# Ratio, multipart

A comparison between **more than two** *quantities* (multitudes or magnitudes) of the *same* type, where we compare them in terms of their **relative size**.

The things being compared are called the **“terms”** of the ratio.

Multipart ratios are written in the form “𝑎 : 𝑏 : 𝑐 …” for each of the quantities (“terms”) being compared.

Multipart ratios are also known as multi-*term* or multi-*step* ratios.

## Usage of Multipart Ratios

Multipart ratios are useful for describing how a thing is made up of its parts, when there are **more than two parts**.

They can provide a quantitative “breakdown” of a *composed* thing into the parts that *compose* it (in terms of their relative quantity).

Multipart ratios are frequently used in **recipes**, to indicate the relative amount of various *ingredients*, and they can involve either **multitudes** (individual quantities) or **magnitudes** (continuous quantities).

### Multipart ratios with multitudes

Multitudes are groups of *individuals*, and a simple example of a multipart ratio of **multitudes** is a recipe for a “smoothie”.

For a **smoothie** consisting of ten apples, three oranges and five lemons, you would write the multipart ratio:
10 : 3 : 5

This smoothie has a total of *eighteen* “parts” (18 = 10 + 3 + 5), where a “part” means a “whole fruit”:

**ten**parts are apples,**three**parts are oranges, and**five**parts are lemons.

If we had *twenty* apples, we would need six oranges and ten lemons for a ratio of “10 *doubling* the total count of each fruit.

### Multipart ratios with magnitudes

A magnitude is a *continuous* quantity, like distance or volume.

A **recipe for a cocktail** is an excellent example of a multipart ratio of **magnitudes**, as they involve volumes of liquids.

Consider the **“cosmopolitan”**, which is described by the following ratio of ingredients:*

- 40 mL lemon flavored vodka,
- 15 mL Cointreau,
- 15 mL fresh lime juice,
- 30 mL cranberry juice.

We can list the **relative quantities** of these ingredients, in whole numbers, as “8 : 3 : 3 : 6”.

This gives a total of *twenty* “parts” of the final volume, since: 8 + 3 + 3 + 6 = 20

Where all twenty parts are the same volume of liquid.

How much liquid is in each part?

Well, it depends on the final volume that we need to make.

If we need a **litre of cosmopolitans**, then we know that each “part” is 50 millilitres (mL), since:
1,000 mL ÷ 20 = 50 mL
(1 litre = 1,000 mL)

Then, we can calculate the *relative* amounts of each ingredient:

**eight**parts out of twenty lemon flavored vodka, which is 400 mL (8 × 50 mL).**three**parts out of twenty Cointreau, which is 150 mL (3 × 50 mL).**three**parts out of twenty fresh lime juice, which is 150 mL (3 × 50 mL).**six**parts out of twenty cranberry juice, which is 300 mL (6 × 50 mL).

And the *same* relations apply, whether we want to make one litre, ten litres or any other volume of cosmopolitans.

* Recipe taken from International Bartenders Association, official cosmopolitan recipe.