Megillah, Chapter Four, Mishnah Three
This mishnah teaches what rituals require a minyan of ten men in order to perform them.
1) They do not recite the Shema responsively,
2) And they do not pass before the ark;
3) And the [the priests] do not lift up their hands;
4) And they do not read the Torah [publicly];
5) And they do not conclude with a haftarah from the prophets;
6) And they do not make stops [at funeral] processions;
7) And they do not say the blessing for mourners, or the comfort of mourners, or the blessing of bridegrooms;
8) And they do not mention Gods name in the invitation [to say Birkat Hamazon];
a) Except in the presence of ten.
9) [For redeeming sanctified] land nine and a priest [are sufficient], and similarly with human beings.
Section one: In the time of the mishnah they recited the Shema in a way that we might call responsivelythe leader would recite one half of the verse and the congregation would respond with the second half. This practice changed some time during the talmudic period. There are actually many different explanations for what they did, but this seems to be the most accepted by scholars.
Section two: Passing before the ark refers to reciting the Shmoneh Esrei or Amidah. Without a minyan there is no public Amidah or repetitioneveryone just does it silently.
Section three: The priestly blessing is recited before the end of the Amidah, but only with a minyan.
Section four: Without a minyan there is no public reading of the Torah.
Section five: Nor is there a haftarah, lest one think that although they cant read from the Torah, they might be able to read from the Torah.
Section six: On the way to the cemetery and on the way back they would make formal stops at which they would recite eulogies. They would do this seven times, but it was only done with a minyan.
Section seven: The blessing for mourners was recited in the public square, whereas comforting mourners was done on the return from the cemetery. The blessing of the bridegrooms refers to the blessings recited under the huppah (the wedding canopy). In mishnaic times they probably recited three blessings, but by the time of the Talmud this had been increased to seven. None of these blessings is recited without a minyan.
Section eight: Before Birkat Hamazon, the blessing after the meal, there is an invitation to bless. This invitation is recited with Gods name only if there are ten present.
Section nine: If someone wishes to dedicate a piece of land to the Temple they estimate the value of the land and then he must pay that amount. The estimate is carried out by ten people, only one of whom must be a priest. Similarly, if a person dedicates himself or someone else to the Temple, and he cant afford to pay the price mandated in Leviticus 27, then they estimate how much he can afford. This estimate is again done by nine regular men and one priest.