The Gemara (29b) records an argument over how to divide the krias hatorah if the rosh chodesh during chanuka falls out on a weekday. Rav Yitzchak says we should read three aliyot from the rosh chodesh laining and one from the chanuka laining, while Rav Dimi says we should read three aliyot from Chanuka and one from rosh chodesh. The Gemara explains that Rav Yitzchak gives the first three out of four aliyot to rosh chodesh because it occurs more often than chanuka, and the general rule is that “tadir u’she’eino tadir tadir adif,” more common halachot take precedence over less common ones. However, Rav Dimi holds that since there is a fourth aliyah only because of rosh chodesh, therefore the fourth aliyah goes to rosh chodesh and the first three go to chanuka.

The Gemara and Shulchan Aruch (OC 684:3) pasken like Rav Yitzchak that we read the first three aliyot from the rosh chodesh laining and the last aliyah from the Chanuka laining. The Rama adds that if by mistake someone began laining for Chanuka, he should stop where he is, and start again with the Rosh Chodesh laining. The Taz (4) argues, and says that once he already began, he should continue the Chanuka laining for three aliyot , and read the fourth aliyah from the rosh chodesh laining. The Mishnah Berurah (17) paskens like the Taz.

This argument seems to revolve around how we understand the principle of “tadir adif,” that we give precedence to more common halachot. Is this a principle that tells us how we should l’chatchilah arrange different mitzvoth, but if we perform them in a different order they are still valid, or does it even determine b’dieved the only order that a person can fulfill the mitzvoth? The Rama feels that since Rosh Chodesh is more common, it must be read first, and if it is not first, the reading is invalid. Therefore, if you mistakenly began reading Chanuka first, you must stop and start again with Rosh chodesh. Otherwise, the laining will not be valid. However, the Taz holds that tadir adif is only a principle how to l’chatchilah perform the mitzvoth, but it won’t invalidate them b’dieved. In our case, even if you read Chanuka first and rosh chodesh second, you fulfill kriat hatorah. Therefore, if you begin laining for Chanuka, you should not stop and switch the laining, because once you begin one mitzvah you shouldn’t leave it even for another one.

This question also comes up regarding benching when Rosh Chodesh falls out on Shabbos. Because Shabbos is more common than Rosh Chodesh, based on the principle of “tadir adif,” a person should say r’tzei before ya’aleh v’yavo in benching. What if he began by misktake ya’aleh v’yavo first? Should he finish it and then say r’tzei, even though they will be out of order, or should he stop where he is, go back to r’tzei and then say ya’aleh v’yavo again? This would seem to be the same question as above: is tadir only l’chatchilah or even b’dieved? In other words, do we have to repeat mitzvoth that were not fulfilled according to the principle of tadir? Most poskim (piskei t’shuvot OC 188:5) rule that once he started ya’aleh v’yavo, he should finish it, and then say r’tzei. This follows the p’sak of the Mishnah Berurah in our sugya, who holds like the Taz, that tadir is only a principle l’chatchilah, but would not make you repeat mitzvoth b’dieved.