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

The Percent Equation - Free Educational videos for Students in k-12


The Percent Equation - By Anywhere Math



Transcript
00:0-1 Welcome to anywhere , Math . I'm Jeff , Jacobson
00:02 and today we're gonna talk about the percent equation .
00:05 Let's get started . Before we get to the first
00:25 example , let's talk about the percent equation . The
00:27 percent equation is a equals P times W Now a
00:34 represents the part , p represents the percent , but
00:41 we write the percent as either a fraction or a
00:44 decimal . So that's really important . We don't write
00:47 it with the percent symbol , so percent as a
00:52 fraction right or decimal . And then w then is
01:01 the whole , so we have the same pieces that
01:05 we would use when we're solving percent problems with proportions
01:09 . It's just written a different way . Let's get
01:11 to the first example . Alright example one . What
01:15 number is 24% of 50 ? Now before I show
01:19 you how to solve this with the percent equation ,
01:22 I want to show you that is the exact same
01:25 thing as solving with the proportion . Just kind of
01:29 one step uh Ahead if you want to think of
01:32 it that way . So if we were going to
01:34 do this as a proportion like we did in the
01:36 last video , well 24% would be 24 out of
01:40 100 equals what number is ? That's the part .
01:45 So that would be X over 50s the whole ,
01:49 so my proportion would look like this X over 50
01:52 equals 20 for over 100 . Now , if you
01:55 were gonna solve this right , we would solve the
01:58 proportion you with cross products or um or simplify and
02:03 then hopefully use some mental math . But you can
02:06 also solve it . Just kind of using some algebra
02:09 . Right ? If you think about it , this
02:10 is an equation . If I want to get X
02:13 alone , solve for X . Well , I would
02:17 multiply both sides by 50 , Right ? So if
02:20 I multiply this side by 50 And this side by
02:23 50 , those cancel out and I'm left with x
02:27 equals 20 for over 100 times 50 . Okay ,
02:34 this is the exact same thing as a percent equation
02:39 . So let's talk about that . Remember the percent
02:41 equation was a Maybe I'll do it and read mm
02:47 percent equation was a equals P . Written as a
02:53 percent right ? The percent written as either a fraction
02:55 or decimal times W . A . Is the part
02:59 W is the whole . If you look at it
03:02 like an equation , like writing an equation . Well
03:05 what number ? Well that's my variable . That's A
03:09 is means equals so that's equals My percent . That's
03:14 the p . So I can either write that as
03:16 a decimal or a or a fraction . Let's write
03:19 it as a fraction . That would be 24 over
03:23 100 of means , multiplication times 50 exactly the same
03:34 . Right as what we got after . We kind
03:36 of did that one step from our proportion , It's
03:40 exactly the same . Right ? So this is just
03:42 a different way to solve the same type of problem
03:45 without using a proportion with using equation . So let's
03:48 finish this , let's solve for that part . Uh
03:51 So here we left it over 100 . We haven't
03:54 simplified because right here is very simple . That becomes
03:58 one that becomes too And 24 divided by two is
04:04 12 . And let's see if that makes sense logically
04:07 . So we're saying 12 is 24% of 50 .
04:11 Well 24% is almost a quarter . Almost exactly 1
04:15 4th 1/4 of 50 . Is that about 12 ?
04:19 And Yeah , it is right . If I multiply
04:21 that by four , that's 48 which is very close
04:23 , so that makes sense . So there is our
04:26 answer . Let's try another example . Okay , example
04:29 to 9.5 is what percent of 25 ? Let's just
04:33 use the percent equation . Not worry about proportions .
04:36 Uh so here we go . 9.5 is means equals
04:41 what percent ? That's what we don't know . That's
04:43 gonna be our variable P . Of means multiplication of
04:48 25 . Okay So 9.5 is the part , 25
04:54 is the whole piece of 1% . And remember that's
04:57 representing percent as a decimal or a fraction ? That's
05:00 really important . Well here we have an equation I'm
05:04 solving for p . So to get P alone ,
05:06 I'm gonna divide both sides by 25 . Mhm .
05:11 Then I get P is equal to 9.5 divided by
05:15 25 . Let's go ahead and do that . 9.5
05:19 divided by 25 . I don't mind that there's a
05:22 decimal there . That's okay . Uh 25 90 times
05:27 By 25 in the 95 would be three at 75
05:32 , 20 At a zero . Bring it down and
05:36 25 into 200 is gonna be eight times . So
05:42 P is 0.38 . We're not quite done . Remember
05:48 ? This is asking what percent ? So 0.38 as
05:54 a percent then is 38% . That's really really important
06:01 . I put a big star next to kind of
06:03 that last step . Remember if you're solving for a
06:07 percent , once you get a decimal or if that's
06:10 a fraction , your last step is then to change
06:12 it back to a percent . Let's try one more
06:15 example . All right , here's our last example .
06:18 39 is 52% of what number ? So here we
06:22 go . Let's start to translate it . Uh 39
06:25 . Mhm . Yeah . Is is equals 52% .
06:29 Were gonna write that as a fraction or decimal in
06:33 this case , I'm gonna write it as a decimal
06:35 0.52 And I'm gonna show you why in a second
06:40 Of what numbers , so that's gonna be our whole
06:44 0.52 w . And the reason hopefully now you can
06:48 see the reason I wrote it as a decimal is
06:52 I'm not multiplying it by any number , it's just
06:55 w uh if I had a number here , maybe
06:58 I read it as a fraction so that I could
07:01 maybe hopefully uh simplify it with that But because I'm
07:05 gonna be solving this by dividing both sides by 0.52
07:09 , it's a little bit easier to work with as
07:11 a decimal . So again yes , we're solving for
07:15 w the whole , so I'm gonna divide both sides
07:18 by 0.52 . Okay , that goes away and I'm
07:25 left with w equals let's do that . 39 ,
07:28 divided by 0.5-39 , divided by 0.52 . Now I
07:37 do mind divided by a decimal . I don't want
07:40 this to be a decimal . So I'm gonna move
07:43 the decimal point twice to the right , Do the
07:46 same thing here . 12 , which makes that 3900
07:52 . There's the decimal point there . So now it's
07:54 52 Uh into 3900 . So 52 and the 39
07:59 , no , 52 in the 390 . That's gonna
08:03 go what ? seven times Seven times at 1435 ,
08:10 Uh Subtract eight at six 26 . Bring down that
08:17 last zero 52 into 260 goes five times exactly .
08:26 Right ? That's 0.1 . 25 . Yeah . So
08:31 finally W is 75 . and remember this is what
08:36 number ? So I don't need to do anything to
08:39 that . That is just 75 . And if we
08:42 want to think , does that make sense ? So
08:45 39 is 52% of 75 . Yeah . 39 is
08:50 about half of 75 and 52% . It's just about
08:56 half , just about 50 good . Here's something to
08:59 try on your own . Thanks so much for watching
09:09 . And if you like this video , please subscribe
00:0-1 .
Summarizer

DESCRIPTION:

OVERVIEW:

The Percent Equation is a free educational video by Anywhere Math.

This page not only allows students and teachers view The Percent Equation videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.


GRADES:


STANDARDS:

Are you the Publisher?

EdSearch WebSearch