NS1.6 Calculate the percentage of increase and decrease of a quantity.

NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

California Standards

SECTION 6-5:

Applying Percent of Increase and Decrease

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Percents can be used to describe a change. Percent of change is the ratio of the amount of change to the original amount.

Percent of increase describes how much the original amount increases.

Percent of decrease describes how much the original amount decreases.

amount of changeoriginal amountpercent of change =

Find the percent of increase or decrease from 16 to 12.

Additional Example 1A: Finding Percent of Increase or Decrease

This is a percent of decrease.

16 – 12 = 4 First find the amount of change.

amount of decrease

original amount4

16Set up the ratio.

Find the decimal form. Write as a percent.

= 0.25 = 25% 416

From 16 to 12 is a 25% decrease.

Find the percent increase or decrease from 45 to 54.This is a percent of increase.

54 – 45 = 9 First find the amount of change.

amount of increase original amount

945

Set up the ratio.

Additional Example 1B: Finding Percent of Increase or Decrease

Find the decimal form. Write as a percent.

= 0.20 = 20%945

From 45 to 54 is a 20% increase.

Find the percent increase or decrease from 50 to 65.

This is a percent of increase.

Check It Out! Example 1A

65 – 50 = 15 First find the amount of change.

amount of increase original amount

15 50

Set up the ratio.

Find the decimal form. Write as a percent.

= 0.30 = 30%15 50

From 50 to 65 is a 30% increase.

Find the percent of increase or decrease from 20 to 17.

Check It Out! Example 1B

This is a percent of decrease.

20 – 17 = 3 First find the amount of change.

amount of decrease

original amount3

20Set up the ratio.

Find the decimal form. Write as a percent.

= 0.15 = 15% 320

From 20 to 17 is a 15% decrease.

When Jim was exercising, his heart rate went from 72 beats per minute to 98 beats per minute. What was the percent increase to the nearest tenth of a percent?

Additional Example 2: Health Application

26 72

Set up the ratio.

98 – 72 = 26 First find the amount of change.

amount of increase original amount

Find the decimal form. Write as a percent.

0.361 36.1%26 72

From 72 to 98 increases by about 36.1%.

In 2005, a certain stock was worth $1.25 a share. In 2006, the same stock was worth $0.85 a share. What was the percent decrease?

Check It Out! Example 2

1.25 – 0.85 = 0.40 First find the amount of change.

amount of decreaseoriginal amount 1.25

0.40Set up the ratio.

Find the decimal form. Write as a percent.= 0.32 = 32%

1.25 0.40

The value of the stock decreased by 32%.

Discount is the difference between the regular price and the sale price of an item. You can use percent of decrease to find discounts.

Markup is the difference between the wholesale cost and the retail price of an item. You can use percent of increase to find markups.

Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price?

Additional Example 3A: Finding Discount and Markup

(450)(0.20) = 90 Find 20% of $450. This is the amount of discount.

450 – 90 = 360 Subtract $90 from $450.

Method 1: Multiply, then subtract.

The discounted price was $360.

Additional Example 3B: Finding Discount and Markup

(85)(0.40) = 34 Find 40% of $85. This is the amount of markup.

85 + 34 = 119 Add $34 to $85.

Method 1: Multiply, then add.

Mr. Olsen has a computer business in which he sells everything 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price?

The retail price is $119.

SUMMARYPercents can be used to describe a change. Percent of change is the ratio of the amount of change to the original amount.

Percent of increase describes how much the original amount _________.

Percent of decrease describes how much the original amount ________.

amount of ______original ______percent of change =

WORDS

Decreases

Amount

Increases

change

SUMMARY

Discount is the difference between the _______ price and the ____ price of an item. You can use percent of decrease to find discounts.

Markup is the difference between the _________ cost and the ______ price of an item. You can use percent of increase to find markups.

WORDS

Wholesale

Regular

Retail

Sale