Calculating percentages are useful in almost all disciplines including biology, chemistry, physics, mathematics, economics and more. Percentages are used in everyday life as well: rates of inflation, media statistics, banking interest rates, and discounts in shops. They are important for understanding a variety of financial changes in everyday life. A percentage is a number expressed as a fraction of 100. It is a common way to compare numbers or observations by standardizing measures using a 0 to 100 scale. In addition, one can compute how to calculate a percent of increase. Imagine an item receives a mark-up from its original value. How can you calculate the percentage of increase? Use the following formula:

% increase = 100 x ((final-initial)/final)

To calculate the percent of increase, one must follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction (PEMDAS). Essentially, the formula can be broken up into three steps:

- Find the difference of the final value and initial value
- Divide the initial value from the difference value from step 1.
- Multiply by 100 and add the percent.

Let’s practice!

#### Example 1

There is a video game being auctioned online. It was initially listed for $20.00. A week later, the game was sold for $30.00. Calculate the percent increase.

% increase = 100 x ((30-20)/20) Plug in values

100 x ((30-20)/20) Solve by using order of operations using parentheses first

100 x 0.50 Divide 10/20

% increase = 50% Multiply and label with a percentage sign

In this example, the video game was sold with a 50% increase of its original price. By utilizing the percent of increase formula, one can calculate the percentage increase of, and difference given the final and initial number.

#### Example 2

Calculate the percent increase from the initial number, 45, to the final number, 70.

% increase = 100 x ((70-45)/45) Plug in values

100 x (25/45) Solve by using order of operations using parentheses first

100 x .556 Divide 25/45

55.56% Multiply and round to the nearest hundredth

Overall, calculating percent increase is important to use for financial analysis, science, mathematics, and much more. It enables individuals and organizations to quantify growth and measure performance through percent changes.

Author: Maerie Morales