Question: Can one brush one’s teeth on a fast day?
Answer: The Gemara (Berachos 14a) relates that there were amoraim who would taste some food while fasting. The rishonim debate whether this applies only to a private ta’anis or even a public one (See Tosafos; Rosh).
The Shulchan Aruch (OC 567:1) writes that one who’s really hungry on the four minor fast days (i.e. not on Tisha B’av or Yom Kippur) may taste some food and spit it out. The Rema doesn’t allow it on any ta’anis.
While the Shulchan Aruch (OC 567:3) forbids one to rinse one’s mouth with a little water and spit it out on a (public) ta’anis, the Magen Avraham (OC 567:6) writes that this is only according to the Rema who forbids tasting food. The Shulchan Aruch would allow one to rinse with less than a revi’is of water (on a minor fast).
While the Kaf Hachaim (OC 567:13) forbids rinsing even with less than a revi’is, most poskim are more lenient, especially when one is uncomfortable. Thus, the Rema (Darchei Moshe OC 567:2), Elya Rabba (567:5) and Baer Heitev (567:5) relate that the Maharil used to rinse his mouth with water while being particular not to swallow any.
The Mishna Berura (567:11 quoting the Chayei Adam 132:20) writes that on one of the minor fasts one may rinse their mouth with water if they are uncomfortable and on Tisha B’av, one may only do so if they are suffering. One doing so should bend over the sink to ensure that they don’t swallow any water. A healthy person cannot rinse one’s mouth on Yom Kippur.
The poskim write that brushing one’s teeth is the same as rinsing one’s mouth (See Minchas Yitzchak 4:109).
R’ Ovadia Yosef (Yalkut Yosef, Ta’anis, 13) writes that if one is uncomfortable not brushing one’s teeth, one may do so, though ensure that one uses less than a revi’is of water and try not to swallow any.
The Aruch Hashulchan (OC 567:3) is more lenient still, allowing one to rinse (but not gargle) even with more than a revi’is of water.In conclusion, one who wants to brush their teeth on a minor ta’anis may do so, though they should ensure that they don’t swallow any water.