## Percent Equation

#### What is a percent?

Good question! Like decimals, a percent is another way of expressing a fraction. The “cent” in percent means $100$ (like how centipedes have $\textbf{100}$ legs), so percent means “out of $100$.” For example, $39\%$ means $39$ out of $100$ and is equal to the fraction $\frac{39}{100}$.

### What is a percent?

Like fractions and decimals, percents are a ratio between two numbers. The “cent” in percent means $100$ (like how centipedes have $\textbf{100}$ legs), so “percent” means “per $100$” or “out of $100$.” A percent is always a ratio out of $100$.

Since percentages are just fractions out of $100$, we can use equivalent proportions to solve problems involving percentages. The equation below relates proportions and percents:

$\frac{{\color{#b5179e}\text{part}}}{{\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}}}{100}$

Click the button below if you need to review proportions!

Let’s rearrange our equation a bit. If we multiply both sides of the equation by “whole,” we can change this equation into a different form.

$\frac{{\color{#b5179e}\text{part}}}{{\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}}}{100}$$\frac{{\color{#b5179e}\text{part }}\times{\sout\color{#3A86FF}\text{ whole}}}{{\sout\color{#3A86FF}\text{whole}}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}$${\color{#b5179e}\text{part}} = \frac{{\color{#4ac783}\text{percent}} \times {\color{#3A86FF}\text{whole}}}{100}$

This equation is called the percent equation. If we know two of the unknowns, we’ll always be able to solve for the third. As you’ll see later, writing the equation in this form makes it easier for us to solve problems involving percentages.