Natural Fractions

Why

We want to express how many parts (of equal size) of a whole there are.

Definition

A fraction (or natural fraction, ratio) is an ordered pair $(a, b)$ of natural numbers where $b \neq 0$. $a$ is called the numerator and $b$ is called the denominator.

If $a < b$ then the fraction is called proper (a proper fractiont). Otherwise, the fraction is called improper (an improper fraction).

The fraction is a unit fraction if $a = 1$.

Notation

We denote the fraction $(a, b)$ by $a/b$ or

\[ \frac{a}{b} \]

Etymology

The word fraction comes from the Latin fractus, meaning broken.