Percent Change
Basics on the topic Percent Change
To calculate how much percent changes, you can use the formula. The percent of change is equal to the change of percent divided by the original value, but sometimes it is hard to figure out what is the original value.
Ask yourself, what percent did the situation start with, and that will be the original value. Sometimes the percent increases and others there is a decrease, but the formula for percent of change remains the same. Why do we study percent of change? Well you know you will be tested on this topic and also, you can use this formula to figure out important things that affect your life.
For example, if the weatherman reports the chance of snow will decrease by 25% in the coming days, you might want use this information to decide if you should wear snow boots or your blue suede shoes. What about to help you decide whether or not to take an umbrella. Well yesterday, there was a 50% chance of rain, but today there is a 75% chance of rain. What is the percent of change? There is a 50% greater chance it will rain today than yesterday – don’t you want to know how to calculate that? Regardless, there is a 100% chance you will enjoy this video!
Analyze proportional relationships and use them to solve realworld and mathematical problems. CCSS.MATH.CONTENT.7.RP.A.1
Transcript Percent Change
Xenia is really into social media. Hoping to increase the number of people following her on VidPicStar, she plans to test out different kinds of content – to learn what people really want to see.
First, she posts a really funny video she took at the zoo. Before the post, she had 240 followers. Her video post is a success! Now she has 312 followers.
The Percentage Change Formula
How successful was her post? Let’s use the percent change formula to calculate the increase in the number of her followers.
I'll write the formula down for you. The percent change is equal to the amount of change divided by the original value.
This will give you a decimal answer, so you will need to multiply the resulting decimal by one hundred to change it to a percent. Use common sense to decide if the percent of change is an increase or decrease.
Percentage Change Example 1
Let's put numbers into the formula. Remember, Xenia started out with 240 followers then increased to 312.
 312 minus 240 divided by 240. The difference is seventytwo.
 Now divide by 240. The answer is threetenths.
 To change to a percent, multiply threetenths by one hundred.
The percent change is a thirty percent increase! Wow! A thirty percent increase is fantastic.
Percentage Change Example 2
Xenia wants even more followers. So she posts a picture of a tasty muffin. Will the muffin picture boost the number of followers? Let's see. Oh no! Quite the contrary. Her followers decreased to 265.
What is the percent change? Let's again write out the calculation using the percent change formula.
 First, find the difference between the two numbers. Three hundred twelve minus 265 then divide by the orginal value of 312. We get fortyseven.
 Now divide this by 312 and we get fifteenhundredths.
 Fifteenhundredths times one hundred is equal to fifteen percent. The number of Xenia's followers decreased by 15%.
Her followers really did not like that last posting, but then again, food pics are so passé. Xenia tries again. This time she posts a selfie. Maybe this glamorous pose will give her the boost she wants.
Percent Change exercise

Explain the difference between increase and decrease.
HintsIf the number of followers changes from a bigger to a smaller number, the percent of change is a decrease.
The percent change depends on the original value.
Percent means 'over $100$'.
The decimal number $0.35$ corresponds with the percentage $35~\%$.
SolutionXenia likes posting videos and pics on social media. She loves to see the number of her followers increase.
First she posts a video. The number of followers increases from $240$ to $312$.
 To calculate the percent change, we calculate the amount of change: $312240=72$.
 We divide the result by the original value, $240$.
 This gives us $\frac{72}{240}=0.3$.
 By multiplying by $100$, and then adding the percent sign, we get the percent change: $30~\%$.
 We calculate the amount of change: $312265=47$.
 Then we divide the result by the original value, $312$.
 This gives us $\frac{47}{312}=0.15$.
 By multiplying by $100$ and adding the percent sign, we get the percent of decrease: $15~\%$.
$\text{percent change}=\frac{\text{amount of change}}{\text{original value}}$
To get the percentage, we multiply the resulting decimal by $100$ then add a percent sign.

Calculate the percent change.
HintsThe percent of change can be calculated by
$\large \frac{\text{amount of change}}{\text{original value}}$
In order to change a decimal to a percent, we have to multiply the decimal by $100$ the add a percent sign.
Remeber to divide by the original value. This is the value we start with.
SolutionLet's have a look at the formula for percent of change:
$\text{percent change}=\frac{\text{amount of change}}{\text{original value}}$
What's the amount of change? It's the difference between the new and the original value: $312240=72$. This amount is divided by the original value. The number of followers before Xenia posted the video: $240$.
This gives us the decimal $\frac{72}{240}=0.3$.
Now we multiply this decimal by $100$, add a percent sign. The posting resulted in an increase of $30~\%$ in the number of her followers.

Identify the most successful posts.
HintsUse the following formula:
$\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$
 Add the result to $260$ in case of an increase.
 Subtract it from $260$ in case of a decrease.
You can also compare the percentages:
 In case of an increase: the higher the percentage, the higher the new value
 In case of a decrease: the higher the percentage, the lower the new value
Solution$260$ is the original value.
The picture of Archimedes in the tub and the picture of Dr.Evil show a decreasing number of followers. How much do the number of followers decrease?
 Posting the picture of Archimedes leads to a decrease of $20~\%$ because there are $52$ fewer followers. The number of followers decreases to $208$.
 The picture of Dr.Evil leads to a decrease of $15~\%$ because there are 39 fewer followers. The number of followers decreases to $221$.
 The boy sitting on a park bench has $15~\%$ increase, meaning there are $39$ more followers. The new number of followers is $299$.
 The picture of lion babies on a scale has a $20~\%$ increase, and there are an additional $52$ followers. The new number of followers is $312$.
 The picture of the beagle has a $40~\%$ change which is an increase of $104$ followers. The new number of followers is $364$.

Estimate the percent of change left in each set of blocks.
HintsSince there are fewer blocks, the percentage will be less than $100$%.
SolutionPercent change is the the amount of change divided by the original amount. If the new number of toy blocks is less than the original number, the percent change is a decrease.
$ p = \frac{\text{amount of decrease}}{\text{original amount}}$
Example (the red set):
First the teacher calculates the change (original amount $$ new amount):
$2724 = 3$.
Then she divides that change by the old amount:
$ p = \frac{3}{27} = \frac19=0, \overline1 \approx 0,11$
In the third step, she converts the decimal to a percentage by multiplying by $100$ then add a percent sign:
$ (p \cdot 100)~ \%= (0,11 \cdot 100) ~ \%= 11~ \%$.
Because we are evaluating for the percentage of blocks that are left and not for the percentage of blocks that have been taken away, we subtract the percent change from $100%$:
$100 ~\%  11 ~\% = 89 ~\%$

Decide which formula you need in order to calculate the percent change.
HintsJust look at the following example:
 Your favorite jeans cost $100~\$$.
 They are now on sale for a reduced price of $80~\$$.
The price decreased by $20~\%$.
$100~\$$ is the original value (original price).
SolutionPercent change is the amount of change divided by the original value:
$\text{percent change}=\frac{\text{amount of change}}{\text{original value}}$
Now we have to multiply the resulting decimal by $100$ then add a percent sign.
 The amount of change is positive, even if a value decreases. We always subtract the smaller from the bigger value.
 This amount will be divided by the original value.
 It won't be divided by the new value.

Determine the percent change for each situation.
HintsPercent change is always a percentage. Therefore, after solving for a decimal answer, multiply the decimal by $100$ then add a percent sign.
Divide the amount of change by the original value then multiply the decimal by $100$.
An example: the ticket price for four tickets is reduced from $\$120$ to $\$100$.
This leads to: $\frac{120100}{120}=0.1\bar 6\approx 0.17$.
By multiplying with $100$, we get a percent change of $17~\%$.
SolutionFor each example we will use the following formula:
$\text{percent change}=\frac{\text{amount of change}}{\text{original value}}$
To determine the percent change we have to multiply by $100$ then add a percent sign.
Skis
$\frac{200175}{200}=0.125=12.5~\%$.
Birthday party
$\frac{12090}{120}=0.25=25~\%$.
Sister
$\frac{300250}{250}=0.20=20~\%$.
Rugby club
$\frac{4640}{40}=0.15=15~\%$.