Rates - Free Educational videos for Students in K-12

Rates - By Anywhere Math

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00:0-1	Welcome to anywhere . Math . I'm Jeff , Jacobson
00:01	. And today we're gonna talk about rates . So
00:23	first of all , what exactly are rates , rates
00:26	are pretty simple . They are a ratio notice right
00:29	off the bat , it's a ratio that's really important
00:32	to know . It's a ratio of two quantities with
00:35	different units . So the main difference between rates and
00:38	ratios is that they have units . If you remember
00:42	from our last video on ratios We would say a
00:46	ratio of 27 23 Okay , notice there are no
00:55	units . There ratios don't have units but rates do
00:59	. So this is a ratio But when I change
01:04	it to $27 . Yeah . For every three pizzas
01:13	. Okay , now this is a rate that's a
01:20	rate . This was just a ratio . Okay ,
01:25	so that's the main difference between rates and ratios rates
01:29	. They've got units . They've got different units here
01:31	. We've got dollars and pizzas . Okay , they
01:34	look the same right where you've got , I can
01:36	write like to I could also use a colon or
01:39	I could put it as $27 Over three Pizzas .
01:44	I could write it like mm fraction . I can
01:47	do the same thing that I can do with ratios
01:49	. But that's the main difference . If I take
01:51	the same rate $27 to 3 pizzas . If you
01:55	notice I can simplify that right ? I could make
01:58	this To buy divide both of these by three .
02:04	and I get one pizza here Is going to be
02:09	equal to $9.9 for one pizza . Now this is
02:14	still a rape . But it has a special name
02:16	. And that is called a unit ray . Sorry
02:21	about that . This is a unit rate . Okay
02:25	. And a unit rate . If you can see
02:28	is where one of the quantities is one . Right
02:32	? Just you can think of it how much for
02:34	just one unit of pizza . Right ? Or uh
02:38	if it's time how fast for one second are or
02:42	how fast for one hour , right ? Where one
02:45	of the quantities is one ? So here's what a
02:48	unit rate is . It just compares a quantity to
02:51	one unit . That's the important thing to one unit
02:54	of another quantity . So again we're comparing quantity here
02:58	$9-1 unit of the other quantity to one pizza .
03:03	So that is the unit rate . Okay let's try
03:06	an example . Okay here's example one We've got an
03:09	asteroid that's coming towards Earth and it's traveling five miles
03:13	Every eight seconds . Okay so every eight seconds it
03:16	goes five miles . My question is well how fast
03:20	is it per second ? How many miles does it
03:23	travel in just one second ? So what I'm gonna
03:27	do here is set up a ratio table . I've
03:29	got miles and seconds . So every five miles it
03:31	goes eight seconds . I want to know how many
03:35	miles does it go in 1/2 . So to do
03:39	that , all I need to do is look from
03:40	here to here , how did I get from 8-1
03:44	? And the answer is I divided by eight .
03:49	Okay , I'm not gonna do uh minus seven .
03:53	That doesn't that doesn't work . We only use adding
03:56	and subtracting if for example if I wanted to go
03:59	. Well how many in uh in 16 seconds ?
04:04	Well then I can think , ok well I add
04:06	it here and then I add five here , that
04:08	would work . But here it doesn't work from 88
04:12	to 1 . Okay ? It has to be multiples
04:15	of of eight in that situation . So here we
04:18	go , divide by eight . Which means I do
04:20	the same thing up here , Divide by eight .
04:23	So 5 divided by eight is just 5.8 . That
04:27	doesn't really going very nicely . But that's okay .
04:29	So the question is uh how many miles will it
04:33	go in one second ? It will go 58 of
04:37	a mile in one second . So that is the
04:42	unit rate right comparing the quantity to one unit of
04:47	another quantity . Okay uh Here's some to try on
04:50	your own example to a chef by £6 of salmon
05:05	for $51 . How much will another £9 costs ?
05:09	So maybe he didn't get enough enough salmon for his
05:13	restaurant and he needs nine more pounds . So he's
05:15	wondering how much is that going to cost ? So
05:18	uh in this situation you might hopefully be thinking what
05:21	we could do it ratio table again . So on
05:23	the top I'm going to have uh dollars . Yeah
05:30	and on the bottom hopefully you know you'll have pounds
05:35	. Okay Well first we know $51 got us uh
05:41	£6. . I want to get to nine lbs .
05:47	Unfortunately , to go from 6-9 is not easy .
05:50	So I'm going to have to do a step in
05:53	between . That's where I'm trying to get . So
05:57	what I can do is first find my unit rate
06:01	. So to do that , I'm going to see
06:02	, well how much does it cost for just £1
06:06	? So if I want to get to one ,
06:09	I'm just going to Divide by six . So here
06:14	I also divide by six . Do the same thing
06:17	. 51 divided by six is $8.5 , Um Yeah
06:26	, so $8.50 for £1 of salmon . Okay ,
06:31	but I don't want £1 . I wanted nine .
06:35	So again from here it's easy from 1 to 9
06:40	. I just multiply by nine So to figure out
06:43	exactly how much that cost the same thing , I'm
06:45	going to multiply by nine . I'm no I'm sorry
06:48	. It's kind of hard to see . Uh So
06:51	8.5 or $8.50 times nine because I'm getting £9 .
06:57	Let's see . That's gonna be 72 plus 4.5 ,
07:02	that it will be 76.5 . So my answer is
07:07	it's going to cost $76 and 50 cents , $76.50
07:15	for £9 of salmon . Let's try another example .
07:19	Example three . This is our last example . Uh
07:22	£2 of halibut cost $16 . What does it cost
07:25	for ? £7 of halibut ? Now this is a
07:28	very similar problem to example two . And we can
07:31	also solve it the same way , but I'm gonna
07:33	give you another method . Uh so my key information
07:37	I got £2 cost $16 . I want to know
07:40	how much for £7. . So instead of uh making
07:45	a ratio table and finding my unit rates I'm going
07:48	to use a double line graph . So here this
07:54	line is gonna be for the pounds . Yeah in
08:00	this line is gonna be for okay uh the cost
08:06	or dollars or I could do either . Uh So
08:09	we're both gonna start at zero . Uh so for
08:14	£2. . Yeah It costs $16 . And simple .
08:19	Right well how about £44 and I can put a
08:23	little dollar sign there ? How much is £4 gonna
08:26	cost ? Well that's easy I'll just add another 16
08:28	so that's $32 . And I can keep going .
08:32	Well in that case £6 Would be $48 . I
08:38	need to get to seven but I can't just go
08:40	okay well seven how much ? So I got to
08:43	go to to to to write every £2 is another
08:46	$16 . So two more pounds Eight would be another
08:50	$16 . So that's going to be $64 . Well
08:56	here I want seven lb 7 is simple . It's
09:01	right halfway between six and eight . Well in that
09:06	case , what's halfway in between 48 and 64 ?
09:10	If you figure that out you will notice that that
09:13	is $56 . Okay ? And that's simple because basically
09:19	I can do well if £2 was $16.1 pound would
09:24	be eight And 48-plus 8 is 56 . So final
09:30	answer . How much does 7lb of healthy cost ?
09:33	It cost 56 dollars . Okay . Here's some more
09:40	to try on your own . Thanks so much for
09:52	watching and if you like this video please subscribe .

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