To teach you that whoever prays for mercy for another... You might ask: How does this prove it? Perhaps she was remembered now because this was the time Hashem set. She needed to give birth on Pesach, and she was remembered on Rosh Hashanah, so it had to be now. The answer is: Rashi himself answered this when he wrote, “He had already remembered her before He cured Avimelech.” And what is the verse teaching us by saying that Hashem cured Sarah first? Perforce, “To teach you that whoever prays for mercy for another...” (Re’m) The Re’m objects: Rashi implies that this section is out of place, for he says, “This section was placed here to teach you...” But this is not so, for on the fifteenth of Nisan the angel foretold to Sarah, and on the sixteenth, Sedom was overturned and Lot was rescued with his daughters. And right after the incident of Lot with his daughters, Avraham traveled to reside in Gerar, where Sarah was taken and Hashem restrained every womb of Avimelech’s house, whereupon Avraham prayed for them and they were cured. And on Rosh Hashanah, Sarah was remembered. Everything is in chronological order! He answers: וה' פקד implies He remembered her before He cured Avimelech. [Had Sarah conceived after, it would say ויפקוד ה'.] Thus, Avimelech’s curing should not have been written before. And why was it? In order “to teach you that whoever prays for mercy for another...”

To Avraham. Not to Sarah, as it says nowhere that Hashem spoke to her [about this]. The Re’m asks: Why did Rashi not explain that also Hashem’s saying was to Avraham and not to Sarah? He answers: Perhaps because it is written there (17:19), “God said, ‘Indeed your wife Sarah will bear you a son,’” [so it is obvious] that this was said to Avraham; Rashi did not need to explain it. And Rashi did not need to explain it even for Hashem’s speaking, since it is written there (15:1), “The word of Adonoy came to Avram.” Rather, Rashi comes to tell us the difference between “Hashem did for Sarah as He had spoken,” and “At the designated time that Elokim had spoken” (v. 2). The former refers to Avraham, while the latter refers to [His declaration of] the designated time, as Rashi explains there. You might ask: Why does Rashi explain this? The answer is: Rashi means that Hashem said only to Avraham, “That one [Yishmael] will not be your heir” (15:4), and never promised that the heir will come from Sarah. Nevertheless, “Hashem did for Sarah,” although He had spoken only to Avraham. (Maharshal)

The designated time that He spoke... Rashi is answering the question: Why is it written אֹתו? It should be vowelized אִתו, since it was spoken to Avraham. Therefore Rashi explains that אֹתו refers to the designated time. And since it cannot be said that one “speaks” a time, Rashi needed to add the phrase “and set” so that the speaking refers to the setting of the designated time.

An expression of praise and esteem... [Rashi is saying] that the word מי is similar to the word מה, which infers greatness and honor, such as (Tehillim 31:20): “How (מה) great is Your goodness!” and (ibid. 92:6): “How (מה) great are Your works!” (Re’m) But it seems to me that [Rashi explained as he did] because if the verse follows its plain meaning, why did Sarah ask, “Who said to Avraham?” Hashem clearly said it to him! Perforce, it is “An expression of praise...”

After he was twenty-four months old. [Rashi knows this because otherwise] it should have written ותגמל (she weaned him). Perforce, ויגמל means the child weaned himself. [And Rashi deduced that this happened] because he was twenty-four months old, when a child rejects his mother’s milk and stops nursing. (Maharshal)

Because the great people of the time were there... Re’m explains that [Rashi knows this because] for a prophet [such as Avraham, unlike for a king such as Achashveirosh,] it makes no difference if his feast was great in its number of days or guests. Perforce, it means that the world’s great people were there.

And make sport before us... [Rashi brings all three explanations] because if Scripture meant only one, Scripture should have stated it expressly. Perforce, the general term מצחק was used to refer to all of them. (R. Meir Stern) Re’m asks: When Hashem asked, “What is Yishmael now, righteous or wicked?” the angels responded: “He is righteous” (see Rashi on v. 17). But according to Rashi here, on the contrary, Yishmael was exceptionally wicked! Re’m answers: Hashem was asking only about the particular sin for which the angels were condemning him [i.e., killing the Jews through thirst]. And similarly Yishmael was not judged as a בן סורר ומורה [who is killed for his future sins] because a בן סורר ומורה has already become involved in activities leading to his eventual death penalty, whereas Yishmael did not as yet do anything to deserve to die of thirst.

That he is my son even if he were not as deserving as Yitzchok... [Rashi knows this] because otherwise, why does it say עם twice? It should say: עם בני יצחק. Perforce, it means that being “my son” is reason enough to exclude Yishmael from the inheritance, as is being “Yitzchok,” each on its own. [Rashi considered this explanation] preferable to that of Targum Yonasan. (R. Meir Stern)

For he heard that he fell into bad ways. Rashi brings both the Midrashic and the simple explanation because with the simple explanation alone, a question arises: In v. 12, Hashem tells Avraham, “Do not consider this wrong on account of the boy and your slave-woman.” This implies that Avraham was perturbed also about his slave-woman. So why does our verse mention only “his son”? Thus Rashi explains our verse [Midrashically,] that Yishmael fell into bad ways—something not relevant to Avraham’s slave-woman. But without the simple explanation, another question arises: [Since Avraham was not perturbed about sending Yishmael away,] why does Hashem then say to Avraham in v. 12: “Do not consider this wrong... regarding all that Sarah tells you, listen to her...”? What does listening to Sarah have to do with Yishmael’s fall into bad ways? Furthermore, the reason that Scripture then gives, “For only through Yitzchok will seed be considered yours,” is irrelevant to Avraham’s concern over Yishmael’s falling into bad ways. This is why Rashi needed the simple explanation as well. It seems that [Rashi learned] the two explanations from על אודות בנו, for it appears to be repetitious. Since אודות means the same as על, why say על twice? It could have simply said על בנו, as in the next verse: אל ירע ... על הנער. Perforce, it comes to tell us that Avraham was perturbed about two things. But only for sending them away did Hashem say (v. 12), “Do not consider this wrong...” (R. Meir Stern)

To the voice of prophecy that was within her. [Note: although this phrase is absent from our version of Rashi here, it parallels an extant comment of Rashi on 16:2.] Rashi deduced this because it could have said, “Listen to her words,” as it said before, “Regarding all that Sarah tells you.” Or [it could have said] שמע אליה, as in (Devarim 11:13): והיה אם שמוע תשמעו אל מצותי. Furthermore, a voice without words is just a meaningless sound. How could Avraham be told to obey a mere sound? Thus Rashi explains that it means the voice of prophecy. I.e., she did not say it on her own; it was the voice of prophecy. The expression יצאה בת קול is somewhat similar to this. And for this reason, כי שמעת לקול אשתך (3:17), written concerning Adam HaRishon, is interpreted in Bereishis Rabba 19:5 to mean that she was wailing over him with her voice. (R. Meir Stern)

But no silver and gold because he despised him... But according to the simple explanation [see Rashi on v. 11] he did not fall into bad ways. Why did Avraham not give him silver and gold? An answer is: Avraham assumed that shortly, after Sarah’s anger subsides, he will bring him back. (Maharshal) But according to R. Meir Stern’s explanation on v. 11, the question does not arise, because the simple explanation does not conflict with the Midrash. Both are needed; see there. Furthermore, Maharshal’s answer cannot be correct. For if it was, Rashi himself should have explained thusly, that Avraham intended to bring him back—as this would satisfy both the simple explanation and the Midrash. Rashi should not have given a reason that satisfies only the Midrash.

He also placed the child on her shoulder... ואת הילד refers to what immediately preceded [שם על שכמה] rather than to ויתן אל הגר. [Rashi knows this] because if Avraham did not place the child on her shoulder, Scripture should state that she picked him up before saying, “And she threw the lad...”

She returned to her family’s idolatry. Rashi deduced this because ותלך connotes going along deliberately and willingly, as הליכה always means. Yet then it says ותתע, connoting that she did not know where she was going, as she lost her way in the desert. One term contradicts the other. And we cannot say that at first she knew where she was going but then lost her way, because why should Scripture tell us she went deliberately? It is obvious that she went where she was going before she lost her way! Furthermore, the verse’s intent is to recount how she lost her way in the desert and therefore had no water, etc. There is no reason to say she went deliberately on the way. Therefore Rashi explains that her ותתע was deliberate, and that is why it says ותלך ותתע — she deliberately went astray. How? She returned to her family’s idolatry. Rashi explained ותתע as idolatry, based on ויהי כאשר התעו אותי (20:13), translated by Onkelos as: “When the nations went astray after idolatry.” (R. Meir Stern)

Because the sick drink a great deal. Rashi deduced this because it should have said, The bread and the water were wused up.” For it said before, “He took bread and a skin pouch of water,” and Avraham assumedly gave them food and drink proportionally, so both should have finished together. Thus Rashi explains that Scripture is telling us that Yishmael drank disproportionately to his eating, as the sick drink a great deal, and that is why it says, “The water was used up,” but not the bread. (R. Meir Stern) But it seems to me that Rashi knows this because it does not say, “And they had no more water to drink.” The expression “the water was used up” implies that it happened unexpectedly, ahead of time. (Nachalas Yaakov)

From afar. Here, נגד does not follow its simple meaning (“in front of”) for if so, why would Scripture need to tell us this? But it is understandable if it means “from afar,” because the verse goes on to give a reason: “She said, ‘Let me not see the lad die.’” We find נגד meaning “in front of,” as in (Tehillim 16:8): “I have placed Hashem in front of me (לנגדי) constantly,” where it has the connotation of closeness. Yet in our verse, following נגד comes the word הרחק, meaning “distant,” one term contradicting the other. Therefore, Rashi explains that מִנגד means the opposite of נגד. It is like saying מִן נגד, the prefix מִ is like מִן. It conveys that she did not sit close, in front of the child. She sat from afar, about two bow-shots away.

The prayer of the sick person is more effective than the prayers of others... Rashi is answering the question: Hagar also cried, as it is written (v. 16), “She wept in a loud voice.” Why did Hashem not hear her voice? [You might object:] The Gemara asks in Berachos 5b, “Why was R. Yochanan unable to heal himself [through prayer]?” and answers, “A prisoner cannot free himself from jail.” The reason must be that R. Yochanan was not able to concentrate [in prayer]. But if he were able to do so, his own prayer would be better. (Re’m)

He is judged according to his present deeds... The question this raises on בן סורר ומורה, who is killed for his future sins (Sanhedrin 71b), will be answered in Parshas Ki Teitzei (Devarim 21:18). Re’m asks: Why did the angels not condemn him for the sins he already did, rather than for those of the future which will be done not by him but by his descendants? He answers: Perhaps this Aggadah is according to R. Shimon, who differs with R. Akiva and all those who interpret מצחק (v. 9) as speaking of [Yishmael’s] misdeeds. But to answer that the Aggados are in disagreement seems to me forced, unless we see clearly that it is so. Thus it seems the answer is: The angels could not condemn Yishmael for his present deeds because the Heavenly Court punishes only from the age of twenty, and Yishmael was just seventeen. [You might ask:] Why did they not condemn him for his present deeds, but in terms of the future [when he will be of punishable age]? The answer is: At the end of his life he repented for his present deeds, as Rashi explains on (25:9): “His sons Yitzchok and Yishmael buried him [Avraham].”

One whose descendants will eventually kill Your children with thirst, You will provide for him a well? You might ask: Is it not written (Devarim 24:16), “Fathers shall not be put to death because of sons”? The answer is: Hashem asked the angels if Yishmael had sinned through water. Regarding water, was he righteous or wicked? They answered he was righteous regarding water but was otherwise wicked, and moreover, “His descendants will kill Your children with thirst. Will You then provide him a well?” Hashem answered: “Since now he is righteous regarding water, I will provide him the well.” (Maharshal)

The feminine form for “witness”... Rashi is explaining that לעדה means “witness” (עדות), not “congregation” (עדה). And it is written לעדה rather than לעד because עדה is the feminine form of עד.

They agreed among themselves that whoever appears at the well... [Rashi knows this] because otherwise, how did Avraham prove it [that he dug the well]? It could not have been through actual witnesses, for if Avraham’s servants had actual witnesses, why did they not make a legal claim before Avimelech?

That year preceded the binding of Yitzchok by twelve years. Rashi was brought to explain this due to the following verse, “After (אחר) these events,” which [ostensibly] means right after, since אחר always implies right after—as Rashi commented earlier on 15:1. Yet the binding of Yitzchok was 12 years later, so why does it say אחר? Thus Rashi explains (on the following verse) that it means “After the words of Satan,” not after the just-mentioned events of Avraham and Avimelech.