I would add another question. Why did the Ran single out Kaddish and Barchu from everything listed in the Mishnah? Reb Chaim suggests that the Ran is contrasting Megillas Esther and the other mitzvos. There is no obligation to hear Megillas Esther with a minyan; the obligation is to publicize the miracle, which must be done with ten men. All other mitzvos that are required to be performed with a minyan can be classified in two categories: those whose obligation only comes about when there are ten adult men, and other mitzvos whereby the obligation is on the individual.
When the obligation is on the individual, as we explained earlier, we can apply the rule of rubo kekulo and it is sufficient if a majority of the minyan has not yet fulfilled its obligation. When the Ran says “ten men or a majority of them,” he is referring to both categories of mitzvos that require a minyan. Some mitzvos require that all ten still be obligated in the mitzvah, while other mitzvos suffice with merely a majority. However, one cannot deduce from the Ran that reading the Torah is a mitzvah that suffices only if there is a majority of a minyan that has not fulfilled its obligation. The Ran only says that Kaddish and Barchu suffice with a majority of the ten men that have not yet fulfilled its obligation.
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