1. I got up early getting ready for the game.
2. I got up early while I was getting ready for the game.
(Is #1 grammatical? Does #2 mean #1?)
3. I helped my friends with teaching them math.
(What about this one? Is this also grammatical?)
4. Eating vegetables is good for you.
5. Eating vegetables and eating fruit are good for you.
(Do we have to use 'is' or 'are'?)
6. I'm sorry that I am late.
7. I'm sorry for being late.
8. I'm sorry that he is late.
9. I'm sorry for his being late.
10. I'm sorry that he was late.
11. I'm sorry for his having been late.
(Is each pair the same and grammatical?)
Rather than have some form of the word "get" in a sentence twice, here's a rephrasing for 1 and 2:
I woke up early to get ready for the game.
3 -- I helped my friends by teaching them math.
4 and 5 -- You have #4 right. #5 should also have "is" instead of "are." The subject is "eating" which is singular.
6 - 11 are all correct, and yes, each pair means the same thing. The phrasing in #11 is rather awkward, though, and rarely used.
Thank you.
3. I helped my friends with teaching them math.
(Is this one ungrammatical?)
It's not ungrammatical; it's just not the correct preposition to use in that phrasing.
You could also say, "I helped my friends with their math." That would mean the same thing, but with slightly different words.
1. Yes, sentence #1 is grammatical. It is a complete and coherent sentence.
2. Sentence #2 is also grammatical. However, it conveys a slightly different meaning than sentence #1. In sentence #2, the phrase "while I was getting ready for the game" suggests that the action of getting up early and getting ready for the game happened simultaneously.
3. The sentence "I helped my friends with teaching them math" is not grammatical. To correct it, you could say "I helped my friends by teaching them math" or "I helped my friends with their math lessons."
4. Both sentences #4 and #5 are grammatical. The choice between "is" and "are" depends on the subject of the sentence. In sentence #4, where "eating vegetables" is the subject, you use "is" because "eating vegetables" is singular. In sentence #5, "eating vegetables and eating fruit" is plural, so you use "are."
6. Both sentences #6 and #7 are grammatical and convey a similar meaning. They are both examples of expressing an apology for one's lateness.
8. Both sentences #8 and #9 are grammatical and convey the same meaning. They both express an apology on behalf of someone else for their lateness.
10. Both sentences #10 and #11 are grammatical and convey a similar meaning. They both express a sense of apology for someone else's past lateness.
It is worth noting that although the pairs in 6-7, 8-9, and 10-11 have similar meanings, the use of "that" versus "for" in each pair can slightly affect the tone and emphasis of the sentence.