Question: I can't remember when and where I had this discussion, but I remember being corrected when I was speaking by a stranger saying that it is never correct to say *give me half of this*; instead, the grammatically correct phrase would be *give me one half of this*. I've never been a pro at where numbers fit in with the English language, so maybe someone here could shed some light on this.

Answer: 
It is perfectly acceptable to say "give me half of that". In English, "half" in understood on its own to mean "[one of two equal parts of something](http://www.merriam-webster.com/dictionary/half "Half - Definition, Merriam-Webster Dictionary\"")".

To put it another way:

* It would make no sense to say "give me no halves of that". You would just say "give me none of that".
* It would make no sense to say "give me two halves of that". You would just say "give me all of that".

Saying "give me one half of that" is redundant. It's equivalent to saying "give me one of one of those two equal parts of that."
You don't need the 'one' in expressions like 'give me half a cookie'. Where you do need the 'one' is in when units of measurement are involved, like "please give me one half pound of sugar". You can use 'a' instead of 'one', but leaving out any determiner is wrong.

Correct:

> 
> Give me one half pound of sugar.  
> 
>  Give me a half pound of sugar.  
> 
>  Give me half a pound of sugar. 
> 
> 
> 

Wrong:

> 
> \*Give me half pound of sugar.  
> 
>  \*Give me one half a pound of sugar.  
> 
>  ?Give me a half a pound of sugar. 
> 
> 
> 

(You do hear the last quite a bit in the U.S., although not in England; this came up in [another question](https://english.stackexchange.com/questions/43294/a-half-a-cup-of-something) here.)