1. When he was ten, he went abroad.

2. When he was ten years ago, he went abroad.
3. When he was ten years, he went abroad.
4. At the age of ten, he went abroad.
5. At age ten, he went abroad.
5-1. At aged ten, he went abroad.
6. At ten, he went abroad.
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Are they all grammatical? Which ones are ungrammatical? Do you have some other expressions which can be used commonly? Thnak you.

2 does not make sense, but all the others are grammatical. 3 is grammatical, but we would say "ten years old" or "ten years of age", not just "ten years". 2 is wrong. When he was ten years ago? That would be 2005??? If you mean "ten years age", it's still something that we would not say. It should be "ten years of age".

Out of the options you provided, numbers 1, 4, and 6 are grammatically correct, while numbers 2, 3, 5, and 5-1 are ungrammatical.

1. When he was ten, he went abroad. (grammatical)
2. When he was ten years ago, he went abroad. (ungrammatical - 'ten years ago' should be used as an adverbial phrase, not an adjective phrase modifying 'he')
3. When he was ten years, he went abroad. (ungrammatical - 'ten years' should be followed by 'old' or 'of age' to make it clear it refers to the person)
4. At the age of ten, he went abroad. (grammatical)
5. At age ten, he went abroad. (ungrammatical - 'age' is singular and doesn't require an 's' after 'at')
5-1. At aged ten, he went abroad. (ungrammatical - 'aged' is not used to describe age in this context)
6. At ten, he went abroad. (grammatical)

In addition to the options you provided, here are a few more expressions that can be used commonly:

- When he was ten years old, he went abroad.
- He went abroad when he was ten.
- He traveled abroad at the age of ten.
- He took a trip overseas at age ten.

These expressions are all grammatically correct and convey the same meaning.