Can infinity be divided by anything? I'm in ninth grade and I've been thinking about this for a while. It's related to a question that came to my mind, namely which is the highest number you can divide 11 by. Is "infinite" a number and is it the highest number by which 11 can divide it?
Thinking and playing with infinity is a popular thing to do, especially for people your age.  To do so correctly however, you need to understand what we actually mean by infinity and what we mean by a "number."

Note: For the remainder of this post, by "division" and "divided by" I will be referring to the usual division operator rather than the related concepts from number theory.

Infinity is not a "real number" (that is not to say it doesn't exist in some contexts, but it does not belong to the set of numbers known as 'the real numbers') so we are not even allowed to refer to operations involving infinity.  It just flat out doesn't make sense in this context.  There is no largest "real number" and so there is no "highest (real) number" that $11$ can be divided by.

Since you are talking about "dividing by infinity" then you are probably working in the extended real numbers rather than the real numbers.  In such a context, yes infinity is the "largest" extended real number and $11$ can indeed be divided by it.  In fact, every real number when treated as an extended real number instead can be divided by infinty and the result would be zero.  In that context, yes... you are correct.

The extended real numbers however is not the usual context to be working in.  If the question was asked "does there exist a largest number that $11$ can be divided by" without any additional clarification about context then the answer would be no.

(Note: infinity and negative infinity can not be divided by infinity)
It is really great to be thinking of stuff like this.  

You will find people all around you who will say infinity is not a number and they will stop there, but there are a set of math classes in your future (Calculus) that are all about dealing with numbers that are virtually infinite--they call them limits.

All those people who say that it's absolutely impossible to deal with infinity will find it perfectly fine to deal with "x as x approaches infinity" and you get the same results you would intuit for infinity (Division by infinity is still a bit tricky if I recall correctly)

Anyway, if you have ever noticed that math is often about describing things, calculus is how you describe strange (arbitrary) curves and such--Exactly how much water fits into your strangely shaped sink, or how long will it take to drain said water since the speed it drains is slower as there is less water in the sink.  

This kind of thing is calculated by slicing up curves into infinitely (Approaching infinite anyway) thin slices and adding the slices together to get an exact result.

(PS, I haven't done much calculus in decades, if this is factually wrong please feel free to fix it rather than just blindly downvoting.  Thanks)