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As far as I understand the scentence below it means that it is necessary to take a break after 15 miutes of using a smartphone and other similar devices.

But with what purpose is 家 used there?

スマートフォンなどを15分使ったあとは休むとで決めることが必要です。

4

The meaning of "家で" here is as simple as "at home". It might also have the nuance of "in a family".

It seems that the sentence is on the context of discipline of children. Here "決める" is "make it a rule" rather than simply "decide". So "家で決める" is "make it a rule at home"; that is, "make it a rule as a part of home discipline".

So the whole sentence is advising us to teach children to take a break after 15 minutes of using a smartphone.

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