Thursday, September 29, 2022

# Math Antics – Calculating Percent Change

So with a customer acquisition cost of 35 and a weighted sales pipeline of 1.2 and a monthly recurring revenue of 2.4 million we had net sales go from 4.9 million apr to approximately 5.1 million per capita but what about the percent change ah yes percent change it's always good to know percent change .

Let i'll i'll explain that all to you right now it's oh sorry i'm getting a phone call i got to take this but then i'll explain all that percent change to you hi i'm rob welcome to math antics in this lesson we're going to learn how to .

Calculate percent increase and decrease known collectively as percent change if you're not very familiar with percents i'd highly recommend watching some of our other videos about them before continuing on lots of times when you have a change in value you just say how much something .

Goes up or down in absolute terms like the population of this city increased by a thousand people or the cost of this shirt decreased by 15 but you can also express those sorts of changes in relative terms using percentages unlike an absolute change a percent .

Change always relates the amount of change to the number 100. the term percent literally means per 100 so percent change means per 100 change or the change per 100 so let's start by imagining that you have 100 of something .

Like 100 bucks oh yeah if you start out with 100 but then you get 20 more that would be a 20 increase because the amount went up by 20 per the original 100. likewise if you start out with exactly 100 bucks but then you lose 15 that would be a 15 decrease because it went down by 15 per the original 100 .

So as you can see it's pretty easy to figure out the percent change when the original amount is exactly 100 but you don't have to start with 100 to express change as a percentage almost any original value and any amount of change can be represented as a percent change thanks to equivalent fractions for .

Example instead of one hundred dollars suppose that you start out with seven hundred fifty dollars then imagine that you get one hundred fifty dollars more what percent increase is that to figure that out let's use a simple diagram this blue bar .

Represents the original seven hundred fifty dollars and this green bar represents the one hundred fifty dollar increase now let's use our imagination and ask what if that original amount was only one hundred dollars what would the equivalent change in value be basically we're asking if you had the .

Fraction 150 over 750 what would an equivalent fraction be that has 100 as the bottom number put another way if you have 750 and get 150 more it's equivalent to having 100 and getting x more we're using the letter x to .

Temporarily represent the missing value the top number of the original fraction is the absolute change and the top number of the equivalent fraction which is currently missing is the percent change so let's figure out what the missing value is in two different ways first visually using our diagram and .

Second using simple arithmetic by definition if you divide any amount up into 10 equal parts then each one of those parts will be 10 of the original amount so if you divided the original 750 up into 10 equal amounts each of those amounts would be 75 that means that a 75 dollar increase .

Would be equivalent to a 10 percent increase of course we had an increase of 150 not seventy five a hundred fifty is exactly seventy five plus seventy five so that would be another ten percent of the original amount as you can see from the diagram .

If you start with seven hundred fifty and then you get one hundred fifty more that's equivalent to starting with 100 and getting 20 more in other words it's a 20 increase now let's see how we could get that same answer without using a diagram using a little basic algebra we can .

Solve for the unknown value x all we need to do is multiply both sides of the equation by 100 doing that gives us x all by itself on this side of the equation because the 100 over 100 cancels out and on the other side we have the change in value 150 divided by the original value 750 .

All times 100. using a calculator 150 divided by 750 equals 0.2 and 0.2 times 100 equals 20 or 20 which is the exact same answer we got from our diagram so the formula for calculating percent change is simple all you have to do is take the absolute change or how much the amount has .

Increased or decreased and divide that by the original amount and then multiply the result by a hundred this formula may look even more intuitive to you if we put it back in the equivalent fraction form these are just two different ways of writing the exact same relationship now that we have a formula for .

Calculating percent change let's try using it in a couple quick examples suppose a doggie day care takes care of 25 dogs on friday but on saturday three more dogs join the group what percent increase is that well the original amount of dogs is 25 and the change in dogs is plus three according to our formula .

We just need to divide the change by the original and multiply it by 100 to get the percent change using a calculator we get 3 divided by 25 equals 0.12 and then 0.12 times 100 equals 12. that means the number of dogs at the daycare increased by 12 percent from friday to saturday that was pretty .

Easy but what about this example suppose you want to buy a pair of shoes that cost 65 but you have a discount coupon that will reduce the price by 15 what would the percent decrease in price b if you use your coupon well the original price is 65 and the change in price .

Will be negative 15. it's negative because it's a decrease so let's plug those numbers into our formula that gives us percent change equals negative 15 divided by 65 times 100 again using a calculator negative 15 divided by 65 equals negative .

0.23 rounded off to two decimal places and negative 0.23 times 100 equals negative 23. so the coupon will decrease the price of the shoes by 23 okay so if you're given an original amount and told how much that amount changes it's really easy to calculate the .

Percent change using this simple formula but sometimes math problems don't tell you what the absolute change in a value is instead they just give you an original value and a new value in that case you need to calculate the change yourself here's how you do that suppose you're given a problem that says .

Last year your school had 420 students but this year it has 441 students what's the percent change in student population this problem doesn't directly say what the absolute change in student population was it just tells us what the value was originally and what it is now .

We know that there was a change because of the difference in the numbers and in math what does the word difference make you think of yep subtraction we can figure out the absolute change just by subtracting but order matters and subtraction so should we subtract the original .

Amount from the new amount or the new amount from the original amount well the standard way of doing it is to start with the new amount and subtract the original amount from it if the new amount is bigger than the original the answer you get will be a positive number which means that you have a .

Percent increase but if the new amount is smaller than the original the answer you get will be a negative number which means you have a percent decrease so if we do that we have 441 minus 420 which is positive 21 so we have an increase .

Of 21 students positive 21 divided by the original amount 420 equals positive 0.05 and 0.05 times 100 equals 5. since that's positive we have a 5 increase in students but what if you subtract it in the wrong order and got negative 21 instead if you plug that into the formula for .

Percent change you'll get negative 21 divided by 420 which equals negative 0.05 and then multiplying by 100 gives you negative 5 which suggests a 5 decrease because the sign is negative but since you're paying attention you'll realize that you couldn't possibly have a five percent decrease in students .

Since the number got bigger over time the problem tells us that it was 420 last year and this year it's 441 so you must really have a 5 percent increase the point here is that in math it's always important to use your intuition and ask yourself if an answer makes sense .

Rather than simply trying to memorize a formula without thinking about what it really means and speaking of intuition before we wrap up i want to explore just a few more situations that will hopefully give you a better intuition about percent increase and decrease .

First let's consider the case where you start with one of something and end up with two what would the percent increase be well the original amount is one and the change is also one plugging those numbers into the formula gives one over one .

Times one hundred which simplifies to one hundred so the percent increase is one hundred percent that may seem kind of odd but it makes total sense if you think about it if you have one and then you get one more you're gaining 100 percent of what you started with and .

That's true any time the original amount doubles if you start with two and get two more for a total of four the increase is one hundred percent because two divided by two times one hundred is one hundred and if you start with five and then get five more for a total of ten .

The increase is a hundred percent because 5 divided by 5 times 100 is also 100 so any time the original amount you have doubles it's an increase of 100 percent but what if you start with two and then end up with one considering what we just learned you might be tempted to think that that's a .

Decrease of a hundred percent but if we use our formula we'll see that that's not the case since the original amount is two we put a two on the bottom of the fraction and the change is negative one since we decreased from two to one so a negative one goes up on top now if we simplify we get negative one .

Divided by two which is negative zero point five and negative zero point five times one hundred is negative fifty or a 50 decrease the reason that the percent changes are different in these two cases doubling the amount versus cutting it in half is that the percent change .

Always compares the change to the original amounts which are different in these two cases finally let's determine what the percent increase would be if you start with one and end up with three and conversely what would the percent decrease be if you start with three and end up with one .

In the first case the change is positive 2 and in the second case it's negative 2. let's plug those values into our formula for percent change along with the original values in each case and see what answers we get going from 1 to 3 positive 2 divided by 1 times 100 equals 200 or a 200 percent .

Increase and going from 3 to 1 negative 2 divided by 3 times 100 equals negative 67 rounded to the nearest whole number or a 67 decrease again even though the magnitude of the change was the same the percent changes are different because we started out with different .

Original amounts and this example also shows that you can get a percent change that's greater than a hundred percent all right so now you know what percent change is and how to calculate it the formula for calculating it is pretty simple so you should be able to remember it after you've used it on several .

Problems and that's the key to learning math you can't just watch videos about it you need to actually use it to solve problems so be sure to practice what you've learned in this video as always thanks for watching math antics and i'll see you next time ah yes percent change so percent change .

In this case is negative one thousand percent so i guess you're all fired that's what my calculator says learn more at mathantics.com

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