1. Learn to solve problems involving percent of change.

2. Vocabulary
percent of change
percent of increase
percent of decrease

3. A percent can be used to describe an amount of change
A percent can be used to describe an amount of change. The percent of change is the amount, stated as a percent, that a number increases or decreases.
If the amount goes up, it is a percent of increase.
If the amount goes down, it is a percent of decrease.
amount of change
original amount
Percent of change =

4. Additional Example 1A: Finding Percent of Change
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
65 is decreased to 38.
65 – 38 = 27
Find the amount of change. 27 65
Substitute values into
formula.
percent of change = 
Divide.
 41.5%
Write as a percent. Round.
The percent of decrease is about 41.5%.
When a number is decreased, subtract the new amount from the original amount to find the amount of change.
Helpful Hint

5. Additional Example 1B: Finding Percent of Change
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
41 is increased to 92.
92 – 41 = 51
Find the amount of change. 41 51
Substitute values into
formula.
Percent of change = 
Divide.
 124.4%
Write as a percent. Round.
The percent of increase is about 124.4%
When a number is increased, subtract the original amount from the new amount.
Helpful Hint

6. Check It Out: Example 1A
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
70 is decreased to 45.
70 – 45 = 25
Find the amount of change. 25 70
Substitute values into
formula.
percent of change = 
Divide.
 35.7%
Write as a percent. Round.
The percent of decrease is about 35.7%.

7. Check It Out: Example 1B
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
37 is increased to 56.
56 – 37 = 19
Find the amount of change. 37 19
Substitute values into
formula.
Percent of change = 
Divide.
 51.4%
Write as a percent. Round.
The percent of increase is about 51.4%

8. When you know the percent of change, you can use an equation to find the actual amount of change.

9. Additional Example 2: Using Percent of Change
The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price?
Step 1: Find the amount of the discount d.
20% · = d
Think: 20% of $42.99 is what number?
0.20 · = d
Write the percent as a decimal.
8.598 = d
Multiply.
$8.60  d
Round to the nearest cent.
The amount of the discount is $8.60.

10. Additional Example 2 Continued
The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price?
Step 2: Find the sale price.
regular price – amount of discount = sales price
$ – $ = $34.39
The sale price is $34.39

11. Step 1: Find the amount of the discount d.
Check It Out: Example 2
The regular price of a computer game is $ It is on sale for 15% off. What is the sales price?
Step 1: Find the amount of the discount d.
15% · = d
Think: 15% of $49.88 is what number?
0.15 · = d
Write the percent as a decimal.
7.482 = d
Multiply.
$7.48  d
Round to the nearest cent.
The amount of the discount is $7.48.

12. Check It Out: Example 2 Continued
The regular price of a computer game is $ It is on sale for 15% off. What is the sales price?
Step 2: Find the sale price.
regular price – amount of discount = sales price
$ – $ = $42.40
The sale price is $42.40.

13. Lesson Quiz
Find each percent of change.
1. 10 is increased to 12.
2. 25 is increased to 45.
3. 10 is decreased to 1.
4. The regular price of a coat is $120. It is on sale for 25% off. What is the sale price?
5. A backpack that sells for $42 is on sale for % off. Find the sale price.
20%
80%
90%
$90
$31.50