Are all integers fractions? In a college class I was asked this question on a quiz in regards to sets:

All integers are fractions. T/F.

I answered False because if an integer is written in fraction notation it is then classified as a rational number. The teacher said the answer was True and gave me the link http://www.purplemath.com/modules/numtypes.htm. As a teacher of mathematics in the K-12 system I have always taught that integers were all whole numbers above and below zero, and including zero. All of the resources I have used agree to my definition. Please clarify this for me.
What is the truth, or are she and I just mincing words?

I think you have a case to take to the teacher on this based on the teacher's use of the word "fraction" instead of "rational number". All integers are rational numbers also, everyone agrees (or should agree) on that. That is because all integers can be expressed as a ratio of integers. So here's the case: 

Is $3$ a binary number?

I'd be surprised if too many people say "yes" to that question. Note that even though $3$ can be expressed as a binary number ($11$), we don't call it a "binary number" unless it is expressed as one.
Similarly, even though every integer can be expressed as a fraction (of integers, even), even mathematicians are likely to agree (for consistency's sake at least) that an integer is not itself a fraction even if it is always a rational number.
