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A minyan (Hebrew: plural minyanim) is traditionally a quorum of ten or more adult (over the age of Bar Mitzvah) male Jews for the purpose of communal prayer; a minyan is often held within a synagogue, but may be (and often is) held elsewhere. It is also used as a collective noun, as in "do we have a minyan?"
A single minyan may be one of several simultaneous prayer services within a synagogue. One synagogue (or any building) can have two or more minyanim meeting at the same time; for example, one Ashkenazi minyan and one Sephardi minyan, or one Orthodox minyan and one Conservative minyan, though the latter would typically only happen in a community center or other communally owned building.
Women are counted as part of the minyan in most non-Orthodox synagogues and prayer gatherings.
According to halakha (Jewish law), a minyan is required for many parts (D'varim SheB'Kedusha "Holy utterances") of the communal prayer service, including Barechu, Kaddish, repetition of the Amidah, the Priestly Blessing, and the Torah and Haftarah readings. Although Judaism has traditionally counted only men in the minyan for formal prayer, traditional sources consider that it is an extremely positive thing for both women and men to pray in minyan. It should be noted however, that there is no absolute obligation for either sex.
Rabbinic Judaism teaches that all men and women are obligated to pray to God each day, but the formal requirements for prayer are different for the sexes. Classical rabbinic authorities are in agreement that men are required to pray from a set liturgy three times a day; however, they were of varied opinions as to precisely what the requirements were for women. In the last 300 years many traditional rabbis have followed a trend in which women are seen as being required to follow many (though not all) of the same requirements as men.
The 19th century posek Yechiel Michel Epstein, author of the Arukh HaShulkhan, notes: "Even though the rabbis set prayer at fixed times in fixed language, it was not their intention to issue a leniency and exempt women from this ritual act". One of the most important codes of law in Ashkenazi Orthodox Judaism (outside of Hasidic Judaism) is the Mishnah Berurah by Rabbi Yisrael Meir Kagan. He holds that the Men of the Great Assembly obligated women to say Shacharit (morning) and Minchah (afternoon) prayer services each day, "just like men". He further states that although women are technically exempt from reciting the Shema Yisrael, they should nevertheless say it anyway. In Conservative Judaism, most rabbis hold this view as well. However, many Jews still rely on the ruling of the (Ashkenazi) Rabbi Avraham Gombiner in his Magen Avraham commentary on the Shulkhan Arukh (section Orach Chayim 106:2), and more recently the (Sephardi) Rabbi Ovadia Yosef (Yabiah Omer vol. 6, 17), that women are only required to pray once a day, in any form they choose, so long as the prayer contains praise of (brakhot), requests to (bakashot), and thanks of (hodot) God. 
While women are not required to pray with a minyan, it is commonly believed that Jewish law requires that men pray in a minyan, but this not exactly correct. None of the Mishnah, Talmud or later codes of Jewish law hold this as requirement. Rather, it is described as a preferred activity, but not as mandatory. The Shulkhan Arukh (section Orach Chayim 90:9) says "A person should make every effort to attend services in a synagogue with a quorum; if circumstances prevent him from doing so, he should pray, wherever he is, at the same time that the synagogue service takes place". According to the author (Rabbi Yosef Karo), no Jew has an obligation to public prayer. That said, communal prayer, which requires a minyan, is historically viewed as an almost-obligation—while not a requirement, it is regarded as anti-social to not join in communal prayer.
According to many Orthodox authorities , women count as part of the minyan of 10 required for a number of mitzvot; including publicizing the miracle of Esther on Purim; public remembrance of Amalek in Parshat Zachor; public recitation of the Birkhat Hagomel blessing after surviving severe illness or danger; and public martyrdom, sanctification of G-d's name "in the midst of the children of Israel." (Leviticus 22:32). A few authorities also hold that 10 women can, at least under some circumstances, constitute a minyan for purposes of zimmun b'shem leading Birkat HaMazon.
While the required quorum for most activities requiring a quorum is usually ten, it is not always so. For example, the Passover sacrifice or Korban Pesach (from the days of the Temple in Jerusalem) must be offered before a quorum of 30. (It must be performed in front of kahal adat yisrael, the assembly of the congregation of Israel. Ten are needed for the assembly, ten for the congregation, and ten for Israel.) According to some Talmudic authorities, women counted in the minyan for offering the Korban Pesach (e.g. Rav, Rav Kahana, Pesachim 79b).
A common misconception is that the requirement of ten to constitute a quorum comes from the fact that Abraham stopped decreasing his requests for God to spare Sodom and Gemorrah at ten "righteous" individuals (Genesis 18). In fact, the requirement comes from the sin of the spies (Numbers 14:27), in which the ten spies who bring a negative report of the land of Israel are referred to as an eidah or congregation (Babylonian Talmud Megillah 23b), though the Jerusalem Talmud (Megillah 4,4) relates it to the ten brothers of Joseph who went down to Egypt to get food during a famine. The quorum of ten men is also referred to in the Book of Ruth 4:2.
The number 10 for a minyan may not always have been consistent throughout history either. In Masechet Soferim (10:7) it is stated that in the Land of Israel, sometimes as few as 6 (i.e., one more than half of 10) men were counted as sufficient to say communal prayers. This view has not been codified as halakha.
Some congregations (based on the Shulkhan Arukh section Orach Chayim 55) will include a boy touching a Torah scroll or holding a printed Tanakh as the tenth person if a minyan can be formed in no other way.
Changes in non-Orthodox forms of Judaism
In the mid 20th century some congregations in Reform Judaism and Conservative Judaism began counting women as part of the minyan. Reform and Reconstructionist rabbis do not see themselves as bound by halakha, and the movements are committed to the equality of the sexes, rejecting historical practices that draw distinctions on the basis of gender; thus they disregard the traditional prohibition of counting women as part of a minyan. Until 1973, Conservative Judaism, which views halakha as its Rabbinate interprets it as binding, did not count women in a minyan. In 1973, the Committee on Jewish Law and Standards of the Conservative Rabbinical Assembly voted to permit synagogues to count women in a minyan if desired and approved by the local Rabbi. Although several responsa (opinions) were proposed at the time, the Committee did not adopt any of them, and did not offer any official reason for irs decision. In 2002, the CJLS for the first time officially adopted a responsum offering a the Conservative movement's halakhic reasons for this practice.  Orthodox Jews do not accept its validity. The practice of counting women in the minyan has spread to most Conservative Jewish synagogues. More traditional Conservative communities and individual women may follow traditional practices if they wish, and a minority do.
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