# Percent Increase vs. Percent of Whole

When talking about percentages, it is very important to understand the distinction between a percent increase/change and a percent of something. A ‘percent of’ equation is a part is a percent of a whole (P=W*x*%). A percent increase is almost exactly the same, except it also includes the whole itself in addition to the equation (I=W*x*%+W).

## Percent Increase vs. Percent of Whole

Hello, and welcome to this Mometrix video lesson on the difference between a percent increase and a percent of a whole number.

**The percent of a whole number means a part of a number.** To determine the percent of a number, simply multiply the whole number by the percent. When you’ve reached an answer, move your decimal point two places to the left.

**It’s important to note, you will NOT label your final number as a percent.**

Here’s what the formula looks like written out:

Let P stand for part of, and let n represent a given number.

P=n(%)

**Now, let’s try a couple of examples.**

What is 40% of 30? To answer this question, let’s follow our formula.

P= 30(40)

P= 1200 Now that we have our number, what should we do next?

That’s right, we need to add our decimal point.

Our final answer is P= 12. 40% of 30 is 12

What is 60% of 55?

P= 55(60)

P= 3,300

Add the decimal point

P= 33. Our final answer is: 60% of 55 is 33.

**That’s just finding the regular percent of a number.** Now we need to look at finding the percent increase of a number. The percent increase of a number is just what it sounds like. It’s finding the percentage by which a number has increased to another number. To find the percent increase of a number, you need to subtract the original number from your new number, divide that answer by the original number and then multiply the final answer by 100. **You WILL label your final answer as a percent.**

Let’s look at the formula written out, that might be a little easier to understand.

Let I stand for increase, N for new number, and O for original number.

I=[[(N-O)/O](100%)]

Working through a couple of examples might help you understand.

What is the percent increase of 78 to 110? First, let’s identify our different parts for our equation! Our Original number (O) is 78. The New number (N) is 110.

I=[[(110-78)/78](100%)]

I=[(32/78)(100%)]

I=(.410)(100%)

I=41%

The percent increase from 78 to 110 is 41%.

What is the percent increase of 17 to 72? The Original number (O) is 17. The New number (N) is 72.

I=[[(72-17)/17](100%)]

I=[(55/17)(100%)]

I=(3.23)(100%)

I= 323%

The percent increase from 17 to 72 is 323%.

Thank you for joining us on learning the differences between percent increase and percent of a whole number. Be sure to “like” this video and “subscribe” to our channel for more help with your math problems. Happy studying!