6.15: Percent of Decrease
Taylor’s Mom is confused about their sales. In one month, the sales have decreased instead of increased in the store. This decrease has happened despite the fact that they have added many new products to their inventory.
“I just don’t understand it,” her Mom said at breakfast. “Last month, we had a terrific month with $15,000 in sales. This month it was only $12,500.”
“We can’t keep losing business,” her Dad said drinking his coffee.
“I wonder how much of a loss it actually is,” thought Taylor. “Maybe if we can figure out why the sales decreased, then we can increase them again.
Taylor began figuring out the percent of the decrease. She started by subtracting, but then got stuck.
Taylor needs some help and this Concept will do the trick. You will learn all about calculating the percent of increase and the percent of decrease in this Concept. Pay attention and you can help Taylor with her arithmetic at the end of the Concept.
Guidance
Prices can increase. Costs can increase. Numbers can increase. We can find the percent of increase when dealing with an increase. All of these things can also decrease. When there has been a decrease from an original amount to a new amount, we can find the percent of decrease.
How do we find the percent of decrease?
The percent of decrease from one amount to another is the ratio of the amount of decrease to the original amount.
To find the percent of decrease, follow these steps
Step 1: Find the amount of decrease by subtracting the two numbers.
Step 2: Write a fraction in which the numerator is the amount of decrease and the denominator is the original amount.
\begin{align*}\text{Percent of decrease} = \frac{ \text{Amount of decrease}}{\text {Original amount}}\end{align*}
Step 3: Write the fraction as a percent.
Take a few minutes to write the steps to finding the percent of decrease in your notebook.
Now let’s look at how to apply these steps.
Find the percent of decrease from 50 to 40.
Step 1: Subtract 40 from 50. \begin{align*}50  40 = 10\end{align*}
Step 2: \begin{align*}\text{Percent of decrease} = \frac{\text{Amount of decrease}}{\text{Original amount}} = \frac{10}{50}\end{align*}
Step 3:
One Way  Another Way 

\begin{align*}\frac{10}{50} = \frac{x}{100}\end{align*} 
\begin{align*}\frac{10}{50} = \frac{10 \div 10}{50 \div 10} = \frac{1}{5}\end{align*} 
\begin{align*}50 x = 1,000\end{align*} 
\begin{align*}\overset{ \ \ 0.20}{5 \overline{ ) {1.00 \;}}} \leftarrow \ \text{Divide to 2 decimal places.}\end{align*} 
\begin{align*}\frac{\cancel{50} x} {\cancel{50}} = \frac{1,000}{50}\end{align*} 
\begin{align*}0.20 = 20 \%\end{align*} 
\begin{align*}x = 20\end{align*} 

\begin{align*}\frac{20}{100} = 20 \%\end{align*} 
The percent of decrease from 50 to 40 is 20%.
Find the percent of decrease from 200 to 170.
Step 1: Subtract 170 from 200. \begin{align*}200  170 = 30\end{align*}
Step 2: \begin{align*}\text{Percent of decrease} = \frac{\text{Amount of decrease}}{\text{Original amount}} = \frac{30}{200}\end{align*}
Step 3:
One Way  Another Way 

\begin{align*}\frac{30}{200} = \frac{x}{100}\end{align*} 
\begin{align*}\frac{30}{200} = \frac{30 \div 10}{200 \div 10} = \frac{3}{20}\end{align*} 
\begin{align*}200 x = 1,800\end{align*} 
\begin{align*}\overset{ \ \ 0.15}{20 \overline{ ) {3.00 \;}}}\end{align*} 
\begin{align*}\frac{\cancel{200} x} {\cancel{200}} = \frac{3,000}{200}\end{align*} 
\begin{align*}0.15 = 15 \%\end{align*} 
\begin{align*}x = 15\end{align*} 

\begin{align*}\frac{15}{100} = 15 \%\end{align*} 
The percent of decrease from 200 to 170 is 15%.
Find the percent of each decrease.
Example A
From 10 to 5
Solution: 50%
Example B
From 25 to 15
Solution: 40%
Example C
From 125 to 70
Solution: 44%
Here is the original problem once again.
Taylor’s Mom is confused about their sales. In one month, the sales have decreased instead of increased in the store. This decrease has happened despite the fact that they have added many new products to their inventory.
“I just don’t understand it,” her Mom said at breakfast. “Last month, we had a terrific month with $15,000 in sales. This month it was only $12,500.”
“We can’t keep losing business,” her Dad said drinking his coffee.
“I wonder how much of a loss it actually is,” thought Taylor. “Maybe if we can figure out why the sales decreased, then we can increase them again.
Taylor began figuring out the percent of the decrease. She started by subtracting, but then got stuck.
Let's use what we have learned to help Taylor. She was right by starting with subtraction.
\begin{align*}15,000  12,500 = 2500\end{align*}
Next, we divide the difference by the original amount.
\begin{align*}2500 \div 15,000 = .1666666\end{align*}
We can round this decimal up to \begin{align*}.17\end{align*}
\begin{align*}.17 = 17%\end{align*}
The amount of the decrease is about \begin{align*}17%\end{align*}
Vocabulary
Here are the vocabulary words in this Concept.
 Percent of Increase
 the percent that a price or cost or number has increased.
 Percent of Decrease
 the percent that a price or cost or number has decreased.
Guided Practice
Here is one for you to try on your own.
Jessie's work schedule went from 20 hours to 18 hours. What was the percent of the decrease?
Answer
To figure this out, we subtract to find the difference.
\begin{align*}20  18 = 2\end{align*}
Next, we divide that number by the original amount.
\begin{align*}2 \div 20 = .1\end{align*}
Finally, we convert this decimal to a percent.
\begin{align*}.1 = 10%\end{align*}
The percent of decrease was 10%.
Video Review
Here is a video for review.
 This is a James Sousa video on percent of decrease.
Practice
Directions: Find the percent of decrease given the original amount. You may round to the nearest whole percent when necessary or leave your answer as a decimal.
1. From 25 to 10
2. From 30 to 11
3. From 18 to 8
4. From 30 to 28
5. From 12 to 8
6. From 90 to 85
7. From 200 to 150
8. From 97 to 90
9. From 56 to 45
10. From 15 to 2
11. From 220 to 110
12. From 75 to 66
13. From 180 to 121
14. From 1500 to 1275
15. From 18,000 to 900
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Here you'll learn to find a percent of decrease.