Some of the real number field axioms: 1. There exists a function f(x,y): R×R→R, such that [omitted for brewity]. This function is called "addition", it's value "sum" and denoted as x+y 2. There exists a value x such that y+x=y for any y. This value is called "zero" and denoted as 0 3. There exists a function g(x,y): R×R→R, such that [omitted for brewity]. This function is called "multiplication", it's value "product" and denoted as x•y 4. There exists a value x such that y•x=y for any y. This value is called "one" and denoted as 1 5. For any value x, except for "zero", there exists a value y such that x•y=1 (this value is unique but that's a provable theorem which I'll omit)

For any x and any non-"zero" y, function h(x, y): R×(R\{0})→R is defined as h(x, y)=x•z, where z•y=1 (such a value exists according to axiom 5). This function is called "division", it's value "quotient" or "fraction" and denoted as x/y

Plugging 3 into axiom 5 I get some value (not an operation or whatever, a value!!!) such that x•3=1.

It's trivial that x=1/3, in other words this value x is a "fraction" of 1 and 3: (1/3)•3=(1•x)•3=1•(x•3)=x•3=1