Percent Proportion - Free Educational videos for Students in K-12

Percent Proportion - 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 solve percent problems using proportions .
00:06	Let's get started . Alright before we get to our
00:25	first example , I want to talk about what this
00:27	lesson is going to be about . Um Here we've
00:31	got a fraction . 1 4th is equal to 25%
00:33	. We know that you should have that memorized um
00:36	The types of problems we're going to deal with now
00:39	is finding different parts of this equation . Now ,
00:43	first we're gonna be using proportions . So the first
00:46	thing , instead of writing it as 25% we're gonna
00:49	write it as a fraction . So that would become
00:52	1/4 equals 25 over 100 right ? This is a
00:58	proportion . Uh These two fractions are equivalent to each
01:03	other right now . Uh we have three types of
01:07	problems . 1st finding the part . So this one
01:12	represents a part , a part of a whole ,
01:18	that four represents the whole . So sometimes in these
01:23	uh percent problems you're gonna be finding the part ,
01:26	Sometimes you're gonna have to be finding the hole and
01:29	sometimes you're gonna be you're gonna have to find the
01:32	percent . So we're gonna do three examples . Each
01:37	one Trying to find a different part of this proportion
01:42	. Okay not the same numbers different numbers but different
01:44	part of the proportion . So let's get started on
01:46	example one Example 1% of What% 15 is 12 . So
01:52	this is a type of problem that you're gonna see
01:54	um first what do they want us to find ?
01:57	Well this is pretty obvious . They are asking what
02:00	percent . So they want us to find the percent
02:03	. So that's easy . That's the thing we don't
02:04	know . So when we're setting up our proportion I'm
02:08	gonna put variable you could put a P . For
02:11	percent if you want . Or just an X .
02:13	Over 100 . You know the percent is always going
02:17	to be over 100 right ? Um So that's what
02:19	we don't know , that's what we're trying to find
02:20	what percent . Now we got to figure out what
02:23	what do we put here ? Um We have a
02:26	part and a whole when you see this of of
02:31	15 that represents the whole . Okay . is is
02:37	the other key word when you see that is is
02:40	12 that represents The part . So on my other
02:46	side of my proportion I'm gonna put 12/15 . So
02:52	this is what I'm trying to solve . I'm trying
02:54	to solve for X . Using proportions now if you
02:58	remember proportions , We have a couple of different ways
03:01	to solve them . one We could use cross products
03:04	and I could do 15 times x equals 12 times
03:08	100 . Um I could also just see if I
03:11	can Kind of use mental math and see well how
03:15	do I get from 15 to 100 and then do
03:18	the same thing here . Um those are kind of
03:20	the two main ways of solving proportions but there's one
03:24	thing to remember that can be really helpful is try
03:29	to simplify any fractions you have before you try to
03:32	solve because that can really help save some time and
03:35	make it a lot easier . So 12/15 I can
03:38	simplify right . Three is a common factor so that
03:41	becomes four and that becomes five . And now mental
03:46	math is really easy . Well five to get to
03:49	100 . I just multiply by 20 so I need
03:54	to do the same to get to figure out what
03:57	X . Is what my missing percent is . I
03:59	just multiply By 20 as well . So four times
04:03	20 is 80 which means what percent ? It's 80
04:10	percent . Okay let's see if that makes sense logically
04:14	. 12 out of 15 is 12 out of 15
04:17	, is that about 8% ? Yeah . Right .
04:19	It's definitely more than half . Uh It's 15 out
04:23	of 15 would be 100% . So it's getting up
04:26	there so yeah , 80% makes sense logically . Let's
04:29	try another example . Okay . example to what number
04:33	is 36% of 50 Now , it's not quite as
04:38	easy as the first one . Well , we know
04:40	we're not fighting the percent . So anytime you have
04:43	a percent , I like to I like to just
04:46	Put that in my proportion just to start with .
04:48	So 36% is going to be 36 over 100 .
04:52	Okay , so now I just need to figure out
04:56	am I trying to find the part or does it
04:59	want me to find the whole right ? Uh The
05:03	key is to look for those keywords is or of
05:06	Well here is what number is remember is represents the
05:10	part . Okay well what number is that's what I
05:13	don't know of 50 that of 50 . Again that
05:18	is the whole . Okay , So 50s the whole
05:23	which means it needs to go in my denominator .
05:26	Alright , sorry , I'll put that as blue .
05:30	That needs to go in my denominator . What number
05:33	is ? That's what I don't know . That's what
05:35	I'm trying to find . So that's gonna be my
05:36	variable . I'll just make it X . Um So
05:39	here's my proportion . Now let's solve again . We
05:43	could do cross products or maybe try to find another
05:46	way and see if we need some mental math because
05:49	really cross products here . 36 times 50 . Mm
05:52	That doesn't look very fun . So let's see if
05:54	we can first simplify uh 36 and 100 . Those
06:00	have common factors , right ? Uh four is a
06:03	common factor of both , Right ? four times 9
06:06	is 36 . four times 25 IS 100 . And
06:13	now look what , look what happened now , it's
06:15	very easy , remember I'm trying to get To the
06:18	variable , so I'm going this direction . Well ,
06:21	25 times two . Well , give me 50 so
06:25	nine times two . Well , Give Me 18 .
06:31	So what number is 36% of 50 18 is 36%
06:36	of 50 . And that makes sense . 25 Is
06:41	50% of 50 . Right ? So 36 is less
06:45	than that . So you would expect that number to
06:47	be less than 25 . So that makes sense .
06:50	Let's try one more example . Here's our last example
06:53	, 150% of what number is 24 . So again
06:58	, I've got a percent , I'm going to start
07:00	with that . 150% , that is 150 over 100
07:06	equals a common mistake . People see 100 and 50
07:09	and they think oh that's greater than 100 so that
07:12	should be in the denominator but don't remember for percent
07:15	your denominator is always 100 right per cent per 100
07:20	. So 150 over 100 . Now I just have
07:23	to figure out what's my part and what's my whole
07:26	and what am I trying to figure out or what
07:29	do they want me to figure out ? So 150%
07:31	of what number is 24 is ? Right , do
07:38	you remember that keyword is telling us that that is
07:41	the part mm Okay uh of what number that is
07:49	the whole okay Which means it's 24 needs to go
07:56	in my numerator and the whole is what we're trying
08:02	to find . That's what I don't know if I'm
08:03	gonna put an X . Okay so here is my
08:07	uh proportion . Now let's solve again . Try to
08:13	simplify before you before you do any solving . So
08:16	first well 150 and 100 , I could easily just
08:21	take off those zeros divide both by 10 . Uh
08:25	15 and 10 five is a common factor . So
08:28	that would become three . That would become too .
08:32	And now again becomes pretty simple to just to use
08:36	mental math . I'm trying to figure out what X
08:39	. Is I'm going this direction So I'm going that
08:42	direction here three Times eight is 24 . So two
08:48	times they will give me uh 16 . Okay now
08:56	you might be thinking well that doesn't seem right because
09:01	16 is less than 24 , right ? Shouldn't the
09:04	denominator be greater ? But if you look we've got
09:08	a percent , that's greater than 100 . So this
09:12	definitely makes sense to have the part greater than the
09:16	whole , Right ? That just 24 out of over
09:19	16 Is greater than one , which is why the
09:23	percent is greater than % 100% . So yes , that
09:27	works . It does make sense . Um , Here's
09:30	something to try on your own . Thank you so
09:39	much for watching . And if you like this video
09:41	, please subscribe .

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