Proportions - Free Educational videos for Students in K-12

Proportions - By Anywhere Math

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00:0-1	Welcome to nowhere . Math . I'm Jeff , Jacobson
00:01	. And today we're gonna talk all about proportions .
00:04	Let's get started . Mhm . Alright . Before we
00:24	get to our first example , let's talk about what
00:26	exactly a proportion is . So , first a proportion
00:30	is just an equation . Right ? We're gonna have
00:33	an equal sign an equation stating that two ratios Are
00:37	equivalent . Here's an example . Two or three .
00:41	That's a ratio 2-3 . 4/6 . That's another ratio
00:45	4-6 and they are equal to each other there in
00:49	an equation . So , this is an example of
00:53	a proportion . The way you read . This is
00:56	Basically saying that two ratios two is 2 three .
01:01	That's the first ratio as that's where you have the
01:06	equal sign as 4 to 6 . That's how you
01:09	would say that proportion out loud . And this is
01:13	how it would be written . All right , let's
01:14	get to our first example . Alright , example ,
01:16	one tell whether 6/4 and 8 12 form a proportion
01:21	. So we want to see if they are equal
01:23	to each other . If we can make an equation
01:25	with those two ratios , I'm gonna show you three
01:28	different methods on how to tell if they form a
01:32	proportion . So the first method is the simplest form
01:36	. We compare each ratio simplest form and if they
01:39	are the same than they would form a proportion .
01:42	So six force in simplest form Would be three hats
01:48	. Okay , compare that with 8 , 12 would
01:51	be 2/3 . These are not equivalent , They're not
01:56	the same . So this no does not form a
02:01	proportion . Those two fractions do not form a proportion
02:04	. I met the two . I'm just gonna call
02:06	mental math . And the way this works is if
02:09	I'm comparing 6/4 , if I'm trying to see is
02:13	that going to be equal to or equivalent to 8/12
02:18	? Right . I got a question there because I'm
02:20	not sure if they form a proportion . I can
02:23	just use a mental math . Well to get from
02:26	4 to 12 I would multiply by three . Anything
02:30	I do to the denominator should do the to the
02:32	numerator if it was going to be equivalent . So
02:35	if I did six times three , does that give
02:38	me eight ? No , six times 3 is 18
02:42	, not eight . So again that would be no
02:46	They do not form a proportion . Okay , Method
02:49	three . We're gonna call cross products . So again
02:53	, if I write it 6/4 , I'm trying to
02:56	see if they are equal to each other . Cross
02:59	products means you take the numerator and the denominator going
03:04	across and you multiply them together . If they are
03:09	proportional . When you multiply them together , you're gonna
03:12	get the same thing on both sides . So if
03:15	I do four times eight , is that equal to
03:18	six times 12:32 ? Which is not equal to 72
03:24	. So once again no they do not form a
03:28	proportion . They're not proportional . If those were equal
03:31	to each other then yes they would be . Let's
03:33	try another example . Okay example to tell whether X
03:36	and Y are proportional . Just like the previous example
03:39	. I have three methods that I could use to
03:41	decide whether X and Y are proportional . But I
03:44	don't want to do all three for me . I'm
03:46	just gonna do simplest form . I'm gonna compare X
03:50	. And Y . If they're proportional so I need
03:51	ratios . My first one would be one half 2
03:56	3 . And if I want to compare that I
03:58	can compare it with either . I'll just compare it
04:01	with 1-6 . You got to make sure that my
04:05	numerator is here . Those are both representing the excess
04:09	. My denominators are both representing the wise . If
04:13	I had this switch it wouldn't work . Uh So
04:16	you gotta make sure numerator numerator are talking about the
04:19	same thing and same thing with denominators . So let's
04:23	compare in simplest form . The nice thing that's already
04:26	done . That's in simplest form . But here I've
04:29	got a complex fraction . 1/2 divided by three is
04:34	the same thing as one half times one third which
04:37	is 16 And what do you know ? 16 is
04:41	equal to 1/6 . So yes they do form a
04:45	proportion . They are proportional and it wouldn't matter if
04:49	I tried another 1 3/2 divided by nine 3/2 29
04:57	There's my ratio . If I put that in simplest
04:59	form that's the same thing as three halves times 1/9
05:05	. Simplify 13 and I get 16 again . And
05:12	sometimes it is a good idea to check more than
05:14	one ratio , but we got 16 again . So
05:16	yes , they are proportional . Here's some to try
05:19	on your own . All right . Here's the last
05:27	example . You swim your first four laps in 2.4
05:32	minutes , you complete 16 laps in 12 minutes is
05:36	the number of laps proportional to your time . If
05:40	we're going to find if they're proportional , we first
05:42	need our ratios , well , our ratios are gonna
05:46	be time to lapse . So if I look ,
05:49	it took me 2.4 minutes to do four laps .
05:55	If I want to compare that with this , it
05:57	took 12 minutes to do 16 laps . If I
06:02	want to compare them , we've got those three methods
06:06	, I could do simplest form , I could do
06:08	mental math or I could also do that cross products
06:11	right here . Maybe you see that mental math would
06:15	be really , really useful To get from 4 to
06:19	16 . I would just times four Times four .
06:26	Times 4 is gonna be 9.6 , Which does not
06:32	equal 12 . So that would tell us no ,
06:35	they're not proportional . But that's just one method .
06:37	Let's try another one . All right . If we
06:38	want to try another method , we could try simplest
06:40	form . Well , right here , we've got a
06:43	decimal in the fraction . So let's first get rid
06:46	of that . So , we would make this times
06:48	10 times 10 . So that would become 24/40 .
06:52	And then if we simplify our common factor looks like
06:55	eight , Divide by eight , divided by eight .
06:59	And we would get three fists . If we simplify
07:03	this common factor is going to be four , we
07:07	would get 3/4 notice . Again , they don't have
07:11	the simplest form so they are not proportional . If
07:15	we want to try another method , we could also
07:18	compare their unit rates . As long as you've got
07:21	both the denominators the same . Then you just look
07:24	at the numerator . So that would be 2.4 right
07:27	, divide by four , divide by four . So
07:30	that we get one in the denominator . 2.4 divided
07:33	by four would be 0.6 . So that means they're
07:38	going it's taking 0.6 minutes for one lap . There's
07:42	my unit rate . How about here , Divided by
07:46	16 divided by 16 . Well 12 divided by 16
07:53	would be 0.16 and 120 would go seven times .
07:58	That's 42 4 , It's 11 . You get eight
08:03	leftover . Bring down to zero 16 in the 80
08:08	would go five times 0.75 minutes to go one lap
08:16	again , comparing their unit rates . They are not
08:20	the same , which means they are not proportional .
08:23	And if you're wondering why , why is the amount
08:26	of time not proportional to your laps ? You're gonna
08:29	get tired . Here's one more to try on your
08:32	own as always . Thank you so much for watching
08:36	, and if you like this video , please subscribe
00:0-1	.

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