Gemara

39a (Rav Ashi citing Rav Kahana): Little flour is added to a cooked beet dish, so we bless on it Borei Pri ha'Adamah. Much flour is added to a cooked turnip dish, so the blessing is Borei Minei Mezonos.

Retraction (Rav Kahana): We bless Borei Peri ha'Adamah on both of them. Much flour is added merely to make it stick together.

41a (Beraisa): If one wants to eat a radish and an olive, he blesses on the radish, and exempts the olive.

Answer: The case is, the radish is Ikar (primary. He eats the olive just to weaken the sharpness of the radish.)

(Rav Papa): The Halachah is, things eaten due to the meal during the meal do not require a blessing beforehand or afterwards.

44a (Mishnah): If one was served first salted food, and bread with it, he blesses on the salted food and exempts the bread, for it is Tefel (secondary) to it.

Question: Do we ever find that salted food is Ikar and bread is Tefel?!

Answer (Rav Acha brei d'Rav Avira): The Mishnah discusses Peros Ginosar.

Rishonim

Rambam (Hilchos Berachos 3:5): The general rule is, when there is Ikar and Tefel, one blesses on the Ikar and exempts the Tefel, whether or not they were mixed.

Rosh (6:26): Do not say that the radish exempts the olive only when one eats them together. The Gemara connotes unlike this. Rather, he ate one after the other, to nullify the bitterness of the radish.

Rosh (6:28): If one ate at the beginning of his meal bread and Peros, and later he eats the Peros without bread, must he bless on them? Logically, he should not, for his meal is based on them. We do not say Batlah Daito Etzel Kol Adam (we are not concerned for his opinion, for the Halachah is based on normal people.) The Yerushalmi says that Rav Huna ate dates with bread. R. Chiya bar Ashi said that he should have left them for after the meal, to bless on them before and after. He answered that they were the Ikar of his meal. This implies that they do not need a Berachah during the meal, even if he eats them without bread. If not, R. Chiya did not need to suggest leaving them for after the meal. He could eat them during the meal without bread! However, this does not prove that if they brought Peros during the meal and he ate some with bread and some without bread, that he need not bless beforehand. Perhaps R. Chiya suggested eating them after the meal in order to bless on them before and after.

Tosfos (44a DH b'Ochlei): The Mishnah discusses one who eats Peros Ginosar, and afterwards salted food, lest he become weak. Why doesn't he bless on the fruits, which are Ikar, and exempt everything else? We can say that he did not eat the fruits in that Ma'amad (session). Alternatively, when he ate the Peros he did not have salted food and bread. He did not know that he will become weak due to the sweetness.

Taz (OC 212:1): According to Tosfos, why did the Tana discuss such a case? He could have simply said that the fruits exempt the salted food and bread! It seems that he teaches about eating something not for its own sake, rather, due to what he ate before, and its sweetness or bitterness is paining him. What he eats now is Tefel. Even so, he must bless, for the Tana exempts only when the Tefel was in front of him when he blessed, or if when he blessed he thought that he will need to eat something to fix matters. R. Yonah explained that the salted food was the Peros themselves. It seems that R. Yonah agrees with Tosfos, who says that the Ikar exempts the Tefel only if he ate them in the same session, or had intent at the time of the Berachah. If he ate them in another session, and the first session was Batel, or he did not intent at the time of the Berachah, he must bless also on the salted food.

Note: At first he exempts whether the latter food was in front of him, or he intended for it. Later, he connotes that if only one was fulfilled, he blesses again! I did not see anyone address this. A Moreh Hora'ah said that the Taz holds that either condition exempts by itself.

Poskim

Shulchan Aruch (OC 212:1): Whenever there is Tefel with Ikar, one blesses on the Ikar, and this exempts the Tefel from a Berachah Rishonah and a Berachah Acharonah.

Beis Yosef (DH u'Mah she'Chasav v'Afilu): The Kolbo was unsure whether the Ikar exempts only from a Berachah Rishonah, or even from a Berachah Acharonah. I say that surely it exempts from both. The Sugya connotes like this. Rav Papa taught that things eaten due to the meal during the meal do not require a Berachah beforehand or afterwards.

Shulchan Aruch (ibid.): This is not only if the Tefel is mixed with the Ikar. It is even if each is separate.

Magen Avraham (1): The majority is the Ikar. If one of them five grains is mixed, it is Ikar, as long as it has substance (208:2,6,7).

Bach (1 DH u'Mah): The Rambam says that one blesses on the Ikar and exempts the Tefel, whether or not they were mixed. The Gemara says so about flour mixed in a beet dish to give taste (208:1). One blesses Borei Minei Mezonos. The Mishnah of salted food (and bread) teaches about an Ikar that was not mixed with the Tefel.

Bach (DH Aval Lashon and DH v'Ika): Tosfos' first answer is that he blessed on and ate the Peros before the salted food, and now he needs to bless on the salted food. In the second answer, he eats Peros also now with the salted food and bread, but when he blessed on the Peros, the salted food and bread were not there. According to both answers, even though he eats the salted food and bread due to the Peros, and he blessed on them with intent to eat the salted food and bread, if they were brought only after he finished the Peros, he must bless on the salted food. Above (176:3), we concluded that if one blessed on bread with intent for Peros that accompany it, even if they were brought later, he need not bless on them! We can say that there, the bread was still there when the Peros were brought.

Magen Avraham (2): 'A different Ma'amad' means that he changed his place. This is unlike Nachalas Tzvi and the Bach (who says that it means that he ate them later - Machatzis ha'Shekel. Eshel Avraham - they hold that the two answers in Tosfos argue with each other). See 178:3. They (Tosfos) connote that if he knew that he will become weak, even if the salted food was not in front of him, the Berachah on the Peros exempts it. The Shulchan Aruch (206:5) connotes like this.

Magen Avraham (215:6): The Shlah says that on Shabbos, one may leave Peros for after the meal in order to bless [also] a Berachah Acharonah. On Shabbos one may cause extra Berachos, in order to complete 100 Berachos. This is difficult, for Yoma 70a discusses Yom Kipur, on which we lack Berachos, and forbade causing extra Berachos! Tosfos (Shabbos 118a DH b'Minchah) forbids breaking the Shabbos morning meal into two, in order to fulfill three meals on Shabbos, due to unnecessary Berachos! We permit this (unlike Tosfos) for the sake of three Shabbos meals, but not for the sake of 100 Berachos! Even during the week, Maharam Galanti permits eating fruits a little at a time, or only after the meal, if he desires this. On Shabbos it is proper to do so for the sake of 100 Berachos. Keneses ha'Gedolah forbids even on Shabbos, even if he told his household not to bring them in front of him during the meal.

Even ha'Ozer (cited in Sha'arei Teshuvah 1): The Yerushalmi (that the Rosh brings) proves that one may leave Peros for after the meal in order to bless on them before and after. This is not considered unnecessary Berachos, since now (if he eats them during the meal) they are exempted through a Berachah that Chachamim did not enact for them. This answers the Magen Avraham's question against the Shlah.

Mishnah Berurah (1): If both foods in a mixture are primary, the majority is the Ikar. Even if each species is by itself and is recognized, we follow the majority. Therefore, on Purim when we take sesame in honey and mix with it ground nuts, if the majority is sesame, we bless Borei Peri ha'Adamah. However, this is only if both of them are important. If one of them is not important, even if it is the majority, it is Batel to the minority. Regarding the five grains, even if they are the minority, if they were added for taste, we follow them and one blesses Borei Minei Mezonos. This is only if there is substance (to the five grains). If one mixed flour in much water, and it is thin enough to drink, one blesses sheha'Kol.

Mishnah Berurah (4): Even if the Tefel was not there when he blessed, if he intended for it when he blessed, or he normally eats the Tefel afterwards, it is exempted. Also, he must eat the Tefel in the same place. He may not change place. If he does not normally eats the Tefel afterwards, and did not explicitly intend for it, he must bless also on the Tefel. However, he blesses only sheha'Kol, like the Rema says below about one who eats the Tefel before the Ikar.

Kaf ha'Chayim (2): If one blessed on the Tefel without intent to exempt the Ikar, if they have different Berachos, he did not exempt it. If they have the same Berachah, he need not bless on the Ikar as long as some of the Tefel is there. If he ate less than a Shi'ur of Ikar and a Shi'ur of Tefel, Meshivas Nefesh says that the bread joins with the fish to a k'Zayis to bless Borei Nefashos Rabos afterwards.

Bi'ur Halachah (DH Im): Derech ha'Chayim says that if two foods are mixed on a plate, Stam, the majority is Ikar. The Chayei Adam says that when two species are separate and recognized, he blesses on each, without concern for the majority or the five grains. It seems that Safek Berachos Lehakel (we do not bless when in Safek). One blesses only on the majority (and Al ha'Michyah afterwards, if he ate a k'Zayis of grain within the time to eat half a loaf, i.e. three or four eggs). Also the Pri Megadim connotes that we follow the majority even when they are separate. I heard people rule like this in the name of a Gaon. One who wants to be concerned for the Chayei Adam can mash the foods so they mix, and bless on the grain or (if there is not one of the five grains) on the majority.