Although of course I have been using division since my elementary years, I still can't out my finger on exactly what division is from a computation standpoint. For example, addition is adding objects (very intuitive), subtraction is adding the additive inverse of an object, and multiplication is adding an object to itself some number of times (again, fairly intuitive); however, I can't really explain what division is. I know that it is the inverse operation of multiplication, but it doesn't seem to be related to it in any intuitive way. I have tried to look up definitions of arithmetic division, but that just seems to add to my lack of understanding. There are definitions which relate to partitioning, there is a quotative definition, and there is a definition which says, "multiplication is the operation of ascertaining how many times one quantity is contained in another (Dictionary.com). In addition, I have no idea how division is used in other applications, such as ratios, proportionality, percentages etc. I don't completely understand how division is used to compare relative quantities, i.e. ratios. All of this said, it would be nice if somebody could give me an intuitive definition for division, how to compute it, along with how this definition fits into the notions of fractions and ratios.