The word percent is made up of the parts "per" and "cent", and literally means "per 100." Therefore, a percent is a part of 100.
A value such as 40 percent, or 40%, means 40 out of 100, or 40 parts per 100 parts.  In other words, a percent is a ratio of one value to 100.

Percents are used, believe it or not, for convenience. Percents give us a way of relating parts of a particular whole amount to another part of a different whole. Since not all wholes have an easily detectible 100 parts, a percent helps us compare different parts to different wholes.

For example, consider a set of Jim's quizzes in his math class. On the first quiz he earned 20 out of 25 points. On the second quiz he earned 16 out of 20 points. Jim wants to know which quiz he scored better on. Can we conclude that he did better on the first because he earned a higher number of points? Actually, we can't. The reason is due to the fact that the quizzes were not based on the same number of points. Using that faulty logic, we would conclude that Jim did better by earning 10 out of 100 points than by earning 5 out of 5 points. Obviously that's not true. So, what do we do?

Here's where a percent comes in. We can compare these two scores by relating each to a certain number of points out of 100. A 20 out of 25 is an 80% (80 points out of 100 - if you're having trouble with that, we'll cover it later). A 16 out of 20 points is also an 80%. So although Jim earned a different number of points on each quiz, he really performed at the same level on both quizzes. See how the percent makes it very easy to compare?

Let's look at the math behind that:
The first quiz grade was a 20 out of 25 points.  That ratio is equal to the ratio of 80 to 100 (they both reduce to 4/5 and their cross products are equal).

So, a 20 out of 25 would be equal to 80 out of 100, or 80%.

The second quiz grade was a 16 out of 20 points. That ratio is also equal to the ratio of 80 to 100.

So, a 16 out of 20 would also be equal to 80 out of 100, or 80%.

In each, we have a certain part of the whole amount of points equaling a part of 100.

This is a proportion, and is the main proportion we use to solve percent problems. Though there are many ways to solve the different types of percent problems, this proportion can be used to solve nearly all of them.

Yes. Percents are actually used in other places besides than Math class! Percents are used everywhere...in business, sports, shopping, cooking, and many other places. That's why we study them in math; they appear everywhere.

There are 3 classic percent problems. Each one deals with finding a particular value. If you take another look at our main percent proportion, you can see which values we refer to. In the percent proportion we have 4 values. A part, a whole, a percent, and 100.
Only 3 of these will vary from situation to situation, for the 100 never changes. Each of the classic percent problems deals with finding either the part, the whole, or the percent.

Here's a typical problem that deals with finding the percent:   20 is what percent of 25?
Here's a typical problem that deals with finding the part:   What is 45% of 80?
Here's a typical problem that deals with finding the whole:   30 is 60 percent of what value?

Do you understand each of those questions? Sometimes its difficult to determine which value you are looking for.
Often there are a few verbal clues that help us. The word "is" is generally connected to the "part."  The word "of" is generally connected to the "whole." And obviously, the word "percent" or the "%" symbol is connected to the "percent".

To solve one of these problems, we can simply fill in the proportion with the values from the question and solve for the one that is missing. Let's solve the second question above: What is 45% of 80?  Take a look below...here we will replace the "%" with the 45, and the "whole" with the 80.  The only value left is the "part." Since we do not know what the part is, we use a variable.


Now, all we have to do is solve the proportion - which is a skill we should already know how to do. Below, you'll see two of the methods we've learned: cross multiplication and using the identity property.  In both cases, a little reducing was done first to provide easier numbers.
                   

Regardless of how we solve, we see the answer (the part) is 36. So, 36 is 45% of 80.