From Worksheet/Article

Percent increase and percent decrease are the two types of percent change. This article focuses on the answers to the worksheet, Percent Change - Grocery Store Shopping.

### What is Percent Decrease?

Percent decrease is a ratio that compares 2 values. It describes the decline in value of something by a specific rate. Percent decrease is evident anytime a number or amount decreases.

### When is Percent Decrease Calculated in the Real World?

- A school principal is comparing student attendance from one semester to another.
- A cell phone company is comparing the number of February text messages to March text messages.

*Example*: The original price for a bag of apples is $3. On Tuesday, the bag of apples sells for $1.80. What is the percent decrease?

Careful, do not find the difference between $3 and $1.80 and say that the percent decrease is $1.20.

Use this formula to find the percent decrease.

Percent decrease = (Older – Newer) ÷ Older.

= (3 – 1.80) ÷ 3

= .40 = 40%

*Note*: To convert a decimal into a percent, move the decimal point twice and stick a percent sign (%) at the end.

### Percent Decrease is Given

In other situations, the percent decrease is known, but the newer value is unknown.

*Example* *1*: Best Bargain wants to sell a laptop computer for $600 to Alan. J’s Electronics will sell the computer to Alan for 20% less than Best Bargain.

1. How much money will Alan save when he buys the computer from J’s Electronics instead of Best Bargain?

Multiply .20 and $600. Alan will save $120.

2. How much will Alan pay for the computer at J’s Electronics?

$600 – $120 = $480

*E**xample 2:* A dress regularly sells for $150. A green tag, marked 40% off, is attached to the dress.

1. What is the discount? .40 * $150 = $60

2. What is the sale price? $150 - $60 = $90

### Exercises with Answers and Explanations

Find the percent decrease for exercises 1 through 3.

1. Ice cream

Original: $4.00

Current: $3.50

Percent decrease:**12.5%**

Percent decrease = (Older – Newer) ÷ Older

(4.00 - 3.50) ÷ 4.00

.50 ÷ 4.00 = .125 = 12.5% decrease

2. Shredded cheese

Original: $2.50

Current: $1.25

Percent decrease: **50%**

Percent decrease = (Older – Newer) ÷ Older

(2.50 - 1.25) ÷ 2.50

1.25 ÷ 2.50 = .50 = 50% decrease

3. Bottled Water

Original: $1.00

Current: $.75

Percent decrease: **25%**

Percent decrease = (Older – Newer) ÷ Older

(1.00 - .75) ÷ 1.00

.25 ÷ 1.00 = .25 = 25% decrease

Calculate the discount, in dollars, for the items in exercises 4 - 6.

4. A box of frozen fish sticks is originally $4.00. This week, it is discounted 33% off the original price.

Discount: 33% * $4.00 = .33 * $4.00 =

$1.32

5. A lemon pound cake originally costs $6.00. This week, it is discounted 20% off the original price.

Discount: 20% * $6.00 = .20 * $6.00 =

$1.20

6. A Halloween costume costs $30.00. The discount rate is 60%.

Discount: 60% * $30.00 = .60 * $30.00 =

$18.00