I know that "advice" is uncountable and thus is incompatible with the article "a".
However, the phrase "Just a friendly advice" seems to be rather widespread.
Is it idiomatic, or incorrect? What is a more grammatical form?
If you use an article with advice you have to use a counter:
No one who is competent in English would say
To omit the article, competent speakers would say
Dear reader: I'm going to offer you a little friendly advice. When checking to see if something is "grammatical," do not rely on a Google search. Google will return hits from blogs and message boards, which are not necessarily reliable sources for determining correct English. Google will also return other odd nuggets, such as a fraction of a user's handle. Instead, use Google books, which restricts the search to published works, where the number of results will be a more reliable indicator.
For example, typing "just a friendly advice" into Google returns roughly 1,000,000 hits! Surely one million hits can't be wrong, right? Well, let's look at a few of these (the text I have bolded may help indicate the reliability of the wording):
As for that last one, I'd love to have that guy stop to help me on the side of the road, but I wouldn't want him proofreading my term paper.
Moving the search to Google books cuts the number of results down from roughly a million to a very small handful.
Some may claim there is "nothing wrong" with it; I suppose that would depend on what was meant by "wrong." If I can say, "Just a friendly hint", shouldn't I also be able to say, "Just a friendly advice"? I suppose I could (after all, this writer did); however – discussion board titles notwithstanding – I think most hearers would find it awkward. I'd be more inclined to follow Robusto's guidance, which sounds much more natural to my ear.
On the topic of a friendly advice having 1,070,000 hits - some friendly advice gets 137,000,000 hits. In other words, the 1,070,000 million, despite the impresive number of digits, is a fraction of 1% of the total and therefore 1,070,000 mistakes.
Advice is uncountable, so it should be be "some friendly advice", which is reflected in the Ngram above.
Assuming you meant "grammatical" in its "grammatically correct" form, then... no. It isn't.
Advice is a non-countable noun and, as such, "an advice" is invalid. Injecting the adjective "friendly" does not change that.
Here are some correct equivalents:
The mistake you made, I think, was in trusting a Google hit count to suggest the correctness of an English phrase; a cursory glance across a few arbitrary websites indicates that this is silly.
Just a friendly advice cannot be said to be ungrammatical as advice is sanctioned as being at least pluralisable on occasion by both the AHD and Collins, and definitely count on occasion (sense 3) by Webster's.
It falls quite close, however, to Colourless green ideas sleep furiously - not breaking rules of grammar (unless context forces the usual non-count meaning of advice to be inferred) (which 'friendly' strictly doesn't) - but semantically unacceptable / needing freewheeling looseness in usage.
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