# Fractions in Lowest Terms

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

So, $\frac{5}{9}$ is written in lowest terms, 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 lowest terms, divide both the numerator and denominator by the greatest common factor , in this case $3$ :

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

So $\frac{6}{9}$ written in lowest terms is $\frac{2}{3}$ .

This is known as reducing fractions .