Ratios and Ratio Tables - Free Educational videos for Students in K-12

Ratios and Ratio Tables - By Anywhere Math

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00:0-1	Welcome to anywhere , Math . I'm Jeff , Jacobson
00:02	. And today we're gonna talk about ratios before we
00:24	get into an example , let's talk about what a
00:26	ratio is . A ratio is pretty simple . It's
00:28	just a comparison of two quantities . Uh And the
00:32	thing is we can write ratios three different ways .
00:35	So for example , if we're comparing A to B
00:39	, I can write the ratio as A to B
00:45	, right . I can spell out the word to
00:47	A to B . I could also write it as
00:49	a with a colon and I would read it as
00:54	a to be as well , but I would use
00:56	this colon to compare the two . Uh And then
00:59	the third way I could write it as a fraction
01:01	uh A to B would be a over B .
01:06	Like that . So those are the three ways that
01:08	we can write ratios . They would all be equivalent
01:11	to each other . It doesn't matter which one you
01:13	use . Um When we start getting into equivalent ratios
01:17	and things like that . Oftentimes you'll write it as
01:20	a fraction just because it makes it a little bit
01:23	easier , but you've got three ways to do it
01:25	now . Let's look at an example . All right
01:27	, here's example one , right ? The following ratio
01:30	. So for part a you're finding the ratio of
01:32	the pennies to quarters . Uh Here's my coins over
01:36	here , so all we need to do is find
01:38	, well first , how many pennies are there ?
01:40	Uh 12345 66 pennies . Then how many quarters we'll
01:51	cue for quarters . So 123 4567 Looks like seven
01:59	quarters . So I can write my ratio as six
02:03	2 7 . Or I could do six 27 like
02:07	that . Or 6/7 . Any one of those three
02:11	would work if you want to try the other three
02:14	on your own . Go ahead , positive video and
02:16	give them a try . But let's let's move on
02:19	quarters . Two dimes . Same thing . We already
02:22	know that there's seven quarters because we counted that before
02:25	now . I just need to know how many times
02:27	. Uh So 72 for dimes D . Right here
02:32	. One 23 73 . Okay good . Next one
02:39	dimes to total coins . Where again there were three
02:42	dimes . So I have that now we're comparing to
02:45	total coins . Well there were six pennies plus seven
02:51	quarters so that's 13 plus three dimes gives me 16
02:56	. So Dimes to total coins would be 3 -
03:00	16 . Okay and the last one d pennies to
03:04	total coins . Uh Again I know that there are
03:08	six pennies because we found that earlier . So six
03:12	to Total coins was 16 . Now here we can
03:20	basically with ratios you know you can write it like
03:23	a fraction infractions we can simplify same thing with ratios
03:27	6 - 16 . I could simplify as three 28
03:36	Okay . And these ratios are equivalent . Their equivalent
03:40	ratios so either one of those would work . Here's
03:43	one to try on your own example to use ratio
03:57	tables to organize equivalent ratios . Uh So we're going
04:01	to talk about more with equivalent ratios right here .
04:06	And like we said in the first example it's basically
04:09	like simply simplifying fractions right ? You have equivalent fractions
04:13	. You can also have equivalent ratios . Uh And
04:16	we're gonna use a ratio table like what you see
04:20	here to help us kind of organize those . So
04:23	first with a You can see we're comparing pens ,
04:27	two pencils for everyone . Pen we have three pencils
04:32	. So the ratio of pens and pencils is 123
04:35	. That's uh in simplest form you can think of
04:39	but we can make equivalent ratios by adding on more
04:44	. So if we look to fill in this table
04:48	. Well if what if I have two pens ?
04:51	Well then how many pencils would I have if I'm
04:53	keeping the same ratio ? If I'm doing an equivalent
04:56	ratio Well If I add one here I would have
05:04	to add three here because for every pen I get
05:09	three pencils . So if I add one pen that
05:11	means I add three pencils which would mean it would
05:14	be too 26 uh Same thing here I added three
05:21	more pencils and for every three pencils I add a
05:24	pen So I would add one here and it would
05:28	be three tonight . So 123226329 Those are all equivalent
05:34	ratios . And it it should be familiar if you
05:37	run it like a fraction one third to 63 nights
05:40	. Those are all equivalent fractions . So the same
05:42	kind of thing . So we can find our equivalent
05:45	ratios by adding like we did there but part B
05:50	. There's another way we could do it . We
05:51	can also think using multiplication or division . uh for
05:56	every four dogs there's six cats . So the ratio
05:59	is 4-6 From 6 to 12 . I can use
06:04	multiplication . Well I multiplied by two . So if
06:08	I'm going to use multiplication or division , I do
06:11	the same thing to both . Okay . Just like
06:14	when you're doing uh fractions , anything you do to
06:17	that denominator or numerator , you do the same thing
06:20	. You denominator if it's multiplication or division . So
06:24	for I'm also gonna multiply by two . So that
06:27	would give me eight . 8 to 12 Is equivalent
06:32	to 4 - six . Uh same thing here from
06:35	8 to 24 at times by three . So here
06:39	I'm also times in by three . 12 times three
06:43	is 36 . Okay , those are all equivalent ratios
06:48	4 to 68 to 12 and 24 to 36 .
06:51	Okay . And I could also go the other way
06:53	here . If you notice 4 to 6 We could
06:56	simplify that . We could divide both of them by
06:59	two And I would get 2-3 , which is also
07:02	an equivalent ratio . Here's something to try on your
07:04	own . Here's our last example example three , the
07:18	label on the box of crackers says that there are
07:21	240 mg of sodium . That's just salt for every
07:25	36 crackers . How much sodium do you consume if
07:29	you ate 15 crackers ? Now if you're thinking how
07:34	can I go about solving this ? If you remember
07:35	to the last example , uh we use ratio tables
07:39	. So let's do the same thing here are ratio
07:43	is 240 mg . Uh 2 36 crackers . So
07:47	242 36 . So on top I'll just do the
07:52	sodium which was measured in milligrams compared with crackers .
08:02	Yeah . Okay . And as always if you want
08:06	to try this on your own , go ahead and
08:07	posit . So 240 2 36 . Now I want
08:14	to get to 15 crackers . Okay well yeah I
08:20	can't just divide 36 by something to get to 15
08:24	. I mean I could but it wouldn't be very
08:26	nice . Uh but if I look at this 240
08:29	and 36 I could simplify that . So maybe I'll
08:32	do that first and that might help . Um the
08:35	greatest common denominator , our greatest common factor of 240
08:39	and 36 is 12 . So if I divide that
08:43	by 12 I get three . And if I divide
08:47	240 x 12 I get 20 . Okay , So
08:52	same thing , I still don't have 15 crackers like
08:55	I want . Uh but Three times five is 15
08:59	. So that would be nice if I just times
09:02	that by five I get 15 . So to get
09:05	my equivalent ratio I would do the same thing to
09:08	the 2020 times five would give me Mhm . 100
09:17	. So the question yeah . How much sodium do
09:20	you consume if you ate 15 crackers ? Well ,
09:24	the answer would just be you would or you would
09:27	consume a 100 milligrams of sodium . Ok , here's
09:33	another to try on your own . As always .
09:46	Thanks for watching it . If you like this video
09:48	, please stop scott .

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