# Fractions in Simplest Form

A
fraction
is said to be in
**
simplest form
**
if its
numerator
and
denominator
are
relatively prime
, that is, they have no common
factors
other than
$1$
. (Some books use "written in lowest terms" to mean the same thing.)

So, $\frac{5}{9}$ is in simplest form, since $5$ and $9$ have no common factors other than $1$ . But $\frac{6}{9}$ is not; $6$ and $9$ have a common factor $3$ .

To write $\frac{6}{9}$ in simplest form, divide both the numerator and denominator by the greatest common factor , in this case $3$ :

$\frac{6\text{\hspace{0.17em}}\xf7\text{\hspace{0.17em}}3}{9\text{\hspace{0.17em}}\xf7\text{\hspace{0.17em}}3}=\frac{2}{3}$

So $\frac{6}{9}$ in simplest form is $\frac{2}{3}$ .

This is known as reducing fractions .