Percent Proportion - Free Educational videos for Students in K-12 | Lumos Learning

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


Percent Proportion - By Anywhere Math



Transcript
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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