~ 4.6 ~

Increasing and Decreasing

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Learning Targets

I can draw a tape diagram that represents a percent increase or decrease.
When I know a starting amount and the percent increase or decrease, I can find the new amount.

Notes

Imagine that it takes Andre ¾ more than the time it takes Jada to get to school. Then we know that Andre’s time is 1 ¾ or 1.75 times Jada’s time. We can also describe this in terms of percentages:

We say that Andre’s time is 75% more than Jada’s time. We can also see that Andre’s time is 175% of Jada’s time. In general, the terms percent increase and percent decrease describe an increase or decrease in a quantity as a percentage of the starting amount.

For example, if there were 500 grams of cereal in the original package, then “20% more” means that 20% of 500 grams has been added to the initial amount, 500 + (0.2) ⋅ 500 = 600, so there are 600 grams of cereal in the new package.

We can see that the new amount is 120% of the initial amount because

500 + (0.2) ⋅ 500 = (1+0.2) 500

Vocabulary

percentage increase: Given an initial amount, and a final amount which is larger than the initial amount, the percentage increase is the difference (final amount minus initial amount) expressed as a percentage of the initial amount.

percentage decrease: Given an initial amount, and a final amount which is smaller than the initial amount, the percentage decrease is the difference (initial amount minus final amount) expressed as a percentage of the initial amount.

Activities

6.2 More Cereal and a Discounted Shirt

A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?
The price of a shirt is $18.50, but you have a coupon that lowers the price by 20%. What is the price of the shirt after using the coupon?

Questions to Ponder before answering:

Did the number of ounces of cereal in the box (or price of the shirt) increase or decrease?
What percentage of the original amount of cereal (original price of the shirt) is the new amount of cereal?

Add to Your Notes

100% always corresponds to the original amount before the change.

Cereal Box

A cereal box says that it now contains 20% more.
This is an example of a percent increase.

Shirt

The price of a shirt lowers the price by 20%.
This is an example of a percent decrease.

6.3 Using Tape Diagrams

Match each situation to a diagram on the right. Be prepared to explain your reasoning.
- Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase.
- This year’s blueberry harvest is 75% of last year’s.
- Compared with last year, this year’s peach harvest decreased 25%.
- This year’s plum harvest is 125% of last year’s plum harvest.
Draw a diagram to represent these situations.
- The number of ducks living at the pond increased by 40%.
- The number of mosquitoes decreased by 80%.

Add to Your Notes

What is another way to describe a 25% increase or decrease?

percent increase → 100% + 25% = 125%
percent decrease → 100% - 25% = 75%

When a quantity is increased or decreased, what percent describes the original or starting value?

The original/starting value is 100%.

What strategies have we used to help us calculate percent increase and decrease?

table, equation, tape diagram, double number line

Summary

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