Have you ever bought anything on sale? Take a look at this dilemma.

A pair of sneakers costs originally cost $165.00. They are on sale for $115.50. What is the percent of the decrease?

**Use this Concept to figure out the sale price of the sneakers. You will use percents and decreases in this Concept.**

### Guidance

Many times in the real world, things change—prices go up and down, your bank account balances go up and down, your weight goes up and down, businesses get more or less business, we have more hurricanes and typhoons than before, etc. Interpreting the amount of change as a percent is oftentimes useful to understand a situation and compare it to others.

**The** *percent of decrease***is the percent that a value decreases.**

**To find the** *percent of decrease,***divide the amount of decrease by the original amount and multiply by 100.**

*Write down this information about the percent of decrease in your notebooks.*

Now let’s look at a situation where there is a percent of decrease.

A helicopter’s altitude went from 350 feet to 38 feet. This was a different of 312 feet. By what percent did the altitude decrease?

\begin{align*}\frac{312}{350} = .891 = 89.1 \%\end{align*}

**The percent of the decrease is 89.1%.**

*Notice that if you haven’t been given the actual amount of the increase or decrease that you may need to subtract to figure this out before you divide.*

Find each percent of decrease.

#### Example A

From 80 to 30.

**Solution: @$\begin{align*}62.5\%\end{align*}@$**

#### Example B

From 90 to 40.

**Solution: @$\begin{align*}55.5\%\end{align*}@$**

#### Example C

From 130 to 100.

**Solution: @$\begin{align*}23\%\end{align*}@$**

Now let's go back to the dilemma from the beginning of the Concept.

**First, let’s look at this problem carefully to understand what they are asking us to find. Because the shoes are 30% off, this is a percent decrease.**

**Now we find the amount of difference.**

@$\begin{align*}165-115.50 =49.50\end{align*}@$

Next, we divide the difference by the original cost.

@$\begin{align*}\frac{49.50}{165}=.3\end{align*}@$

Now convert the decimal to a percent.

@$\begin{align*}.3 = 30\%\end{align*}@$

**This is the percent of the decrease.**

### Guided Practice

Here is one for you to try on your own.

What is the percent of decrease from 2500 to 400?

**Solution**

First, find the difference.

@$\begin{align*}2500 - 400 = 2100\end{align*}@$

Now divide the difference by the original amount.

@$\begin{align*}\frac{2100}{2500} = .84\end{align*}@$

Next, multiply the answer by 100.

@$\begin{align*}.84 = 84\%\end{align*}@$

**This is the answer.**

### Video Review

Finding the Percent of Decrease

### Explore More

Directions: Calculate the percent of decrease. You may round to the nearest whole percent.

- From 74 to 35, a decrease of 39
- From 4 to 1, a decrease of 3
- From 576 to 476, a decrease of 100
- From 200 to 175, a decrease of 25
- From 150 to 100, a decrease of 50
- From 325 to 290, a decrease of 35
- From 45 to 18, a decrease of 27
- From 19 to 1, a decrease of 18
- From 22 to 10
- From 34 to 20
- From 230 to 220
- From 350 to 250
- From 700 to 350
- From 130 to 7
- From 890 to 700