杰克喜欢和他的同学打羽毛球用英文怎么说？

Jack likes to play badminton with his classmates.

注意一下，原句中虽然没明说“一起”，但中文语境里“和他的同学打”通常隐含集体活动，所以翻译加上 "together" 或者保留 "with his classmates" 都能传达这个意思。不过严格来说，Jack likes to play badminton with his classmates. 是最地道且准确的表达，不需要强行加 together，语感更自然。

语法完全正确，不过口语中常说 play badminton with his friends/classmates，用 classmates 稍显正式，日常聊天用 friends 更自然。

翻译没问题，不过更地道的说法其实是用 "badminton buddies" 或者直接说 "play badminton with his classmates"。另外注意 likes 后面接 to play 或 playing 都可以，但 to play 更偏向习惯性动作，playing 更强调享受过程，看你想表达哪种 nuance。

这个翻译没问题。不过平时口语里说 classmates 也可以直接说 friends 或者 pals，显得更亲切自然一些。

这句话没问题，不过口语里有时也会说 Jack enjoys playing badminton with his classmates.