05:41	has a 10 in the denominator . What do we
05:43	have to figure out ? The answer is to the
05:45	numerator . Now we're going to use the magnets but
05:48	we're going to do it at the end here .
05:49	What I'd like to do is solve the problem and
05:51	then check that the answer is right . So what
05:53	we know is we have this fraction for fits .
05:55	We can multiply that fraction by any number we want
05:58	. As long as we do it to the top
06:00	and the bottom , then we will find a new
06:01	equivalent fraction . That will look different . But it
06:04	will mean the same thing . I can multiply this
06:06	fraction top and bottom by two . If I want
06:08	, I can multiply top and bottom of this fraction
06:10	by six . If I want , I can multiply
06:12	top and bottom of that fraction by 17 if I
06:14	want I can multiply top and bottom of the fraction
06:17	by 1000 if I want you see it doesn't matter
06:19	what I multiply by , I'm free to do what
06:21	I want . But I must multiply top and bottom
06:24	by the same number in order to keep the fraction
06:27	equivalent here . But notice the new denominator is a
06:31	10 . So what I'm really going to do is
06:33	I'm going to take this 4/5 and I know that
06:36	now I need to multiply by two on the top
06:39	and two on the bottom . Why do I know
06:40	that ? Because this denominators 10 ? I'm trying to
06:43	find an equivalent fraction that has a 10 in the
06:45	bottom . So I must multiply this by two to
06:48	get 10 . And then of course I have to
06:49	multiply the top as well . So the bottom is
06:52	five times two is 10 and the top is four
06:54	times two is eight . And so the answer is
06:56	8/10 . Now , I don't know about you ,
06:58	but I cannot look at the fraction 8/10 and know
07:02	that it's the same as for fifth , I just
07:03	don't know that , you know off the top of
07:06	my head , I don't know that , but we
07:08	can show ourselves that it's the case . Let's take
07:11	a look at the fraction . 4/5 here's 1/5 here's
07:15	2/5 here's 3/5 here's 4/5 . Of course if we
07:19	had 5/5 it would be the whole circle , the
07:22	whole entire thing . But here we have actually 4/5
07:24	right here , that's this fraction . And we're saying
07:28	that the equivalent fraction to that is 8/10 . So
07:31	here is a smaller slice , because the pizzas now
07:33	cut into 10 pieces . 1/10 2 10th , 3/10
07:38	4 10th . Uh here's 5/10 . Here's 6/10 .
07:43	Here's 7/10 and here's 8/10 . Now it's kind of
07:49	hard to prove exactly . But I think if you
07:51	squint long enough , you can realize that these are
07:53	exactly the same . Maybe I rotated like this ,
07:55	these are the same as this . If I put
07:56	pick this up and put it over here . This
07:59	covers those . This one covers those to this one
08:03	covers those two , and then this one covers those
08:05	two . So these are exactly the same . Now
08:07	, again , on a test , you're not gonna
08:09	have magnets to do this . So you can't use
08:11	tools to help you , we have to know how
08:13	to do it with math . Multiply the top and
08:15	bottom by two in this example to get us to
08:18	the final answer . All right , let's take a
08:21	look at the next problem . Let's say let's mix
08:23	it up a little bit . Let's say we have
08:25	The number two equals something over three . Now ,
08:29	this one looks completely different actually than uh than before
08:33	, because we have the number two here , and
08:35	two doesn't really look like a fraction . Look at
08:37	the other problems I gave you a fraction is equal
08:40	to something over six . A fraction is equal to
08:43	something over 10 . But here I gave you something
08:46	weird . I gave you two . But if you
08:48	think about and remember what we learned about fractions in
08:51	the very beginning , any whole number fraction , you
08:53	can write it as that number over one . So
08:56	, this too , I'm going to rewrite the problem
08:59	and I'm gonna say that really what it is is
09:01	to over one is equal to something over three .
09:05	How do I know they do that ? Because remember
09:07	fractions are the same as division , right to over
09:11	one is the same as two divided by one .
09:13	And you know that two divided by one is too
09:16	. So any whole number you ever see , you
09:18	can always write it as a fraction over one .
09:20	If I give you the whole number 105 you could
09:24	just write it as 105 over one . If I
09:27	give you 88 as a whole number you could write
09:29	88/1 . If I give you seven as a number
09:32	you could write 7/1 . So here we just take
09:35	this and turn it into a fraction and now we
09:37	see what to do because this is a fraction 2/1
09:43	. And what I need to do is turn it
09:45	into a new fraction with a three on the bottom
09:46	. So what I'm going to have is the fraction
09:49	2/1 . I need to turn that denominator into A
09:53	three . How do I do it by multiplying the
09:55	denominator by three . So if I multiply the denominator
09:59	by three , I must also multiply the top by
10:01	three in order to keep this thing balance because fractions
10:04	are like seesaws , they're like balances . If I
10:07	multiply the top by three , I must multiply the
10:09	bottom by three to keep it balanced . So what
10:12	do I have ? Two times three is six on
10:14	the top and one times three is three on the
10:17	bottom . So what we are saying is that the
10:21	number two Is exactly the same as the fraction 6/3
10:26	. Because what we found over here is that this
10:27	number that goes in here , I'll just kind of
10:29	put it over here , it should be 6/3 .
10:32	Now let's take a minute to see if this actually
10:35	makes sense . So what I'm gonna do is grab
10:37	my thirds , this is one third and we can
10:40	keep counting but notice how many thirds do we have
10:43	? We have six thirds , so there's one third
10:45	, there's two thirds , there's three thirds , three
10:49	thirds is one whole , but here's four thirds ,
10:52	here's five thirds and here is six thirds . Notice
10:56	what happens six thirds , which is what we got
10:58	is our answer is equal to two whole pizzas .
11:00	So it doesn't look like it would work out .
11:02	But remember anytime you have an improper fraction where the
11:05	top number is bigger , you're going to have a
11:08	total number of pizzas or whatever larger than one .
11:11	And so here by having if it were 3/3 it
11:14	would just be one whole pizza . But double the
11:16	number of slices , 6/3 means we have two Whole
11:19	Pizzas . That's why that works out now . Up
11:22	until this point we have done the math but we
11:24	have also used magnets to kind of like make sure
11:29	it's correct . But now we're gonna drop the training
11:31	wheels and solve the rest of the problems without using
11:33	any pictures . And you can just kind of like
11:37	take comfort in knowing that if you were to draw
11:39	these all , you would show yourself graphically that they're
11:42	all correct . Let's take a look at the problem
11:45	. 6 , 7th And find an equivalent fraction that
11:48	has a 14 in the bottom . So what we
11:51	know is we can multiply this fraction 67 by any
11:54	number we want . Um But we want a fraction
11:57	has a 14 in the bottom . That means I
11:59	have to multiply it by a two on the bottom
12:02	. But if I do that also multiply it by
12:04	a two on the top , right ? Because seven
12:07	times two is 14 , Right ? So on the
12:08	bottom , I'm gonna get that 14 that I want
12:11	and on the top six times two is 12 .
12:14	So , what we have figured out is that 67
12:17	is exactly the same thing as 12 14th . And
12:20	if I had magnets in seventh and 14th and put
12:24	it all out there , we would show ourselves that
12:25	that is the case . All right , Let's take
12:29	a look . Let's go off to the next board
12:31	. Let's take a look at the problem 5/8 .
12:36	And we're gonna set that equal to a new fraction
12:38	with 24 on the mall . So , we have
12:41	this fraction we can of course multiplied by anything we
12:43	want . So we rewrite everything and say , what
12:45	do we want to multiply by ? Well , we
12:48	know we want to 24 on the bottom , so
12:50	we have to multiply by three on the bottom .
12:53	And then therefore we must multiply it by three on
12:55	the top to keep it balanced on the bottom .
12:59	Eight times three is 24 on the top , five
13:01	times three is 15 . And so the answer is
13:04	15 24th and that's the final answer . All right
13:10	. Moving right along . Let's take a look at
13:13	the fraction 3/5 And we're gonna set it equal to
13:17	or say that we have an equivalent fraction with 15
13:19	in the denominator . How do we do that ?
13:21	So we take our intact fraction 3/5 and we can
13:25	multiply top and bottom of that fraction by anything we
13:28	want . But we know we need to multiply by
13:30	three . Why ? Because five times three is 15
13:32	, that's what we're trying to get to . So
13:34	three on the top three times three is nine and
13:37	five times three is 15 . So , the answer
13:41	is that 3/5 of a pizza is exactly the amount
13:43	of the same amount of pizza is 9/15 of a
13:46	pizza , Exactly the same thing . All right .
13:49	I think we can squeeze the next problem kind of
13:51	over here . Let's take a look at two nights
13:55	And we have an equivalent fraction of that . That
13:58	has a 27 in the denominator . So what do
14:02	we do ? We can take this fraction two nights
14:05	And we can multiply top and bottom by anything we
14:07	want . But we know we're going to want to
14:09	multiply by three . What are we doing that ?
14:12	Because nine times three is 27 . And so in
14:14	the answer will get our 27 and two times three
14:17	on the top is six . And so we're saying
14:19	that the fraction six , 27th is exactly the same
14:23	as two nights . Yeah . Alright , we're way
14:27	past the halfway mark . Way past the halfway mark
14:32	. Let's go back here and take a look at
14:35	the following . Let's take a look at 56 .
14:38	And we're going to say that the answer is has
14:41	an equivalent fraction of 30 in the denominator . So
14:45	, we have the fraction 56 . We can multiply
14:47	that fraction by anything we want . What are we
14:49	going to choose ? Yeah , well , we want
14:53	30 . So , we're gonna multiply times five here
14:55	because six times five is 30 and to keep everything
14:58	balanced , will multiply by five over there . So
15:00	six times five is 30 and then five times five
15:04	is 25 . So , what we figured out is
15:06	that 25 30 ? It is exactly the same as
15:08	5/6 . All right . What about The fraction 8
15:14	11th . And over here , the new fraction the
15:18	equivalent fraction has a 33 in the denominator . So
15:22	we can take this fraction multiplied by whatever we want
15:25	. 8/11 . What ? We're going to multiply by
15:28	We're trying to get a 33 here . So we
15:30	have to multiply by three because of that . We're
15:33	multiplying also the top by three . So then on
15:36	the top eight times three is 24 on the bottom
15:39	11 times three is 33 . So , what we're
15:42	saying is that the fraction 24 33rd is the same
15:47	as 8/11 here . All right . I think we
15:51	only have one more problem and we're gonna work it
15:53	over here . Let's take a look at this problem
15:56	over here . What about the problem ? Six is
15:59	equal to some fraction with a four on the bottom
16:01	. Again , this looks different . It looks weird
16:03	because there's a whole number here . But remember we
16:05	already said any whole number , you can write it
16:08	as a fraction . The whole number of six will
16:11	be written as a fraction 6/1 because six divided by
16:14	one is six . So these are the same thing
16:17	. And then your new fraction has a denominator of
16:20	four . So we can take this fraction of 6/1
16:24	and we can multiply it by anything we want ,
16:26	but we're going to choose to multiply it by four
16:28	on the bottom . And for in the top .
16:30	Why ? Because one times four is four , That's
16:32	what I'm shooting for . So one times four is
16:35	four and six times four is 24 . And so
16:38	the answer is 24 4th . Now something I want
16:41	to tell you is that we got an answer of
16:43	24 4th . But remember every fraction is the same
16:46	thing , It means the same thing as division .
16:48	Right ? So this 24 force means 24 divided by
16:52	four . In terms of what it means in division
16:55	, what is 24 divided by 4 ? 24 divided
16:57	by four is six . So this is an equivalent
17:00	fraction to this because when I divide it I get
17:02	six , that's why it works as an answer as
17:05	well . Just another way of thinking about it .
17:06	So here we have conquered the idea of equivalent fraction
17:09	. Specifically finding equivalent fractions . You can multiply a
17:13	fraction by any number you want , as long as
17:15	you do it to the top and to the bottom
17:17	when you do it like that where it's balanced on
17:19	the top and the bottom , then the fraction doesn't
17:22	look the same anymore . But it means the same
17:24	thing and that's why these are equivalent . That's why
17:26	these have equal signs in them . Because when I
17:28	put an equal sign between these fractions , it means
17:31	that they that they represent the same amount of pizza
17:34	or pie or whatever it is we're talking about .
17:37	So I'd like you to go back through these ,
17:38	solve them all yourself . Follow me on the part
17:40	two , we'll get a little more practice with equivalent
17:43	fractions .

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