The earliest Christian writings do not call the eucharist the eucharist. They call it the breaking of bread, and they use the phrase as the name of the gathering itself, which tells you how central the gesture was before any theology had been written about it. A loaf broken and shared is a picture that needs no explanation, and the letters of Paul make the argument explicitly: the bread that is broken is one, and those who share in the one loaf are one body. Every later tradition has kept that reading of the action whatever else it disagrees about.
Gregory Dix argued in 1945 that the seven distinct actions of Jesus at the supper were compressed by the liturgy into four, taking, giving thanks, breaking and giving, and that this fourfold shape underlies every historic rite. The proposal organised a generation of liturgical study and shaped a great many twentieth century revisions, which were written to make the four actions visible again.
In the developed rites the fraction acquired accompaniments. In the Roman rite it is covered by the Agnus Dei, ordered to be sung at that point by Pope Sergius I at the end of the seventh century, and it ends with the commixture, a particle dropped into the chalice. In the Byzantine rite the Lamb is divided into four along the lines of the seal that was pressed into the loaf before baking, and one of the four goes into the cup, followed by the zeon, hot water poured in before the communion. Small individual wafers eventually made the western fraction almost invisible, which is precisely what the modern revisions set out to reverse.