# Ratio

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

For example:

- A
*count*of apples to a*count*of oranges, since both are**multitudes**(a “count”). - A
*distance*of one mile to a*distance*of five miles, since both are**magnitudes**(“distance”) of the*same*type.

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

Ratios are written in the form “𝑎 : 𝑏 ” for the two quantities (“terms”) being compared.

The first term, 𝑎, is called the *antecedent* term, and the second term, 𝑏, is called the *consequent* term.

The convention for writing ratios uses:

**whole numbers**, so “3 : 2” rather than “1.5 : 1”**lowest terms**, so “2 : 1” rather than “4 : 2”.

**Related terms:** rational number, irrational number

## Why Ratios Matter

A ratio is a comparison that takes place in the mind.

But they describe very real relationships between things in the world.

The ratio of your *income* to your *expenses*, is the difference between *saving money* or being driven into *debt*.

The ratio of *deaths* from a disease to people *infected* (with the disease), tells you how *deadly* the disease is.