Proportion - how to see if ratios are in proportion - Free Educational videos for Students in K-12

Proportion - how to see if ratios are in proportion - By tecmath

Transcript


00:0-1	Good day . Welcome to take Math Channel . What
00:02	we're going to be having a look at in this
00:03	video Is ratios and proportions . Okay . And pretty
00:07	much how we can see whether or not two sets
00:09	of ratios are in proportion . So what do I
00:13	mean by this ? Well consider we have two ratios
00:17	are say it was the amount of cordial we were
00:20	putting in water and I'll draw the amount of cordial
00:23	in red . We had three parts cordial for every
00:28	seven parts of water . I'll put the water in
00:31	blue there and then I was comparing this to a
00:33	different glass of water where this time we had six
00:37	parts cordial for every 14 parts of water . And
00:43	so say I wanted to see whether or not these
00:46	glasses were the same strength that is they were in
00:49	proportion to one another . These ratios were equivalent .
00:53	Then how could I do this ? There's a couple
00:55	of ways I could do this . Now first off
00:56	this is a fairly simple example . So I'll go
00:59	this this nice simple way doing it . If we
01:01	have a look at the chord your first off ,
01:03	what's happened is we have three parts in this one
01:05	and six parts in this one . So what we
01:08	have is two times as much cordial as we go
01:11	from one glass to the other As we have a
01:13	look at the water . We have seven parts here
01:15	and 14 parts here . So seven To 14 is
01:20	also a doubling . So these ratios are said to
01:24	be in proportion . These glasses of Korea would have
01:27	that same strength . Okay , so you could use
01:29	this whether or not you're looking at pictures or something
01:32	like this . Okay . And so what we're going
01:34	to look at in this video is we're going to
01:35	have a look at how we can simply see where
01:38	there are two sets of ratios are in proportion .
01:41	That is Are they equivalent ? And also how we
01:43	can easily determine how much of each quantity is required
01:46	to keep something equivalent to get two sets of ratios
01:50	equivalent . Okay . How to keep them in proportion
01:53	. So what about I'll show you first off how
01:57	we can do all this very simply . And the
02:00	way we're going to do this is through this method
02:02	method of cross multiplication . So when you're comparing two
02:06	ratios , I'm going to call them A . Is
02:08	to be what we call the second ratio C .
02:11	Is two D . And if we wanted to see
02:14	whether these were in proportion . Well the first thing
02:16	we do is we write these as fractions . So
02:20	I want to write this is A over B .
02:24	And I'm gonna write the second ratio is C over
02:27	day . Yeah . We're gonna pretend are these guys
02:32	equal ? And now what we do is we cross
02:35	multiply . What I mean by this is we're going
02:39	to multiply this number by this number and then I'm
02:42	going to multiply This one by this one . Okay
02:47	. And if they are proportionate what we should end
02:50	up with is the same result . That is to
02:53	say I times t should equal C times B .
02:59	And this idea we're going to use to work out
03:02	a whole bunch of things . Okay , so bear
03:04	with us and I'll show you what I mean by
03:05	this . So Let's consider two ratios here . Okay
03:10	, so we had a look at two ratios and
03:14	these are those we're going to have a look at
03:17	What about four is 2 , 14 And we're going
03:22	to have a look at six is 221 and I
03:25	want to see whether these are in proportion . Okay
03:28	, so I'm going to write them first off as
03:30	fractions For over four days And 60s to 21 is
03:35	going to become six . Over 21 . Pretty much
03:38	what we're seeing is are these two fractions equivalent ?
03:42	So let's have a look . We're going to cross
03:45	multiply like I said , so this one times this
03:47	one . So four times 21 is 84 . Now
03:53	, what we're gonna do is we're gonna multiply this
03:56	one by this 16 times four day There's also 84
04:02	because these guys are equal to one another . These
04:05	guys are said to these two ratios are said to
04:08	be in proportion . What about another example here ?
04:12	So that's how you can test to see whether or
04:14	not to ratios are in proportion if those two results
04:17	of the cross multiplication are equal to one another .
04:20	What about another set sales having a look at 13
04:25	is to 15 . And I was comparing this to
04:28	a second ratio of six is the seven . So
04:34	the first thing we do we write them as fractions
04:37	13/15 . And we're gonna write this one as 6/7
04:44	. Now what we're gonna do is we're going to
04:46	cross multiply again . 13 time seven is 91 .
04:54	Uh 15 Times six is Naughty . Yeah you're gonna
05:00	look they're pretty close but there are they're not the
05:04	same number at all . So these two ratios are
05:07	not in proportion . Okay so that's how you can
05:10	use cross multiplication to work out whether or not to
05:14	ratios are in proportion . Um We can also use
05:19	this to solve some other types of proportion problems such
05:22	as where we want to know how much we need
05:25	to uh say add in the quantity to keep two
05:27	ratios in proportion . Okay so I'll give you an
05:30	example this So we had uh we had a recipe
05:34	and in this recipe , what it said is we
05:36	needed one cup of rice and three cups of water
05:39	. So we have this ratio of rice to water
05:43	of one is 23 Ok . One part one cup
05:47	of rice . Three cups of water . And what
05:49	I wanted to know is say I had five Cups
05:52	of Water . How much rice would I add ?
05:56	How much to keep this in that same ratio ?
05:59	This one here , we do not know . I'm
06:01	going to put it down . I don't know what
06:03	happened there . I'm going to put this one down
06:06	as Okay . X . It's an unknown . All
06:10	right . And this is how we're gonna solve this
06:12	. A bit of a bit of Eldora magic here
06:14	. So what we do is we first set these
06:16	up as fractions What is the 3 ? And this
06:21	one is X . This unknown number over five .
06:26	You can probably see what we're going to do here
06:27	. We're gonna do this cross model application . Right
06:29	? What we're going to do This number times this
06:32	number one times 5 is five . This number is
06:37	this one by this one , three times x is
06:41	three x . And remember we're trying to keep these
06:45	equivalent . Okay , so what we can now do
06:48	is we can just solve X like you are due
06:51	in a bit of a basic algebra , so we
06:53	decide three into both sides . So if we divide
06:56	this side by three , we're going to get rid
06:58	of this and this one is going to be 5/3
07:02	. Okay , equals x . five divided by three
07:06	is one with two reminders . So we get that
07:08	as one and two thirds . So you see how
07:12	that works . So that's how we can use this
07:14	. You just have to set your question up to
07:18	be uh , you know which ratios , but then
07:20	you just for the unknown to put an X .
07:22	Okay . What about another example ? What about to
07:25	go the other rice ? Another rice example here .
07:27	What about we are We had two cups of rice
07:31	And it would serve six people . It's going to
07:33	be a 2-6 ratio . And okay , so we
07:37	invite , this is rice to people and we invite
07:40	11 people to a particular shedding that we're doing and
07:45	we want to know how much rice we need to
07:46	keep to cook . Okay , so this is the
07:49	only one here . We're going to call this X
07:53	. Okay , set them up as fractions . This
07:55	is to over six . This is X over 11
08:01	. Okay , Get to keep these guys equal .
08:04	Let's cross multiply two times 11 is 22 . Okay
08:08	just go on this one times this one And this
08:11	is equal to six times x . six x .
08:15	Once again we're gonna devoid you know we're gonna get
08:18	this X . By itself so we're gonna divide both
08:20	sides by six . This six Extra 5 or six
08:25	. Well it's just x . divided by six .
08:28	So 22 Divided by six is equal to X .
08:33	So this is three cups . The cake is 22
08:37	divided by six is 36 Threes 18 with 4/6 .
08:42	And we could simplify that further into three and two
08:45	thirds . So you see the way that works okay
08:49	. Uh Anyway hopefully that helps you out that's the
08:52	way that we can work out how to keep things
08:54	in proportion and that sort of deal . Um Anyway
08:59	we'll see you next time . Bye .

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