아이들하고 노는 것이 재미있어요. It is fun to play with kids
Is it also OK to translate it as "playing with kids is fun"?
Actually what I am confused is whether to translate 노는 것 as "to play" or "playing".
Source: Fun Korean
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In Korean, adding -는 것 is a 'nominalisation' (a way of making a 'noun') that still keeps the sense of the action 'happening'.
'To play' in your examples is called the infinitive in English, and 'playing' is called the gerund.
Both of these forms can represent a noun form of a verb that keeps the sense of the action 'happening', so they are both good translations of your example sentence.
In English, the gerund and the infinitive aren't always interchangeable. For example, these have very different meanings:
I stopped to smoke.
I stopped smoking.
however, when used with 'I like', the meaning is usually very similar...
I like to smoke.
I like smoking.
If there's a slight difference in usage in English, it's that the infinitive form is often used when you're being more specific:
I like to smoke illegal drugs when I visit my grandmother.
I like smoking. (in general).
More information on this at http://www.englishpage.com/gerunds/gerund_or_infinitive_same_list.htm
However, when it comes to 'playing with kids', it's harder to imagine that a person would like to do it only in some specific circumstances; usually the opportunity to play with kids would, in itself, represent quite a specific situation. So in your example, I don't think there's much of a difference.