1. He helped Mother wash the dishes.
2. He helped Mother with the dishes.
3. He helped his brother study math.
4. He helped his brother with math.
5. He helped study math.
6. He helped with math.
7. He helped his brother study math.
8. He helped me study math.
9. He helped them study math.
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Are they all grammatical?
Does #5 mean either 7,8,or 9?
Is #6 grammatical?
#5 and #6 are vague. Who did he help? How did he help? The others are excellent.
1. He helped Mother wash the dishes. (Grammatical)
2. He helped Mother with the dishes. (Grammatical)
3. He helped his brother study math. (Grammatical)
4. He helped his brother with math. (Grammatical)
5. He helped study math. (Not grammatical)
6. He helped with math. (Grammatical)
7. He helped his brother study math. (Grammatical)
8. He helped me study math. (Grammatical)
9. He helped them study math. (Grammatical)
Regarding your questions:
- Are they all grammatical?
No, sentence #5 is not grammatical. It is missing an object after the verb "helped." In this case, there is no specific person or group mentioned who is being helped with studying math.
- Does #5 mean either 7, 8, or 9?
No, sentence #5 does not mean any of sentences 7, 8, or 9. Without a specific object, it is unclear who is being helped with studying math. It could be anyone or no one in particular.
- Is #6 grammatical?
Yes, sentence #6 is grammatical. It is a general statement that someone helped with math, without specifying who was helped.