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# Percent of Decrease

## Percent of Decrease = Amount of Decrease/Original Amount

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Percent of Decrease

At the end of the summer season, the local farmer’s market marked down its swan gourds to $1.00 apiece. Throughout the summer, the swan gourds had sold for$3.50 each. What was the percent of decrease in cost?

In this concept, you will learn how to calculate the percent of decrease.

### Finding Percent of Decrease

Prices can increase. Costs can increase. Numbers can increase. You 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 lower amount, you can 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:

First, find the amount of decrease by subtracting the lower amount from the higher amount.

Next, write a fraction in which the numerator is the amount of decrease and the denominator is the original amount.

Percent of Decrease =Amount of DecreaseOriginal Amount\begin{align*}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}\end{align*}

Then, write the fraction as a percent.

Now let’s look at how to apply these steps.

Find the percent of decrease from 50 to 40.

First, subtract 40 from 50.

5040=10\begin{align*}50 - 40 = 10\end{align*}

Next, write the fraction:

Percent of Decrease =Amount of DecreaseOriginal Amount=1050\begin{align*}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{10}{50}\end{align*}

Then, write the fraction as a percent.

One Way

105050x50x50x====x1001,0001,0005020\begin{align*}\begin{array}{rcl} \frac{10}{50}&=&\frac{x}{100} \\ 50x &=& 1,000 \\ \frac{\cancel{50}x}{\cancel{50}} &=& \frac{1,000}{50} \\ x &=& 20 \end{array}\end{align*}

Another Way

1050=10÷1050÷10=155)1.00¯¯¯¯¯¯¯¯¯¯¯¯  0.20Divide to 2 decimal places.0.20=20%\begin{align*}&\frac{10}{50}=\frac{10 \div 10}{50 \div 10}=\frac{1}{5} \\ & \overset{ \ \ 0.20}{5 \overline{ ) {1.00 \;}}} \qquad \leftarrow \text{Divide to} \ 2 \ \text{decimal places.} \\ &0.20 = 20 \% \end{align*}The answer is the percent of decrease from 50 to 40 is 20%.

Let’s look at another example.

Find the percent of decrease from 200 to 170.

First, subtract 170 from 200.

200170=30\begin{align*}200 - 170 = 30\end{align*}

Next, write the fraction: Percent of Decrease =Amount of DecreaseOriginal Amount=30200\begin{align*}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{30}{200}\end{align*}

Then, write the fraction as a percent.

One Way

30200200x200x200x====x1003,0003,00020015\begin{align*}\begin{array}{rcl} \frac{30}{200}&=&\frac{x}{100} \\ 200x &=& 3,000 \\ \frac{\cancel {200}x}{\cancel{200}} &=& \frac{3,000}{200} \\ x &=& 15 \end{array}\end{align*}

Another Way

30200=30÷10200÷10=32020)3.00¯¯¯¯¯¯¯¯¯¯¯¯  0.15Divide to 2 decimal places.0.15=15%\begin{align*}&\frac{30}{200}=\frac{30 \div 10}{200 \div 10}=\frac{3}{20} \\ & \overset{ \ \ 0.15}{20 \overline{ ) {3.00 \;}}} \quad \leftarrow \text{Divide to} \ 2 \ \text{decimal places.} \\ &0.15 = 15 \%\end{align*}The answer is the percent of decrease from 200 to 170 is 15%.

### Examples

#### Example 1

Earlier, you were given a problem about the end of summer sale at the farmer’s market.

The swan gourds were marked down from $3.50 to$1.00. What was the percent of decrease?

First, subtract to find the difference.

3.501.00=2.50\begin{align*}3.50 - 1.00 = 2.50\end{align*}

Next, divide that difference by the original amount.

2.50÷3.50=0.714\begin{align*}2.50 \div 3.50 = 0.714\end{align*}

Finally, convert this decimal to a percent.

0.714=71.4%\begin{align*}0.714 = 71.4 \%\end{align*}

The answer is the percent of decrease from $3.50 to$1.00 is 71.4%.

#### Example 2

Jessie’s work schedule went from 20 hours to 18 hours. What was the percent of the decrease?

First, subtract to find the difference.

2018=2\begin{align*}20 - 18 = 2\end{align*}

Next, divide that difference by the original amount.

2÷20=0.1\begin{align*}2 ÷ 20 = 0.1\end{align*}

Finally, convert this decimal to a percent.

0.1=10%\begin{align*}0.1 = 10 \%\end{align*}

The answer is the percent of decrease from 20 hours to 18 hours was 10%.

#### Example 3

Find the percent of decrease from 10 to 5.

First, subtract 5 from 10.

105=5\begin{align*}10 - 5 = 5\end{align*}

Next, write the fraction: Percent of Decrease =Amount of DecreaseOriginal Amount=510\begin{align*}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{5}{10}\end{align*}

Then, write the fraction as a percent:

51010x10x10x====x1005005001050\begin{align*}\begin{array}{rcl} \frac{5}{10}&=&\frac{x}{100} \\ 10x &=& 500 \\ \frac{10x}{10} &=& \frac{500}{10} \\ x &=& 50 \end{array}\end{align*}

The answer is the percent decrease from 10 to 5 is 50%.

#### Example 4

Find the percent of decrease from 25 to 15.

First, subtract to find the difference.

2515=10\begin{align*}25 - 15 = 10\end{align*}

Next, divide that difference by the original amount.

10÷25=0.4\begin{align*}10 \div 25 = 0.4\end{align*}

Finally, convert this decimal to a percent.

0.4=40%\begin{align*}0.4 = 40 \%\end{align*}

The answer is the percent of decrease from 25 to 15 is 40%.

#### Example 5

Find the percent of decrease from 125 to 70.

First, subtract 70 from 125.

12570=55\begin{align*}125 -70 = 55\end{align*}

Next, write the fraction: Percent of Decrease =Amount of DecreaseOriginal Amount=55125\begin{align*}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{55}{125}\end{align*}

Then, write the fraction as a percent:

55125125x10x125x====x1005,5005,50012544\begin{align*}\begin{array}{rcl} \frac{55}{125}&=&\frac{x}{100} \\ 125x &=& 5,500 \\ \frac{10x}{125} &=& \frac{5,500}{125} \\ x &=& 44 \end{array} \end{align*}

The answer is the percent decrease from 125 to 70 is 44%.

### Review

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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### Vocabulary Language: English

Percent of Decrease

The percent of decrease is the percent that a value has decreased by.

Percent of Increase

The percent of increase is the percent that a value has increased by.