# Ratios

#### Common Questions

#### What is a ratio?

Great question to start with! A ratio is a comparison of two quantities. It tells us how much of one thing there is compared to another thing.

For example if there are $3$ pink starbursts and $5$ orange starbursts in a pack, the ratio of pink to orange starbursts is $3to5$.

Read below to learn more.

#### Common Questions

### What is a ratio?

A ratio is a comparison of two quantities. It tells us how much of one thing there is compared to another thing.

Let’s say we have a bag of Starbursts that contains the following:

Color | Amount |
---|---|

Yellow | 13 |

Orange | 12 |

Red | 25 |

Pink | 30 |

All | 80 |

### Types of Ratios

There are two types of ratios we can express from this data: part-to-part and part-to-whole.

A part-to-part ratio compares one part of a group to another part of the same group. For example, we can compare the number of orange starbursts to the number of red starbursts.

A part-to-whole ratio compares one part of a group to the total parts in the group. For example, we can compare the number of orange starbursts to the total number of starbursts.

### Writing Ratios

We can write these two types of ratios in three different ways:

Format | Example (Orange Starbursts to Red Starbursts) |
---|---|

$atob$ | $12to25$ |

$a:b$ | $12:25$ |

$ba $ | $2512 $ |

That last one is how we write a ratio as a fraction. To convert one of the other ratio forms to a fraction, just put the left side on top and the right side on the bottom.

You can also convert the fraction form of a ratio into a percentage if you want. For example, if the ratio is $21 $, then in percentage form, the ratio is 50%.

### Equivalent Ratios

Let's say we have a group of 80 Starbursts and 30 are pink. That means for every 40 Starbursts, 15 are pink. It also means that for every 8 Starbursts, 3 are pink.

So if we wanted to give someone an idea of how many pink Starbursts there are compared to the total number of Starbursts, we can say the ratio is

These ratios are all equivalent. So, as long as you multiply or divide both sides of the ratio by the same number, you'll have equivalent ratios.

### Simplified Ratios

You might get asked for the simplest form of a ratio or to simplify a ratio. The simplest form of a ratio is when there are no more numbers that both sides of the ratio can be divided by (other than 1!).

For example, 30 : 80 is not simplified, because we can divide both sides by 2 to get 15 : 40.

It's still not totally simplified because we can divide both sides by 5 to get 3 : 8. Now, it's completely simplified because we can't divide both sides by any more numbers.

### Interpreting Ratios

Now that we know how to write ratios, determining what they represent should be a piece of cake! For each of the following Starburst ratios, identify which two things are being compared and what type of ratio it is.

### Quick Practice 1 / 5

What's being compared?