1. She want___ play the piano on the party. 2. We can___ speak English and German. 3. You have___ work hard because you want_ be rich. 4. I want___ travel around the world. 5. The students should _ study very well to be professionals. 6. May I___ come in? 7. They heard _ her words. 8. He would rather find another trip, because this one is not interesting. 9. He did not want___ play tennis any more. 10. Would you like ___ try my apple pie 11. I’ve decided ... start a new project. 12. She is trying ... learn Italian. 13. Can you ... lend me your dictionary, please? 14. Mother forgot ... book the tickets. 15. You shouldn’t ... argue with your father. 16. Henry promised ... help her. 17. This old photograph made me ... cry. 18. I really hope ... get an interesting job soon. 19. You must ... pay for the service. 20. Let me ... introduce myself.

1. She wants to play the piano at the party.
Explanation: The word "want" requires the base form of the verb after it, so it should be "wants." Additionally, the word "to" is required before the verb in this case, so it should be "to play."

2. We can speak English and German.
Explanation: The word "can" doesn't require any additional words before the verb, so it remains as "can" here.

3. You have to work hard because you want to be rich.
Explanation: The word "have" requires the preposition "to" before the verb in this case, so it should be "have to." The word "want" also requires the preposition "to" before the verb, so it should be "want to."

4. I want to travel around the world.
Explanation: The word "want" requires the preposition "to" before the verb, so it should be "want to."

5. The students should study very well to be professionals.
Explanation: The word "should" doesn't require any additional words before the verb, so it remains as "should" here.

6. May I come in?
Explanation: This sentence is grammatically correct as it is.

7. They heard her words.
Explanation: This sentence is grammatically correct as it is.

8. He would rather find another trip because this one is not interesting.
Explanation: The phrase "would rather" requires the base form of the verb after it, so it should be "find." Additionally, the word "because" is used to join clauses, so it should be placed before "would rather" to form a complete sentence. Therefore, the correct sentence would be "He would rather find another trip because this one is not interesting."

9. He did not want to play tennis anymore.
Explanation: The word "want" requires the preposition "to" before the verb, so it should be "want to." The word "anymore" should be written as one word to indicate "not anymore" in this context.

10. Would you like to try my apple pie?
Explanation: The word "like" requires the preposition "to" before the verb, so it should be "like to."

11. I've decided to start a new project.
Explanation: The word "decided" requires the preposition "to" before the verb, so it should be "decided to."

12. She is trying to learn Italian.
Explanation: The word "trying" requires the preposition "to" before the verb, so it should be "trying to."

13. Can you lend me your dictionary, please?
Explanation: This sentence is grammatically correct as it is.

14. Mother forgot to book the tickets.
Explanation: The word "forgot" requires the preposition "to" before the verb, so it should be "forgot to."

15. You shouldn't argue with your father.
Explanation: The word "shouldn't" doesn't require any additional words before the verb, so it remains as "shouldn't" here.

16. Henry promised to help her.
Explanation: The word "promised" requires the preposition "to" before the verb, so it should be "promised to."

17. This old photograph made me cry.
Explanation: This sentence is grammatically correct as it is.

18. I really hope to get an interesting job soon.
Explanation: The word "hope" requires the preposition "to" before the verb, so it should be "hope to."

19. You must pay for the service.
Explanation: This sentence is grammatically correct as it is.

20. Let me introduce myself.
Explanation: This sentence is grammatically correct as it is.