Math Antics - Ratios And Rates - Free Educational videos for Students in K-12

Math Antics - Ratios And Rates - By Mathantics

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00:03	Uh huh . Hi , welcome to Math Antics .
00:08	In this lesson we're going to learn about ratios what
00:11	the world's ratio . Well let's look it up in
00:13	a math book to find out . It says here
00:17	that a ratio is a comparison of two numbers by
00:20	division . Well that's true but it's also a little
00:24	confusing and it's confusing because most of us think of
00:28	comparing numbers is trying to decide if a number is
00:31	greater than less than or equal to another number .
00:34	But with ratios were not trying to compare numbers like
00:37	that . Instead we're really trying to see how to
00:41	numbers relate to each other . And so at Math
00:43	Antics we like to think of ratios as a relationship
00:47	between two numbers by division . Okay , but how
00:50	do you compare or show how to numbers are related
00:53	by division ? Well , to see what the by
00:56	division part really means . Let's look at an example
00:59	of a ratio . Excuse me . That's not a
01:04	ratio . That's a fraction . Oh it's a ratio
01:08	. Alright . Mathematically , ratios and fractions are basically
01:12	the same thing . It's just that when we use
01:14	a fraction in a particular way , we call it
01:17	a ratio . Well , sure everybody knows that .
01:21	Well . Like I was saying , ratios are basically
01:24	just like fractions . The difference is how we use
01:27	them to describe things in the real world to see
01:31	what I mean . Let's look at examples of how
01:33	we could use the fraction 1/2 and the ratio 1/2
01:37	. Mathematically , these are both the same thing .
01:40	They're just the division problem , one divided by two
01:44	. But in the case of the fraction , we
01:45	usually treat it as if it's just a single number
01:48	. For example , at lunchtime you might eat one
01:51	sandwich or if you're really hungry you might eat two
01:54	sandwiches . But if you're not very hungry you might
01:56	just have half a sandwich . We can use the
02:01	fraction one half just like we use one or two
02:04	to show how many sandwiches you eat . It's just
02:06	that in the case of one half , we know
02:08	that it's only part of a sandwich . Just a
02:10	fraction of one . Mhm . Now let's see how
02:13	we can use the ratio 1/2 with the ratio we
02:16	don't treat it as if it's just a single number
02:19	. Instead we pay close attention to the top and
02:22	bottom numbers because we use them to refer to different
02:25	things . For example , let's say we're planning to
02:28	go on a picnic and for every two people that
02:31	are going on the picnic , we're only bringing one
02:34	sandwich . In that case we would say that the
02:36	ratio of sandwiches to people is 1-2 or one sandwich
02:42	for two people . Do you see the difference between
02:45	our fraction and our ratio ? The math part of
02:48	each of them is the same but with a fraction
02:51	, both the top and bottom numbers are referring to
02:54	the same thing the sandwich , however , with the
02:57	ratio the top and bottom numbers are referring to different
03:00	things , sandwiches and people . The fraction shows a
03:05	part of something but the ratio shows a relationship or
03:09	a comparison between two different things . And you can
03:13	see that they're the same thing mathematically because if you
03:16	did have the ratio of one sandwich for every two
03:19	people on a picnic , guess how much of a
03:21	sandwich each person would get , yep , half a
03:25	sandwich . Mhm . All right . So now ,
03:30	you know that fractions and ratios are basically the same
03:33	thing but since they're used differently in math sometimes are
03:37	also showing differently once in awhile . Instead of seeing
03:40	, the standard division form ratio might be represented with
03:44	this symbol . When you see a ratio written this
03:46	way , it just means 1-2 or one per two
03:51	. For example , in this picture , you can
03:54	say that the ratio of dogs two cats is 3-2
03:58	, three dogs , 2 two cats . And you
04:01	can also write it in the standard division form three
04:03	dogs over two cats . They're just different ways to
04:07	write the same ratio ratios are used all the time
04:11	to represent all sorts of things in real world situations
04:15	. So let's see a few more examples to help
04:17	you really understand what ratios are . Have you ever
04:21	wanted to compare apples to oranges ? But someone told
04:24	you you couldn't ? Well you can with a ratio
04:27	. Now let's say a fruit stand sells five apples
04:29	for every three oranges . They sell the ratio of
04:32	apples to oranges would be 5-3 . Or have you
04:36	ever helped someone big cookies ? The recipe might tell
04:39	you that for every two cups of flour you need
04:42	one cup of sugar . That means that the ratio
04:44	of flour to sugar is 2-1 . Or what about
04:49	your T . V . Screen or your computer monitor
04:51	? Have you ever heard someone say that the size
04:54	or aspect ratio is 16-9 . 16 - nine is
04:59	the ratio of the screen's width to its height .
05:02	So if the screen is 16 wide then its height
05:06	would be nine taller . Uh Here's another good ratio
05:10	that you might use in your car . 40 mph
05:13	. Ha ha didn't you say that a ratio was
05:17	a relationship between two numbers ? But 40 MPH is
05:20	just one number . Looks like someone's got some explaining
05:24	to do . Actually there are two numbers . Do
05:28	you remember how any number can be written like a
05:30	fraction just by writing one as the bottom number ?
05:33	Well 40 mph is the ratio 40 miles per one
05:37	hour . Well I guess you have an answer for
05:40	everything , don't you ? 40 mph is a type
05:45	of ratio that we call a rate . A rate
05:47	is just ratio that usually involves a period of time
05:52	. Here are some common examples of rates 10 ,
05:56	m/s $12 per hour , three Meals per day .
06:00	50 games per year notice that the bottom numbers and
06:04	each of these ratios relate to a period of time
06:08	, seconds , hours , days , years . And
06:11	that's why we call them a rate . All right
06:14	. So that's simple enough . But you might be
06:17	wondering Why are the bottom numbers of all these rates
06:20	one Couldn't you ever rate like 90 m per nine
06:24	seconds or $60 per five hours ? We sure could
06:29	. But most of the time when we have rates
06:31	like that , we want to convert them into an
06:33	equivalent rate that has one as the bottom number .
06:37	And that's because whenever the bottom number represents only one
06:40	unit of time , like one hour or one day
06:44	it makes comparing different rates much easier . For example
06:49	, imagine two cars driving at two different rates .
06:52	The first cars rate is 120 mph three hours And
06:57	the second cars rate is 150 miles per five hours
07:01	. Which car is going faster ? Well , it's
07:04	not all that easy to tell when the rates have
07:06	different bottom numbers . Fortunately it's really easy to change
07:11	a rate so that has one as the bottom number
07:14	. All you have to do is divide the top
07:16	number by the bottom number . The answer you get
07:20	is the top number of the new equivalent rate .
07:23	And the bottom number is just one Rates like this
07:27	are called unit rates because unit means one . All
07:32	right , let's convert the rates of speed for our
07:34	two cars into unit rates so that we can compare
07:37	them easily . The first cars rate was 120 mph
07:42	three hours . So if we take 120 and divide
07:46	it by three , we get 40 . That means
07:48	that the unit rate for the first car is 40
07:52	mph . The second cars rate was 150 miles per
07:56	five hours . So if we divide 150 x five
08:01	, we get 30 . So the unit rate for
08:04	the second car is 30 mph . And now you
08:08	can easily tell that the first car is going faster
08:12	and you can tell why unit rates are so helpful
08:15	. Okay , so that's it for this lesson .
08:18	We've learned that a ratio is basically just like a
08:21	fraction , but instead of showing what part of something
08:25	you have , it shows the relationship between two different
08:28	things . We also learned that when one of those
08:32	two things is time we call the ratio or rate
08:35	. And last of all , we learned how to
08:37	convert a rate into a unit rate for easy comparison
08:40	as always . Thanks for watching Math Antics and I'll
08:43	see you next time learn more at Math Antics dot
08:48	com .

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