How many people must participate in the davening in order to have a minyan?
In order to daven with a minyan (quorum), ten Jewish males over the age of bar mitzvah have to be present. How many of them have to be participating depends on the section of davening in question:
Chazaras hashatz (the repetition of the amidah) requires that the chazzan (the one leading the davening) recite the brachos with tish’ah onim (nine people answering “Amein”). If one of the nine present can’t answer “Amein”, whether because he’s at a part of davening like krias shema where he’s forbidden to respond, or even if he’s at a part like pesukei d’zimra where he may respond, but is preoccupied with davening—or even if some of them are busy talking and aren’t paying attention—it’s as if they aren’t there, and the chazzan may not begin chazaras hashatz until there is a proper minyan present. The term used to describe reciting chazaras hashatz in such a situation is “karov lihyos birchosav l’vatala” (it’s almost as if the chazzan’s blessings are being recited in vain).
Other parts of davening, such as kaddish, require ten people physically present, but only five of them—representing the majority of the required minyan (including the chazzan as the sixth)—have to respond. Therefore, if some of those present are still davening when the chazzan finishes shemoneh esreh of Maariv, he may begin reciting kaddish as soon as five people can answer. #509?1
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