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Math Antics - Calculating Percent Change - YouTube
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so with a customer acquisition cost of
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35 and a weighted sales pipeline of 1.2
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and a monthly recurring revenue of 2.4
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million we had net sales go from 4.9
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million apr to approximately 5.1 million
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per capita
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but what about the percent change
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ah yes percent change
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it's always good to know percent change
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let i'll i'll explain that all to you
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right now it's oh sorry i'm getting a
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phone call i got to take this but then
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i'll explain all that percent change to
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you
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[Music]
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hi i'm rob welcome to math antics in
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this lesson we're going to learn how to
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calculate percent increase and decrease
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known collectively as percent change
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if you're not very familiar with
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percents i'd highly recommend watching
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some of our other videos about them
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before continuing on
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lots of times when you have a change in
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value you just say how much something
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goes up or down in absolute terms like
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the population of this city increased by
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a thousand people or the cost of this
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shirt decreased by 15
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but you can also express those sorts of
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changes in relative terms using
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percentages
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unlike an absolute change a percent
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change always relates the amount of
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change to the number 100. the term
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percent literally means per 100 so
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percent change means per 100 change or
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the change per 100
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so let's start by imagining that you
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have 100 of something like 100 bucks oh
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yeah
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if you start out with 100 but then you
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get 20 more that would be a 20 increase
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because the amount went up by 20 per the
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original 100.
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likewise if you start out with exactly
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100 bucks but then you lose 15 that
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would be a 15 decrease because it went
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down by 15 per the original 100
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so as you can see it's pretty easy to
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figure out the percent change when the
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original amount is exactly 100 but you
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don't have to start with 100 to express
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change as a percentage almost any
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original value and any amount of change
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can be represented as a percent change
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thanks to equivalent fractions for
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example instead of one hundred dollars
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suppose that you start out with seven
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hundred fifty dollars
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then imagine that you get one hundred
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fifty dollars more what percent increase
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is that
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to figure that out let's use a simple
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diagram this blue bar represents the
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original seven hundred fifty dollars and
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this green bar represents the one
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hundred fifty dollar increase now let's
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use our imagination and ask what if that
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original amount was only one hundred
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dollars
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what would the equivalent change in
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value be
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basically we're asking if you had the
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fraction 150 over 750 what would an
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equivalent fraction be that has 100 as
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the bottom number
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put another way if you have 750 and get
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150 more it's equivalent to having 100
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and getting x more we're using the
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letter x to temporarily represent the
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missing value
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the top number of the original fraction
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is the absolute change and the top
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number of the equivalent fraction which
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is currently missing is the percent
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change
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so let's figure out what the missing
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value is in two different ways
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first visually using our diagram and
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second using simple arithmetic
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by definition if you divide any amount
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up into 10 equal parts then each one of
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those parts will be 10
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of the original amount
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so if you divided the original 750 up
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into 10 equal amounts each of those
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amounts would be 75
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that means that a 75 dollar increase
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would be equivalent to a 10 percent
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increase
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of course we had an increase of 150 not
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seventy five
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a hundred fifty is exactly seventy five
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plus seventy five so that would be
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another ten percent of the original
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amount
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as you can see from the diagram if you
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start with seven hundred fifty and then
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you get one hundred fifty more that's
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equivalent to starting with 100 and
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getting 20 more in other words it's a 20
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increase
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now let's see how we could get that same
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answer without using a diagram
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using a little basic algebra we can
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solve for the unknown value x
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all we need to do is multiply both sides
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of the equation by 100 doing that gives
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us x all by itself on this side of the
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equation because the 100 over 100
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cancels out
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and on the other side we have the change
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in value 150 divided by the original
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value 750 all times 100.
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using a calculator 150 divided by 750
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equals 0.2
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and 0.2 times 100 equals 20 or 20
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which is the exact same answer we got
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from our diagram
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so the formula for calculating percent
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change is simple all you have to do is
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take the absolute change or how much the
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amount has increased or decreased and
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divide that by the original amount and
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then multiply the result by a hundred
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this formula may look even more
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intuitive to you if we put it back in
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the equivalent fraction form these are
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just two different ways of writing the
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exact same relationship
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now that we have a formula for
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calculating percent change let's try
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using it in a couple quick examples
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suppose a doggie day care takes care of
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25 dogs on friday but on saturday three
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more dogs join the group what percent
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increase is that
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well the original amount of dogs is 25
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and the change in dogs is plus three
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according to our formula we just need to
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divide the change by the original and
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multiply it by 100 to get the percent
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change
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using a calculator we get 3 divided by
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25 equals 0.12 and then 0.12 times 100
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equals 12. that means the number of dogs
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at the daycare increased by 12 percent
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from friday to saturday
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that was pretty easy but what about this
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example suppose you want to buy a pair
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of shoes that cost 65
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but you have a discount coupon that will
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reduce the price by 15
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what would the percent decrease in price
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b if you use your coupon
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well the original price is 65 and the
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change in price will be negative 15.
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it's negative because it's a decrease so
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let's plug those numbers into our
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formula
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that gives us percent change equals
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negative 15 divided by 65 times 100
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again using a calculator negative 15
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divided by 65 equals negative 0.23
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rounded off to two decimal places and
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negative 0.23 times 100 equals negative
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23.
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so the coupon will decrease the price of
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the shoes by 23
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okay so if you're given an original
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amount and told how much that amount
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changes it's really easy to calculate
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the percent change using this simple
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formula
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but sometimes math problems don't tell
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you what the absolute change in a value
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is
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instead they just give you an original
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value and a new value in that case you
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need to calculate the change yourself
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here's how you do that
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suppose you're given a problem that says
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last year your school had 420 students
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but this year it has 441 students what's
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the percent change in student population
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this problem doesn't directly say what
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the absolute change in student
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population was it just tells us what the
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value was originally and what it is now
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we know that there was a change because
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of the difference in the numbers and in
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math what does the word difference make
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you think of yep subtraction
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we can figure out the absolute change
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just by subtracting
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but order matters and subtraction so
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should we subtract the original amount
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from the new amount or the new amount
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from the original amount
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well the standard way of doing it is to
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start with the new amount and subtract
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the original amount from it if the new
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amount is bigger than the original the
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answer you get will be a positive number
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which means that you have a percent
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increase but if the new amount is
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smaller than the original the answer you
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get will be a negative number which
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means you have a percent decrease
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so if we do that we have 441 minus 420
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which is positive 21 so we have an
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increase of 21 students
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positive 21 divided by the original
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amount 420 equals positive 0.05 and 0.05
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times 100 equals 5. since that's
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positive we have a 5 increase in
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students
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but what if you subtract it in the wrong
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order and got negative 21 instead if you
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plug that into the formula for percent
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change you'll get negative 21 divided by
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420 which equals negative 0.05 and then
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multiplying by 100 gives you negative 5
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which suggests a 5 decrease because the
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sign is negative
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but since you're paying attention you'll
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realize that you couldn't possibly have
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a five percent decrease in students
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since the number got bigger over time
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the problem tells us that it was 420
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last year and this year it's 441 so you
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must really have a 5 percent increase
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the point here is that in math it's
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always important to use your intuition
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and ask yourself if an answer makes
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sense
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rather than simply trying to memorize a
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formula without thinking about what it
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really means
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and speaking of intuition before we wrap
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up i want to explore just a few more
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situations that will hopefully give you
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a better intuition about percent
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increase and decrease
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first let's consider the case where you
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start with one of something and end up
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with two
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what would the percent increase be well
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the original amount is one and the
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change is also one
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plugging those numbers into the formula
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gives one over one times one hundred
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which simplifies to one hundred so the
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percent increase is one hundred percent
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that may seem kind of odd but it makes
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total sense if you think about it if you
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have one and then you get one more
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you're gaining 100 percent of what you
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started with and that's true any time
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the original amount doubles
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if you start with two and get two more
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for a total of four the increase is one
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hundred percent because two divided by
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two times one hundred is one hundred
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and if you start with five and then get
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five more for a total of ten the
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increase is a hundred percent because 5
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divided by 5 times 100 is also 100
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so any time the original amount you have
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doubles it's an increase of 100 percent
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but what if you start with two and then
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end up with one
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considering what we just learned you
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might be tempted to think that that's a
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decrease of a hundred percent
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but if we use our formula we'll see that
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that's not the case
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since the original amount is two we put
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a two on the bottom of the fraction and
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the change is negative one since we
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decreased from two to one so a negative
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one goes up on top
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now if we simplify we get negative one
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divided by two which is negative zero
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point five and negative zero point five
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times one hundred is negative fifty or a
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50 decrease
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the reason that the percent changes are
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different in these two cases doubling
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the amount versus cutting it in half is
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that the percent change always compares
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the change to the original amounts which
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are different in these two cases
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finally let's determine what the percent
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increase would be if you start with one
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and end up with three and conversely
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what would the percent decrease be if
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you start with three and end up with one
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in the first case the change is positive
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2 and in the second case it's negative
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2. let's plug those values into our
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formula for percent change along with
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the original values in each case and see
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what answers we get
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going from 1 to 3 positive 2 divided by
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1 times 100 equals 200 or a 200 percent
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increase
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and going from 3 to 1
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negative 2 divided by 3 times 100 equals
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negative 67 rounded to the nearest whole
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number or a 67
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decrease
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again even though the magnitude of the
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change was the same the percent changes
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are different because we started out
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with different original amounts
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and this example also shows that you can
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get a percent change that's greater than
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a hundred percent
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all right so now you know what percent
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change is and how to calculate it the
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formula for calculating it is pretty
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simple so you should be able to remember
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it after you've used it on several
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problems
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and that's the key to learning math you
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can't just watch videos about it you
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need to actually use it to solve
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problems so be sure to practice what
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you've learned in this video as always
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thanks for watching math antics and i'll
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see you next time
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ah yes percent change so percent change
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in this case
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is negative one thousand percent
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so i guess you're all fired
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that's what my calculator says
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learn more at mathantics.com
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