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How would you explain the difference between 'nine cases out of ten' and nine cases of ten'?
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I might say nine cases IN ten, but not OF ten.

That would be the same as OUT OF ten, i.e., 90% of the time.
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OK,GG. Then what is the difference between 'nine out of ten students' and 'nine of ten students'?
I just wouldn't say the latter.

Is this a BrE/AmE difference?
Grammar GeekI just wouldn't say the latter. Is this a BrE/AmE difference?
You wouldn't say it as saying something like 'five of them' when Y in 'X of Y' is an actual number?
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If you want to refer to a percentage, as in "nine ____ ten students interviewed have..." to mean 90%, then I would not use "nine of ten."

If you have a specific group of ten students, and you want to say that nine of those specific ten, then I would say "nine of the ten said..."

I would not say "nine of ten."

Any BrE speakers want to say if "nine of ten" is common there? Or an American from another region?