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 | . |
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