Giving to God what belongs to God
“So each of us shall give an account of himself to God.” Romans 14: 12
"Obey your leaders and submit to them; for they are keeping watch over your souls, as men who will have to give account.” Hebrews 13: 17
Fraction, not doing it
GIRM (all quotes from the 2011 USCCB official English translation), Chapter II, The Fraction of the Bread, #83:
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"The Priest breaks the Eucharistic Bread, with the assistance, if the case requires, of the Deacon or a concelebrant. The gesture of breaking bread done by Christ at the Last Supper, which in apostolic times gave the entire Eucharistic Action its name, signifies that the many faithful are made one body (1 Cor 10:17) by receiving Communion from the one Bread of Life, which is Christ, who for the salvation of the world died and rose again. [....]"
"The Priest breaks the Bread and puts a piece of the host into the chalice to signify the unity of the Body and Blood of the Lord in the work of salvation, namely, of the Body of Jesus Christ, living and glorious. [....]"
GIRM, Chapter IV, #155:
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"After this, the Priest takes the host, breaks it over the paten, and places a small piece in the chalice, saying quietly, Haec commixtio (May this mingling). [....]"
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GIRM, Chapter VI, par. 321:
"[....] Moreover, the gesture of the fraction or breaking of bread, which was quite simply the term by which the Eucharist was known in apostolic times, will bring out more clearly the force and importance of the sign of the unity of all in the one bread, and of the sign of charity by the fact that the one bread is distributed among the brothers and sisters."
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Redemptionis Sacramentum, par. 73:
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"In the celebration of Holy Mass the breaking of the Eucharistic Bread – done only by the Priest celebrant, if necessary with the help of a Deacon or of a concelebrant – begins after the exchange of peace, while the Agnus Dei is being recited. For the gesture of breaking bread “carried out by Christ at the Last Supper, which in apostolic times gave the whole eucharistic action its name, signifies that the faithful, though they are many, are made one Body in the communion of the one Bread of Life who is Christ, who died and rose for the world’s salvation” (cf. 1 Cor 10,17). For this reason the rite must be carried out with great reverence. Even so, it should be brief. The abuse that has prevailed in some places, by which this rite is unnecessarily prolonged and given undue emphasis, with laypersons also helping in contradiction to the norms, should be corrected with all haste."
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For more more information about the Fraction, see the GIRM. For an explanation of what the Fraction is and why it is done, see Father Edward McNamara, LC's posts in the EWTN Library: The Fraction Rite and Why the Host is Placed in the Chalice.