SHAFAQNA – The Grand Ayatollah Sistani answered a question about brushing teeth when fasting.
Question: Can washing mouth and teeth with brush and paste, void fasting?
The Grand Ayatollah Sistani: Brushing teeth in the month of Ramadhan does not void the fasting if the person who is fasting does not swallow bits of tooth paste which are mixed with saliva. And a small amount which disappears in saliva does not harm fasting.
Source: PERSIAN SHAFAQNA