Percent Change

Percent Change exercise

• Explain the difference between increase and decrease.

  Hints

  If 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 $35~\%$.

  Solution

  Xenia 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: $312-240=72$.
  • 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: $30~\%$.

  Now, Xenia tries to increase the number of followers even more. She posts a picture of a muffin. But, the number of followers decreases from $312$ to $265$. We can calculate the percent of decrease in a similar manner:

  • We calculate the amount of change: $312-265=47$.
  • 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: $15~\%$.

  The percent change is the amount of change divided by the original value:

  $\text{percent change}=\frac{\text{amount of change}}{\text{original value}}$

  To get the percentage, we multiply the resulting decimal by $100$ then add a percent sign.

• Calculate the percent change.

  Hints

  The 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.

  Solution

  Let'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: $312-240=72$. 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.

  Hints

  Use 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 $221$.

  In all the other pictures, the number of followers increases.

  • 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.

  Hints

  Since there are fewer blocks, the percentage will be less than $100$%.

  Solution

  Percent 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):

  $27-24 = 3$.

  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.

  Hints

  Just look at the following example:

  • Your favorite jeans cost $100~\$$.
  • They are now on sale for a reduced price of $80~\$$.

  Calculate the percent of change.

  The price decreased by $20~\%$.

  $100~\$$ is the original value (original price).

  Solution

  Percent 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.

  Hints

  Percent 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: $\frac{120-100}{120}=0.1\bar 6\approx 0.17$.

  By multiplying with $100$, we get a percent change of $17~\%$.

  Solution

  For 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

  $\frac{200-175}{200}=0.125=12.5~\%$.

  Birthday party

  $\frac{120-90}{120}=0.25=25~\%$.

  Sister

  $\frac{300-250}{250}=0.20=20~\%$.

  Rugby club

  $\frac{46-40}{40}=0.15=15~\%$.