Mishnah Berakhot 7:1

Three that have eaten together, it is their duty to invite [one another to say Birkat Hamazon]. One who ate demai, or first tithe whose terumah has been separated, or second tithe or sanctified property which have been redeemed, or an attendant who has eaten as much as an olive’s worth of food, or a Samaritan may be included [in the three]. But one who ate untithed produce, or first tithe whose terumah has not been separated, or second tithe or sanctified property which have not been redeemed, or an attendant who has eaten less than the quantity of an olive or a Gentile may not be counted.

שְׁלשָׁה שֶׁאָכְלוּ כְאֶחָד, חַיָּבִין לְזַמֵּן. אָכַל דְּמַאי, וּמַעֲשֵׂר רִאשׁוֹן שֶׁנִּטְּלָה תְרוּמָתוֹ, וּמַעֲשֵׂר שֵׁנִי וְהֶקְדֵּשׁ שֶׁנִּפְדּוּ, וְהַשַּׁמָּשׁ שֶׁאָכַל כַּזַּיִת, וְהַכּוּתִי, מְזַמְּנִין עֲלֵיהֶם. אֲבָל אָכַל טֶבֶל, וּמַעֲשֵׂר רִאשׁוֹן שֶׁלֹּא נִטְּלָה תְרוּמָתוֹ, וּמַעֲשֵׂר שֵׁנִי וְהֶקְדֵּשׁ שֶׁלֹּא נִפְדּוּ, וְהַשַּׁמָּשׁ שֶׁאָכַל פָּחוֹת מִכַּזַּיִת, וְהַנָּכְרִי, אֵין מְזַמְּנִין עֲלֵיהֶם:

Babylonian Talmud, Folio 45a–49b (on Mishnah 7:1–2)
Jerusalem Talmud, Halakhah 7:1

Mishnah Berakhot 7:2

Women, children and slaves they do not recite an invitation over them. How much [must one have eaten] in order for them to recite an invitation? As much as an olive. Rabbi Judah says: as much as an egg.

נָשִׁים וַעֲבָדִים וּקְטַנִּים, אֵין מְזַמְּנִין עֲלֵיהֶם. עַד כַּמָּה מְזַמְּנִין, עַד כַּזָּיִת. רַבִּי יְהוּדָה אוֹמֵר, עַד כַּבֵּיצָה:

The Babylonian Talmud discusses this mishnah with 7:1 above.

Jerusalem Talmud, Halakhah 7:2

Mishnah Berakhot 7:3

How do they invite [one another to recite the Birkat Hamazon]? If there are three, he [the one saying Birkat Hamazon] says, “Let us bless [Him of whose food we have eaten].” If there are three and him he says, “Bless [Him of whose food we have eaten]” If there are ten, he says, “Let us bless our God [of whose food we have eaten].” If there are ten and he says, “Bless.” It is the same whether there are ten or ten myriads (ten ten thousands). If there are a hundred he says, “Let us bless the Lord our God [of whose food we have eaten]. If there are a hundred and him he says, “Bless.” If there are a thousand he says “Let us bless the Lord our God, the God of Israel [of whose food we have eaten].” If there are a thousand and him he says “Bless.” If there are ten thousand he says, “Let us bless the Lord our God, the God of Israel, the God of hosts, who dwells among the cherubim, for the food which we have eaten.” If there are ten thousand and him he says, “Bless.” Corresponding to his blessing the others answer after him, “Blessed be the Lord our God the God of Israel, the God of hosts, who dwells among the cherubim, for the food which we have eaten.” Rabbi Yose the Galilean says: According to the number of the congregation, they bless, as it says, “In assemblies bless God, the Lord, O you who are from the fountain of Israel.” Rabbi Akiba said: What do we find in the synagogue? Whether there are many or few the he says, “Bless the Lord your God.” Rabbi Ishmael says: “Bless the Lord your God who is blessed.”

כֵּיצַד מְזַמְּנִין, בִּשְׁלשָׁה אוֹמֵר נְבָרֵךְ. בִּשְׁלשָׁה וְהוּא, אוֹמֵר בָּרְכוּ. בַּעֲשָׂרָה, אוֹמֵר נְבָרֵךְ לֵאלֹהֵינוּ. בַּעֲשָׂרָה וָהוּא, אוֹמֵר בָּרְכוּ. אֶחָד עֲשָׂרָה וְאֶחָד עֲשָׂרָה רִבּוֹא. בְּמֵאָה אוֹמֵר, נְבָרֵךְ לַייָ אֱלֹהֵינוּ. בְּמֵאָה וְהוּא, אוֹמֵר בָּרְכוּ. בְּאֶלֶף, אוֹמֵר נְבָרֵךְ לַייָ אֱלֹהֵינוּ אֱלֹהֵי יִשְׂרָאֵל. בְּאֶלֶף וְהוּא, אוֹמֵר בָּרְכוּ. בְּרִבּוֹא, אוֹמֵר, נְבָרֵךְ לַייָ אֱלֹהֵינוּ אֱלֹהֵי יִשְׂרָאֵל אֱלֹהֵי הַצְּבָאוֹת יוֹשֵׁב הַכְּרוּבִים עַל הַמָּזוֹן שֶׁאָכָלְנוּ. בְּרִבּוֹא וְהוּא, אוֹמֵר בָּרְכוּ. כְּעִנְיָן שֶׁהוּא מְבָרֵךְ, כָּךְ עוֹנִין אַחֲרָיו, בָּרוּךְ יְיָ אֱלֹהֵינוּ אֱלֹהֵי יִשְׂרָאֵל אֱלֹהֵי הַצְּבָאוֹת יוֹשֵׁב הַכְּרוּבִים עַל הַמָּזוֹן שֶׁאָכָלְנוּ. רַבִּי יוֹסֵי הַגְּלִילִי אוֹמֵר, לְפִי רֹב הַקָּהָל הֵן מְבָרְכִין, שֶׁנֶּאֱמַר בְּמַקְהֵלוֹת בָּרְכוּ אֱלֹהִים, יְיָ מִמְּקוֹר יִשְׂרָאֵל (תהלים סח). אָמַר רַבִּי עֲקִיבָא, מַה מָּצִינוּ בְּבֵית הַכְּנֶסֶת, אֶחָד מְרֻבִּין וְאֶחָד מֻעָטִין אוֹמֵר, בָּרְכוּ אֶת יְיָ. רַבִּי יִשְׁמָעֵאל אוֹמֵר, בָּרְכוּ אֶת יְיָ הַמְבֹרָךְ:

Babylonian Talmud, Folio 49b–50a
Jerusalem Talmud, Halakhah 7:3

Mishnah Berakhot 7:4

Three persons who have eaten together may not separate [to recite Birkat Hamazon]. Similarly four and similarly five. Six may separate, up until ten. And ten may not separate until there are twenty.

שְׁלשָׁה שֶׁאָכְלוּ כְאֶחָד, אֵינָן רַשָּׁאִין לֵחָלֵק, וְכֵן אַרְבָּעָה, וְכֵן חֲמִשָּׁה. שִׁשָּׁה נֶחֱלָקִין, עַד עֲשָׂרָה. וַעֲשָׂרָה אֵינָן נֶחֱלָקִין, עַד שֶׁיִּהְיוּ עֶשְׂרִים:

Babylonian Talmud, Folio 50a–51b (on Mishnah 7:4–5)
Jerusalem Talmud, Halakhah 7:4

Mishnah Berakhot 7:5

Two eating companies that were eating in the same room: When some of them can see some of the other they combine [for a zimun], but if not each group makes a zimun for itself. They do not bless over the wine until they put water into it, the words of Rabbi Eliezer. The sages say they bless.

שְׁתֵּי חֲבוּרוֹת שֶׁהָיוּ אוֹכְלוֹת בְּבַיִת אֶחָד, בִּזְמַן שֶׁמִּקְצָתָן רוֹאִין אֵלּוּ אֶת אֵלּוּ, הֲרֵי אֵלּוּ מִצְטָרְפִים לְזִמּוּן. וְאִם לָאו, אֵלּוּ מְזַמְּנִין לְעַצְמָן, וְאֵלּוּ מְזַמְּנִין לְעַצְמָן. אֵין מְבָרְכִין עַל הַיַּיִן עַד שֶׁיִּתֵּן לְתוֹכוֹ מַיִם, דִּבְרֵי רַבִּי אֱלִיעֶזֶר. וַחֲכָמִים אוֹמְרִים, מְבָרְכִין:

The Babylonian Talmud discusses this mishnah with 7:4 above.

Jerusalem Talmud, Halakhah 7:5

The Mishnah: English translation: Joshua Kulp, Mishnah Yomit (Conservative Yeshiva), via Sefaria, licensed CC BY; changes made (line breaks, spacing, a typo, and Kulp's study notes removed from five mishnayot). Hebrew: Torat Emet 357, public domain; Bikkurim chapter 4 from Dan Be'eri's edition of the Kaufmann manuscript, public domain.

The Jerusalem Talmud: English translation and Hebrew/Aramaic text: Heinrich W. Guggenheimer, The Jerusalem Talmud: Edition, Translation, and Commentary (Berlin: De Gruyter, 1999-2015), via Sefaria, licensed CC BY 4.0; changes made (his footnotes and the page markers removed).

The Babylonian Talmud: English: Berakhot, A. Cohen, The Babylonian Talmud: Tractate Berakot (Cambridge University Press, 1921), public domain; Sukkah and Megillah, Daf Shevui (Conservative Yeshiva), CC0; Ta'anit, Henry Malter, The Treatise Ta'anit of the Babylonian Talmud (Jewish Publication Society, 1928), public domain; Chagigah, A. W. Streane, A Translation of the Treatise Chagigah from the Babylonian Talmud (Cambridge University Press, 1891), public domain; Makkot, Sefaria Community Translation, CC0. Hebrew and Aramaic: Ta'anit, Malter's critical text (1928, public domain; his notes not reproduced); the others, Wikisource Talmud Bavli (Vilna edition), via Sefaria, licensed CC BY-SA 3.0 (this site's cleaned copy of that text is shared under the same license); changes made (markup and images removed).