# Percent Change: Increase and Decrease

Percent increase and percent 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. In this, 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 or not 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 — by calculating the differences in numbers of customers in your store daily to calculating how much money you’d save on a 20-percent-off sale.

### Understanding How to Calculate Percent Change

Whether it’s a percent increase or a percent decrease, knowing how to calculate the different elements of a percent change formula will help to solve everyday math problems related to percent change.

Take, for instance, a store that usually sells apples for three dollars, but one day decides to sell them for a dollar and 80 cents. To calculate the percent change, which we can see is a percent decrease since \$3 is more than \$1.80, we would first need to subtract the new amount from the original (\$1.20), then divide the change by the original amount (.40). In order to see the percent change, we would then multiply this decimal by 100 to make it 40 percent, which is the percent of the total amount that the price went down at the supermarket.

A school principal who is comparing student attendance from one semester to another or a cell phone company that is comparing the number of February text messages to March text messages would need to understand how to calculate the percent change in order to accurately report on the differences in attendance and text messages.

### Understanding 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 will happen more often than not 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 wanting to sell a laptop to a college student for \$600 while an electronics store nearby promises to match and reduce the price of any competitor by 20 percent. The student would clearly want to choose the electronics store, but how much would the student save?

In order to calculate this, multiply the original number (\$600) by the percent change (.20) to get the amount discounted (\$120). To figure out the new total, simply subtract the discount amount from the original number to see that the college student would only be spending \$480 at the electronics store.

### Additional Exercises for Percent Change

For each of the following, calculate the discount price and the final sale price with the discount applied:

1. A silk blouse regularly costs \$45. It’s on sale for 33% off.
2. A leather purse regularly costs \$84. It’s on sale for 25% off.
3. A scarf regularly costs \$85. It’s on sale for 15% off.
1. A sundress regularly costs \$30. It’s on sale for 10% off.
2. A woman’s silk romper regularly costs \$250. It’s on sale for 40% off.
3. A pair of women’s platform heels regularly costs \$90. It’s on sale for 60% off.
4. A floral skirt regularly costs \$240. It’s on sale for 50% off.

Check your answers, as well as the solutions for calculating percent decreases, here:

1. The discount is \$15 because (.33) * \$45 = \$15, which means the sale price is \$30.
2. The discount is \$21 because (.25) * \$84 = \$21, which means the sale price is \$63.
3. The discount is \$12.75 because (.15) * \$85 = \$12.75, which means the sale price is \$72.25.
4. The discount is \$3 because (.10) * \$30 = \$3, which means the sale price is \$27.
5. The discount is \$100 because (.40) * \$250 = \$100, which means the sale price is \$150.
6. The discount is \$54 because (.60) * \$90 = \$54, which means the sale price is \$36.
1. The discount is \$120 because (.50) * \$240 = \$120, which means the sale price is \$120.
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