Math Antics - Calculating Percent Change - Free Educational videos for Students in K-12

Math Antics - Calculating Percent Change - By Mathantics

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00:0-1	So with the customer acquisition cost of 35 and awaited
00:02	sales pipeline of 1.2 and a monthly recurring revenue of
00:06	2.4 million , we had net sales go from 4.9
00:09	million . A pr to approximately 5.1 million per capita
00:14	. But what about the percent change ? Ah yes
00:17	, percent change . It's always good to know percent
00:20	change . I'll explain that all to you right now
00:24	. It's oh sorry , I'm kidding a phone call
00:26	. I got to take this but then I'll explain
00:28	all that percent change to you . Oh , oh
00:36	hi , I'm rob . Welcome to math antics .
00:39	In this lesson . We're going to learn how to
00:41	calculate percent increase and decrease . Known collectively as percent
00:45	change . If you're not very familiar with Percents ,
00:48	I'd highly recommend watching some of our other videos about
00:50	them before continuing on Lots of times when you have
00:54	a change in value , you just say how much
00:56	something goes up or down in absolute terms like the
00:59	population of this city increased by 1000 people , or
01:02	the cost of the shirt decreased by $15 . But
01:06	you can also express those sorts of changes in relative
01:08	terms using percentages . Unlike an absolute change , a
01:12	percent change always relates the amount of change to the
01:16	number 100 . The term literally means per 100 So
01:21	change means per 100 change or the change per 100
01:26	. So let's start by imagining that you have 100
01:28	of something like 100 bucks . Oh yeah If you
01:32	start out with 100 but then you get 20 more
01:35	, that would be a 20 increase because the amount
01:37	went up by 20 per the original 100 . Likewise
01:41	, if you start out with exactly 100 bucks ,
01:43	but then you lose 15 , that would be a
01:45	15 decrease because it went down by 15 per the
01:49	original 100 . So as you can see , it's
01:52	pretty easy to figure out the change when the original
01:54	amount is exactly 100 . But you don't have to
01:57	start with 100 to express change as a percentage .
02:00	Almost any original value and any amount of change can
02:03	be represented as a percent change thanks to equivalent fractions
02:07	. For example , instead of $100 , suppose that
02:10	you start out with $750 , then imagine that you
02:14	get $150 more . What percent increases that ? To
02:18	figure that out ? Let's use a simple diagram .
02:21	This blue bar represents the original $750 And this green
02:25	bar represents the $150 increase . Now let's use our
02:29	imagination and ask what if that original amount was only
02:33	$100 , what would the equivalent change in value B
02:37	. Basically we're asking if you had the fraction 150
02:41	over 750 , what would an equivalent fraction b .
02:45	That has 100 as the bottom number ? Put another
02:48	way if you have 750 and get 150 more it's
02:52	equivalent to having 100 and getting X more . We're
02:57	using the letter X to temporarily represent the missing value
03:00	. The top number of the original fraction is the
03:03	absolute change and the top number of the equivalent fraction
03:06	which is currently missing is the percent change . So
03:10	let's figure out what the missing value is in two
03:12	different ways . First visually using our diagram and second
03:16	using simple arithmetic . By definition , if you divide
03:20	any amount up into 10 equal parts , then each
03:23	one of those parts will be 10 of the original
03:26	amount . So if you divided the original $750 up
03:31	into 10 equal amounts , each of those amounts would
03:33	be $75 . That means that a $75 increase would
03:38	be equivalent to a 10 increase . of course we
03:42	had an increase of $150 not 75 , 150 is
03:47	exactly 75 plus 75 . So that would be another
03:50	10 of the original amount . As you can see
03:53	from the Diagram , if you start with 750 and
03:57	then you get 150 more , that's equivalent to starting
04:00	with 100 and getting 20 more . In other words
04:04	, it's a 20 increase . Now let's see how
04:07	we could get that same answer without using the diagram
04:10	Using a little basic algebra . We can solve for
04:12	the unknown value X . All we need to do
04:15	is multiply both sides of the equation by 100 .
04:18	Doing that gives us X all by itself on this
04:21	side of the equation , because the 100 over 100
04:24	cancels out . And on the other side we have
04:26	the change in value 150 divided by the original value
04:31	750 . All Times 100 . Using a calculator .
04:35	150 , divided by 750 equals 0.2 And 0.2 times
04:41	100 equals 20 or 20% , which is the exact
04:45	same answer we got from our diagram . So the
04:48	formula for calculating percent change is simple . All you
04:51	have to do is take the absolute change or how
04:53	much the amount has increased or decreased and divide that
04:57	by the original amount and then multiply the result by
05:00	100 . This formula may look even more intuitive to
05:03	you . If we put it back in the equivalent
05:05	fraction form these are just two different ways of writing
05:08	the exact same relationship . Now that we have a
05:11	formula for calculating percent change . Let's try using it
05:14	in a couple quick examples . Suppose a doggy daycare
05:18	takes care of 25 dogs on friday , but on
05:20	saturday three more dogs joined the group . What percent
05:23	increases that ? Well , the original amount of dogs
05:27	is 25 and the change in dogs is plus three
05:30	. According to our formula . We just need to
05:32	divide the change by the original and multiply it by
05:35	100 to get the change . Using a calculator ,
05:39	we get three divided by 25 equals 0.12 and then
05:43	0.12 times 100 equals 12 . That means the number
05:47	of dogs at the daycare increased by 12 from Friday
05:51	to Saturday . That was pretty easy . But what
05:54	about this example suppose you want to buy a pair
05:56	of shoes that cost $65 but you have a discount
05:59	coupon that will reduce the price by $15 . What
06:03	would the percent decrease in price be if you use
06:05	your coupon ? Well the original price is 65 and
06:09	the change in price will be negative 15 . It's
06:12	negative because it's a decrease . So let's plug those
06:15	numbers into our formula that gives us percent change equals
06:20	negative 15 divided by 65 times 100 . Again using
06:25	a calculator negative 15 , divided by 65 equals negative
06:29	0.23 rounded off to two decimal places and negative 0.23
06:35	times 100 equals negative 23 . So the coupon will
06:39	decrease the price of the shoes by 23% . Okay
06:44	, so if you're given an original amount and told
06:46	how much that amount changes , it's really easy to
06:49	calculate the percent change using this simple formula . But
06:53	sometimes math problems don't tell you what the absolute change
06:56	in value is . Instead they just give you an
06:59	original value and a new value . In that case
07:02	you need to calculate the change yourself . Here's how
07:04	you do that . Suppose you're given a problem that
07:07	says last year your school had 420 students but this
07:11	year it has 441 students . What's the % change
07:15	in student population ? This problem doesn't directly say what
07:19	the absolute change in student population was . It just
07:22	tells us what the value was originally and what it
07:24	is . Now we know that there was a change
07:27	because of the difference in the numbers and in math
07:30	what does the word difference make you think of ?
07:32	Yep subtraction . We can figure out the absolute change
07:36	just by subtracting but order matters in subtraction . So
07:40	should we subtract the original amount from the new amount
07:43	? Or the new amount from the original amount ?
07:45	Well the standard way of doing it is to start
07:48	with the new amount and subtract the original amount from
07:51	it . If the new amount is bigger than the
07:53	original the answer you get will be a positive number
07:55	which means that you have a percent increase . But
07:58	if the new amount is smaller than the original the
08:01	answer you get will be a negative number which means
08:03	you have a percent decrease . So if we do
08:06	that we have 441 -420 which is positive 21 .
08:11	So we have an increase of 21 students Positive 21
08:16	divided by the original amount 420 equals positive 0.05 and
08:21	0.05 times 100 equals five . Since that's positive ,
08:26	we have a five increase in students . But what
08:30	if you subtracted in the wrong order and got negative
08:32	21 instead ? If you plug that into the formula
08:35	for percent change , you'll get negative 21 divided by
08:38	420 which equals negative 0.5 And then multiplying by 100
08:43	gives you negative five , which suggests a five decrease
08:47	because the sign is negative . But since you're paying
08:51	attention , you'll realize that you couldn't possibly have a
08:53	five decrease in students since the number got bigger over
08:57	time . The problem tells us that it was 420
09:00	last year and this year it's 441 . So you
09:03	must really have a five increase . The point here
09:08	is that in math it's always important to use your
09:11	intuition and ask yourself if an answer makes sense .
09:14	Rather than simply trying to memorize the formula without thinking
09:17	about what it really means . And speaking of intuition
09:20	before we wrap up , I want to explore just
09:23	a few more situations that will hopefully give you a
09:25	better intuition about percent increase and decrease first . Let's
09:30	consider the case where you start with one of something
09:32	and end up with two . What would the percent
09:34	increase be ? Well , the original amount is one
09:37	and the change is also one . Plugging those numbers
09:40	into the formula gives 1/1 times 100 which simplifies to
09:45	100 . So the percent increase is 100% . That
09:49	may seem kind of odd . But it makes total
09:51	sense if you think about it , if you have
09:53	one and then you get one more , you're gaining
09:56	100% of what you started with and that's true .
09:59	Any time the original amount adults If you start with
10:02	two and get two more for a total of four
10:05	that increases 100% . Because two divided by two times
10:09	100 is 100 . And if you start with five
10:12	and then get five more for a total of 10
10:15	that increases 100 because five divided by five times 100
10:19	is also 100 . So any time the original amount
10:22	you have doubles it's an increase of 100% . But
10:27	what if you start with two and then end up
10:28	with one Considering what we just learned . You might
10:32	be tempted to think that that's a decrease of 100%
10:35	. But if we use our formula we'll see that
10:37	. That's not the case . Since the original amount
10:40	is too we put a two on the bottom of
10:42	the fraction and the changes negative one since we decreased
10:45	from 2-1 . So a negative one goes up on
10:48	top . Now if we simplify we get negative one
10:52	divided by two which is negative 0.5 and negative 0.5
10:56	times 100 is negative 50 or a 50 decrease the
11:01	reason that the percent changes are different in these two
11:04	cases doubling the amount versus cutting it in half .
11:07	Is that the percent change always compares the change to
11:10	the original amounts which are different in these two cases
11:13	. Finally , let's determine what the percent increase would
11:17	be if you start with one and end up with
11:19	three and conversely , what would the percent decrease be
11:22	if you start with three and end up with one
11:25	. In the first case the changes positive two and
11:27	in the second case it's negative too . Let's plug
11:30	those values into our Formula four change along with the
11:33	original values in each case and see what answers we
11:36	get going from 1 to 3 positive two divided by
11:40	one times 100 equals 200 or a 200% increase and
11:46	going from 3 to 1 -2 divided by three times
11:50	100 equals negative 67 rounded to the nearest whole number
11:54	or a 67 decrease again , even though the magnitude
11:59	of the change was the same . The percent changes
12:01	are different because we started out with different original amounts
12:05	. And this example also shows that you can get
12:07	a percent change that's greater than 100% . All right
12:12	. So now you know what percent changes and how
12:14	to calculate it . The formula for calculating it is
12:17	pretty simple . So you should be able to remember
12:19	it after you've used it on several problems and that's
12:22	the key to learning math . You can't just watch
12:24	videos about it . You need to actually use it
12:26	to solve problems so be sure to practice what you've
12:29	learned in this video as always . Thanks for watching
12:31	math antics and I'll see you next time . Ah
12:35	Yes , percent change . So percent change in this
12:37	case Is negative 1000% . So I guess you're all
12:42	fired . That's what my calculator says . Learn more
12:47	at Math Antics dot com .

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