# How to Use Percents Greater Than 100

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• 0:03 Finding the Percentage…
• 2:13 Percentages Greater Than 100
• 3:28 Another Example
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we'll look at taking the percentage of a number and we'll specifically look at percentages that are greater than 100. We'll see how to work with these types of percentages and look at some examples.

## Finding the Percentage of a Number

It is almost certain that you have come across percentages in your everyday life. For instance, suppose you work at a job making \$18 an hour. You're doing a great job, and your boss calls you into the office to tell you that you are getting a hefty 20% raise. Awesome!

Percent means per hundred, and the percentage of a number can be found by considering the number to be 100% and finding the specified part of that number. Consider your raise. You are currently making \$18 per hour, and your going to get a 20% raise. To figure out how much more you will be making per hour, you consider 18 to be 100 parts, and you want to figure out how much 20 of those parts are worth.

This may sound a bit confusing, but don't worry, we are going to put this into mathematical terms, which will give us a nice algorithm for finding the percentage of a number. We said we wanted to consider 18 to be 100 parts. To do this, we divide 18 by 100.

Next, we want to consider 20 of those parts, so we multiply the result by 20.

We see that you will be making \$3.60 per hour more! Wow! That's a great raise - good job!

Now, let's consider this in general to make this process even simpler. If we want to find n% of x, we take x, divide by 100, and multiply by n. We can rearrange this as follows.

We see that to take n% of x, we just need to divide n by 100 and multiply the result by x. Again, consider your 20% raise. We would divide 20 by 100 to get 0.2, and then multiply that by 18.

Once again, we see you get a \$3.60 per hour raise.

Alright, so we know what percentages are and how to find the percentage of a number. Now, suppose you go into your boss's office, and rather than being told you are getting a 20% raise, you are told that you're going to get a 112% raise. Yes, I realize this is in dreamland, but stay with me here. Putting the unlikeliness of this happening aside, consider the 112% raise. This may look different to you since it is a percentage greater than 100. Let's take a look at these types of percentages and how to use them.

## Percentages Greater Than 100

When we want to take a percentage that is greater than 100 of a number, we can consider this in the same way that we consider percentages less than 100. Basically, we still consider the number we are taking the percentage of to be 100%, so a percentage of the number that is greater than 100 will be larger than the number itself.

The good news is that finding the percentage of a number when the percentage is greater than 100 involves the same process that we just saw for percentages less than 100. That is, the process of finding n% of x can be broken into the following two steps, regardless of whether n is less than or greater than 100:

1. Divide n by 100
2. Multiply the result by x

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