Percent Equation: Definition & Example

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  • 0:00 Percents as Fractions…
  • 1:28 Percent Equation Overview
  • 5:57 Lesson Summary
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Lesson Transcript
Instructor: Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

Percentages are everywhere, but have you ever heard of the percent equation? This lesson will explain the equation and give you several examples so you can use it to solve all of your percentage problems.

Percents as Fractions & Decimals

There are percentages everywhere. But, what exactly does percent mean? Well, percent means a part of 100 that's represented by this symbol: %. For instance, if 50% of the people in your city have brown hair, that means that 50 out of every 100 people have brown hair. So how do you change regular numbers into percentages and back again? And how do you express percentages as regular numbers?

Well, for the sake of an example, let's talk about the percentage 40%. 40% can be written without the percent symbol in the following two ways:

  1. As a fraction: 40/100
  2. As a decimal: 0.40

To express these numbers, you're going to have to convert between a percent and a decimal, so let's take a moment to go over that. If you see 40%, it means 40 per 100, or 40/100, and there's our fraction. If you divide 40 by 100, you get 0.40, and there's our decimal. If you want to convert a decimal to a percent, you need to remember that 0.40 is the same as 40/100, which means 40%.

However, an even easier trick is to just multiply your decimal by 100 to make it a percent. For example: 0.40 x 100 = 40 and then you just reattach the percent symbol.

Percent Equation Overview

Chances are, you'll eventually find a problem that asks you to find the percent of something. The formula you'll use is called the percent equation, which is:

part = percent x whole

But what does that mean? Let's use examples to explore this formula and practice solving for the part, the percent and the whole.

Example One: Solving for the Part

What is 80% of 20?

There are some word clues in math that can help you write out an equation for this question. As you search for them, think of yourself as a detective trying to decode the question into the language of math. In this example, notice that the question is asking 'what number', which means we don't know the number. Here, you'll have to use a variable, or a letter used to represent an unknown number. Let's use n, so go ahead and write n down. This example also includes the word 'is'. In math, 'is' means equals, so go ahead and write that down.

After the word 'is' comes 80%. We can't plug 80% into our equation, so you'll need to change it to a decimal. Do you remember how to do that? Yep, we get 0.80. Do you see the word 'of' in the example problem, which in math means multiply? This gives you the next part. Lastly, plug the number 20 into your equation and you should end up with: n = 0.80 x 20.

When you do the math, you should get n = 16. So 16 is 80% of 20. If you go back to our formula, the part is 16, the percent is 80% and the whole is 20. We can use variables to represent the basic equation as: n = p x w. Where n = part, p = percent and w = whole. This will come in handy shortly.

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