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Percent increase and decrease are the two types of percent change, which is used to express the ratio of how an initial value compares to the result of a change in value. A percent decrease is a ratio that describes a decline in value of something by a specific rate, while a percent increase is a ratio that describes an increase in the value of something by a specific rate.

The easiest way to determine whether a percent change is an increase or a decrease is to calculate the difference between the original value and the remaining value to find the change then divide the change by the original value and multiply the result by 100 to get a percentage. If the resulting number is positive, the change is a percent increase, but if it is negative, the change is a percent decrease.

Percent change is highly useful in the real world, for example, allowing you to calculate the difference in the number of customers who come into your store daily or to determine how much money you'd save on a 20-percent-off sale.

### How to Calculate Percent Change

Suppose 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? Note that you would not find the difference between $3 and $1.80 yielding and answer of $1.20, which is the difference in price.

Instead, since the cost of the apples has decreased, use this formula to find the percent decrease:

Percent decrease = (Older - Newer) ÷ Older.

= (3 - 1.80) ÷ 3

= .40 = 40 percent

Note how you convert a decimal into a percent by moving the decimal point twice to the right and tacking on the word "percent" after that number.

### How to Use Percent Change to Alter Values

In other situations, the percent decrease or increase is known, but the newer value is not. This may occur at department stores that are putting clothing on sale but don't want to advertise the new price or on coupons for goods whose prices vary. Take, for example, a bargain store selling a laptop for $600, while an electronics store nearby promises to beat the price of any competitor by 20 percent. You would clearly want to choose the electronics store, but how much would you save?

To calculate this, multiply the original number ($600) by the percent change (0.20) to get the amount discounted ($120). To figure out the new total, subtract the discount amount from the original number to see that you would only be spending $480 at the electronics store.

In another example of altering a value, suppose a dress regularly sells for $150. A green tag, marked 40 percent off, is attached to the dress. Calculate the discount as follows:

0.40 x $150 = $60

Calculate the sales price by subtracting the amount you save from the original price:

$150 - $60 = $90

### Exercises With Answers and Explanations

Test your skills in finding percent change with the following examples:

1) You see a carton of ice cream that originally sold for $4 now selling for $3.50. Determine the percent change in the price.

Original price: $4

Current price: $3.50

Percent decrease = (Older - Newer) ÷ Older

(4.00 - 3.50) ÷ 4.00

0.50 ÷ 4.00 = .125 = 12.5 percent decrease

So the percent decrease is** **12.5 percent.

2) You walk to the dairy section and see that the price of a bag of shredded cheese has been reduced from $2.50 to $1.25. Calculate the percent change.

Original price: $2.50

Current price: $1.25

Percent decrease = (Older - Newer) ÷ Older

(2.50 - 1.25) ÷ 2.50

1.25 ÷ 2.50 = 0.50 = 50 percent decrease

So, you have a percent decrease of 50 percent.

3) Now, you're thirsty and see a special on bottled water. Three bottles that used to sell for $1 are now selling for $0.75. Determine the percent change.

Original: $1

Current: $0.75

Percent decrease = (Older - Newer) ÷ Older

(1.00 - 0.75) ÷ 1.00

0.25 ÷ 1.00 = .25 = 25 percent decrease

You have a percent decrease of 25 percent.

You're feeling like a thrifty shopper, but you want to determine the altered values in your next three items. So, calculate the discount, in dollars, for the items in exercises four through six.

4.) A box of frozen fish sticks was $4. This week, it is discounted 33 percent off the original price.

Discount: 33 percent x $4 = 0.33 x $4 = $1.32

5.) A lemon pound cake originally cost $6. This week, it is discounted 20 percent off the original price.

Discount: 20 percent x $6 = 0.20 x $6 = $1.20

6.) A Halloween costume usually sells for $30. The discount rate is 60 percent.

Discount: 60 percent x $30 = 0.60 x $30 = $18