# Ratios & Percentages

### Topics

## Introduction to :

In this section we will solve each percentage problem using two different methods.

After you try the two methods, take your pick of which one works best for you. It’s your call, boss.

**Method 1: Using Ratios and Proportions**

All percent problems can be set up as proportions. The tricky part is figuring out what goes where in the proportion. Here are a few things to know when setting it up:

- A percent is a proportion where the whole is equal to 100. "Per" means "of" and "cent" is a Latin prefix meaning "hundred." Think of the words century (100 years) and centimeter (one-hundredth of a meter).
- You are looking for a percentage of the number that will become the denominator of the ratio. An easy way to think about this is that whatever comes after the "of" is the denominator.
- The word "what" represents the thing you are trying to find, so "what" is our variable.

Take a look at Examples 1-4 to see how Method 1 works.

**Method 2: Using Equations**

Each of these problems can also be set up as equations. All you have to do is "translate" the sentences. Here is what you have to remember:

*What*means the variable,*x**Is*means equals*Of*means to multiply- Write all percents as decimals in your equation.

Check out the examples for this section to see how Method 2 works.

#### Method 1 Example 1

What is 15% of 72? |

#### Method 1 Example 2

80% of 40 is what number? |

#### Method 1 Example 3

30% of what number is 15? |

#### Method 1 Example 4

What percent of 60 is 20? |

#### Method 2 Example 1

What is 15% of 72? |

#### Method 2 Example 2

80% of 40 is what number? |

#### Method 2 Example 3

30% of what number is 15? |

#### Method 2 Example 4

What percent of 60 is 20? |