What do you mean by a/b? (a divides b)

[Guest]

So in my class they thought us a/b meant that b=k.a
Where a , b were integers . But when it comes to take examples they take examples like 2/6 . But when I ask the internet in some parts they told that the true meaning is that when a/b, the remainder must be zero .

So I tried this to a basic property ( ie) if a/b and a/c then a/(b+c)
So I took 'a' as 100 and b as 2 ,
But my teacher said it was wrong
Because there is no integer k such that 100= (k)2
But in common language , like in calculators the answer will be a 50 which is a integer! Am I getting the concept wrong?
PLEASE HELP!