Finding the Percentage Decline and Percentage Increase

What is a percent decline?

A percent decline is the comparison of the amount by which something has decreased from its original quantity. Favorite percent declines are discounts and sales, when items at a store are sold at lower prices. We have a few other examples on percent declines and how to compute them below.

Example 1

Imagine that at the start of the week, you had a box of a hundred chocolate bars, but by the end of the week only thirty chocolate bars remained. The decrease was seventy chocolate bars. Therefore, to calculate our percent decrease of the box of chocolate bars, we will take the number by which the bars have reduced and divide it by a hundred. Below is a worked out example.

Take the original number of chocolate and subtract the number of the remaining bars.

100 – 30 = 70

To get the percentage decline, divide the number by one hundred. You will get 0.7. Now convert the decimal number into a percentage by multiplying it by 100 to get your percentage decline.

From the above example, we can deduce a general formula that we can use to calculate our percentage decline.

(initial amount – remaining amount) / initial amount = percentage decline

Let us look at another example.

Example 2

Mary's pencil was 12 inches long on Monday morning. However, on Friday afternoon, she found it was only 5 inches long. Calculate the percentage decrease in her pencil's length.

To solve the above problem, the first step would be to know the original length of the pencil and the length on the last day, and find their difference. After you get the difference, divide it by 100 to get the percentage decrease.

12 cm – 5cm = 7cm

7/12 = 0.58

Convert 0.58 into percentage form.

0.58 = 58%

We apply percentages in many areas of our lives and it is therefore important to know how to work with percentages. Just like working with decimal numbers and fraction which are related to percentage, we have seen how easy it is to solve basic percentage problems.

The above formula of calculating the percentage decrease can also be used to compute the percentage increase. However, when calculating the percentage increase, we take the final figure and subtract the initial figure. Below are the two formulas:

Percentage increase = (final amount - initial amount) / initial amount

Percentage decrease = (initial amount – remaining amount) / initial amount

In real life, we apply this equation to compute the percentage loss or profit made by a business.

Example 3

The buying price of a pen was \$10. John sold the pen for \$5. Calculate the percentage loss that John suffered.

Our buying price becomes our initial amount while the selling price becomes our final amount. Therefore, our equation will look as below.

Loss percent= (\$10 - \$5) /\$10

Loss percent = (5/10)

Loss percent = 0.5

Convert 0.05 into percent.

0.5 = 50%

Resource

 Browse Common Decimals Browse Common Fractions