## Percent Decrease Situations

## Opening

# Percent Decrease Situations

Think about the percent increase problems you worked on.

- What types of situations do you think would involve percent
*decrease*? Can you think of an example? - Share your ideas.

Think about the percent increase problems you worked on.

- What types of situations do you think would involve percent
*decrease*? Can you think of an example? - Share your ideas.

Represent and solve percent decrease problems.

A store manager reduces the price of a jacket by 15%. The jacket originally cost $60. What is the new price?

- Copy and complete the table.
- Write an equation.
- Write the solution as a complete sentence.

- Remember that the price has been decreased—not increased. What should you do differently in setting up the equation as compared to the way you set up an equation to represent percent increase?
- Is the unknown amount the starting amount, the final amount, or the percent change? How can you represent the unknown amount in your equation?

A sign on a dress in a store window says: “20% off! Sale price $40!” What was the price of the dress before the sale?

- Copy and complete the table.
- Write an equation.
- Write the solution as a complete sentence.

- Remember that the price has been decreased—not increased. What should you do differently in setting up the equation as compared to the way you set up an equation to represent percent increase?
- Is the unknown amount the starting amount, the final amount, or the percent change? How can you represent the unknown amount in your equation?

A bus ticket normally costs $45. As a special offer, the bus company reduces the price to $27. What is the percent change?

- Copy and complete the table.
- Write an equation.
- Write the solution as a complete sentence.

- Remember that the price has been decreased—not increased. What should you do differently in setting up the equation as compared to the way you set up an equation to represent percent increase?
- Is the unknown amount the starting amount, the final amount, or the percent change? How can you represent the unknown amount in your equation?

Prepare a presentation in which you show and explain each part of your work for all three of the percent decrease problems.

Explain how you used the distributive property to solve percent increase problems. Can you use the distributive property in this way to solve percent decrease problems?

Take notes about your classmates’ approaches and explanations for solving the three percent decrease problems.

As your classmates present, ask questions such as:

- Is the unknown amount the starting amount, the final amount, or the percent change?
- Where is the unknown amount in your equation?
- Why does your solution make sense in this situation?
- Should the solution be greater than or less than the given amount?
- Should the solution be greater than or less than 100%?
- How did you use the mathematical structure of the situation to help you solve the problem?
- How is solving a percent decrease problem similar to solving a percent increase problem? How is it different?

**Read and Discuss**

- A percent can describe a change in a value that decreases. Such a percent is called a
*percent decrease*. - If an amount decreases by
*x*%, you can multiply that amount by (100% −*x*%) to determine the final amount. - For example, if the percent decrease is 5% and the original amount is
*m*, then 100 − 5 = 95% = 0.95

0.95*m*= the final amount

Can you:

- Explain how to calculate a percent decrease?
- Give examples of situations that involve percent decrease?
- Describe how to use a table to organize the information in a percent decrease problem?

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Percent increase and percent decrease problems are different because …**