Percents of Increase and Decrease - Free Educational videos for Students in K-12

Percents of Increase and Decrease - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff , Jacobson and
00:02	today we're gonna talk about percent of increase and decrease
00:06	. Let's get started . Today's lesson is all about
00:27	percent of change . And basically instead of saying that
00:32	something increased by $100 , the price of something increased
00:35	by $100 or the price of something decreased by $100
00:39	. Instead of saying the amount that it increased or
00:42	decreased as a as a price or something , we're
00:45	changing that into a percent saying something like well the
00:50	price of that new iPhone increased by 20 Or the
00:55	price of that used iPhone decreased by 20% . All
00:59	we're doing is changing it from amount of increases or
01:01	decreases to a percent that it increases or decreases right
01:06	? So sometimes this will be a percent of increased
01:08	if the new amount is more than the original ,
01:12	sometimes it will be a percent of decrease if the
01:15	amount is less than the original . So percent of
01:19	change is pretty simple . All you do is look
01:21	at the amount of change oh divided by the original
01:35	amount . And again just use some logic . If
01:40	the new amount is more then the original amount will
01:44	then you've got an increase of percent increase . If
01:48	the new amount is less than the original amount ,
01:52	well then it decreased , right ? You have a
01:53	percent decrease . Let's try our first example . Here's
01:57	example one . What is your percent of change in
02:00	your time online ? From saturday to sunday ? So
02:04	here's a little table on saturday . We spent two
02:07	hours online surfing the net on sunday 4.5 hours online
02:11	. Okay . So what is that percent of change
02:15	? Well if we remember percentage changes this , the
02:17	amount of change Over original amount and then we're gonna
02:21	make that into a 1% . So what's the amount
02:24	of change ? How much did it change while we
02:26	started ? We're going from saturday to sunday , saturday
02:29	it was two hours , sunday was 4.5 . So
02:32	how much did it change ? Well it increased .
02:35	So we know this is gonna be a percent increase
02:38	and increased by 2.5 hours . So At 2.5 goes
02:44	in my numerator and the denominator . What's my original
02:48	amount ? Well where did I start ? I'm starting
02:50	from Saturday , that's my original . So I'm going
02:53	to .5 over two . Okay um Now this doesn't
02:59	look like a percent right so let's get to a
03:02	percent . So first I'm going to do that division
03:05	, I'm going to do 2.5 divided by two ,
03:08	2.5 divided by two . Well that goes in 10
03:14	Bring down the five . There's my decimal two and
03:17	five is two . That's four . To track I
03:20	get one at a zero . Bring it down to
03:24	into 10 . Is five , so I get 1.25
03:31	. Again that does not look like a% 2% . Hopefully
03:38	you remember ? Well we just move the decimal point
03:40	twice to the right , Which means that becomes 125
03:46	percent . Now I'm not quite done because 125% ,
03:52	that's half of it . I got to remember .
03:54	Is this 125% increase Or 125% decrease in change ?
04:00	Well we remember that from Saturday to Sunday we increased
04:03	so that is 125% increase increase of hours online .
04:11	Okay now you might also be looking at this and
04:14	think well did I have to divide it like that
04:17	? Couldn't I have just maybe made this over 100
04:20	and Yeah , you could if you notice that .
04:22	Great . So remember if we have a fraction ,
04:25	if we can somehow get the denominator to 100 then
04:28	it's really easy to change to a percent . So
04:31	if I multiply the numerator and denominator by 50 ,
04:35	I could also , that becomes 100 , 2.5 times
04:40	50 . Well , two times 50 is 100 half
04:44	0.5 times 50 is 25 . So that's 1 25
04:48	125 over 125 per 100 125% . Here's him to
04:56	try and you're up . Alright , example to what
05:06	was the percent of change in home runs ? From
05:08	2012 to 2013 ? So , let's look at the
05:11	table over here , you can notice uh in 2012
05:14	there were 28 home runs in 2013 , there were
05:17	only 20 so right off the bat , you should
05:20	realize that this is going to be a percent decrease
05:23	. Right , well , how much did it decrease
05:25	by ? What was the amount of change From 28
05:28	home runs to 20 ? Well , that change was
05:31	a it decreased by eight home runs . Uh what
05:35	was the original amount ? Well , we're starting in
05:38	2012 , so in 2012 there were 28 home runs
05:44	, So 8/28 . Now , we just need to
05:46	convert that to a percent . And if you notice
05:49	here says round to the nearest 10th of a percent
05:52	, if in case we get decibels that keep going
05:54	, We can ride to the nearest 10th of a
05:56	percent . Now to make my life a little bit
05:59	easier . I'm gonna simplify this before I start to
06:01	do my long division Four is a common factor of
06:04	eight and 28 , so that would become too ,
06:07	and that becomes seven . So now I got to
06:09	convert to seven into a percent . And to do
06:12	that first step is to change it to a decimal
06:15	. So I'm gonna do some long division , I'm
06:17	gonna get two divided by seven . Well seven to
06:23	to go zero times . So I'm gonna add my
06:26	decimal at a zero 7-20 goes twice . That's 14
06:30	. subtract I get six at a zero seven into
06:35	60 goes eight times . That's 56 . Subtract I
06:39	get four at another zero seven into 45 times .
06:46	That's 35 . Subtract I get five . Now remember
06:50	I can round to the nearest 10th of a percent
06:55	when I change this decimal to a percent , I'm
06:58	moving the decimal point twice to the right so I'm
07:02	not quite far enough because I don't know if this
07:05	five needs to stay a five or round up to
07:08	a six . I need one more , one more
07:11	number here before I'm able to stop . Um So
07:15	add one more zero , bring it down seven into
07:19	57 times . Okay , that's 49 and I can
07:24	stop there because I can round to the nearest 10th
07:26	of a percent . So uh 0.2857 as a percent
07:33	. I'll just rewrite that 0.2857 as a percent .
07:40	All I need to do is move the decimal point
07:42	twice to the right , Which would get excuse me
07:47	give me 28 .57% . But we want to round
07:54	to the nearest 10th of a percent , which is
07:57	right here . So am I rounding up or is
08:00	it stayed out of five ? Well seven is greater
08:03	than five , so that becomes 28.6 and last last
08:12	step , is this a percent increase or decrease ?
08:16	And remember 2012 was 28 home runs , 2013 was
08:21	20 it decreased . So that is my final answer
08:28	. 28.6% decrease in home runs from 2012 to 2013
08:35	. Let's try one more example , Here's our last
08:37	example . You estimate that the length of the classroom
08:41	is 16 ft . The actual length is 21 ft
08:44	. Find the percent air . Well , we haven't
08:47	talked about percent air . So let's first mention what
08:49	that is . Right ? Percent Air . Percent air
08:54	is basically . What kind of what percent are you
08:58	off by on your estimates ? Right ? So percent
09:01	air is just the amount of your air . How
09:06	much are you off by amount of air ? Yeah
09:14	. Over the actual amount . Okay , so the
09:23	amount of the air that's just saying , well ,
09:25	how much is your how much off is your estimate
09:28	? Right ? This is always going to be positive
09:31	, You're never gonna have a negative percent air .
09:33	Sometimes your estimate estimate might be too low , sometimes
09:37	it might be too high , it doesn't matter .
09:39	Um That's always going to be a positive number .
09:42	So amount of the air over the actual amount .
09:45	Um and then we write that as a percent just
09:47	like we do for percent increase or decrease . So
09:50	let's figure this out . Um My estimate Or your
09:55	estimate was 16 ft . The actual Length is 21
10:02	. Well how much was there air ? How how
10:06	much how far off were we ? Well from 16
10:09	to 21 we were five ft off . Right ,
10:11	that was our air . So five is our air
10:15	. The actual amount , the actual length was 21
10:19	. Mhm . So there's our fraction . Now ,
10:22	we just need to convert that into a decimal and
10:25	then 8% from there . So let's do our long
10:28	division . I'll just go ahead and do it over
10:30	here . five Divided by 21 . Well that goes
10:34	zero times to add a zero . My decimal 21
10:38	- 50 goes twice . That's 42 . Subtract out
10:42	yet . eight ah add another zero . Bringing down
10:46	21 into 80 Goes three times 63 . Subtract I
10:53	get 17 again , I'm not done At another 0
10:58	21 into 170 . Let's see that's gonna go 678
11:06	. Not quite yeah eight times . That's 1 68
11:12	. subtract I get to add another zero And I'm
11:16	going to do the same thing here that I did
11:18	on the last example we're going to round to the
11:21	nearest 10th of a percent because we don't need to
11:24	keep going on forever . Um So lastly 21 into
11:30	20 Well that goes zero times And if we look
11:34	at my decimal , is that far enough to be
11:37	able to round to the nearest 10th of a percent
11:40	? Yes , because I'm gonna move it twice to
11:42	the right , There's the 10th place . So I
11:46	already know that I'm not going to have to to
11:48	round that up , that's just going to stay in
11:49	a so final answer . I mean I'm gonna put
11:54	that just because it's approximately because we rounded , I
11:57	should have done that before , but Uh is approximately
12:01	23.8 percent . Okay , we don't need to say
12:07	increase or decrease . That's just the percent air 23.8%
12:11	off for my estimate . Okay , final answer .
12:17	Here's some to try on your own as always ,
12:26	thank you so much for watching and if you like
12:28	this video , please subscribe .

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