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He spent one and a half hour / hours taking after his children.
Since one and a half is greater than one you should use the plural hours (pure math).
one (hour) and a half hour.
(one and a half) hours.
Vincent TeoHe spent one and a half hour / hours taking after his children.In the context of your question the only one that sounds right to me is "one and a half hours."
And "taking care of" not "taking after."
Note however that in other contexts "one and a half hour" is correct, as in these examples:
A one and a half-hour narrated sightseeing cruise.
A one and a half hour ride taking in the stillness of the early morning.
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