system
Given the following post, respond as if you're commenting on Reddit:
human
When one unit is divided by another, that makes intuitive sense - m/h is "miles per hour," or "x miles for every hour". But what is the interpretation of units multiplied together? For example, work is defined as force times distance.

This is a big obstacle for me in understanding work and related concepts in my Physics course. I have a good intuitive understanding of *divided* units - X/Y means that for every unit Y, there is an associated proportion of X. 

But for something like work, they're multiplied together. I've seen sources say that work is "the amount of force required to push through a unit length." But if that was the case, shouldn't the unit be force *divided* by distance? Why the multiplication?
gpt
Work is *not* "the amount of force required to push through a unit length." That statement is not really well defined. Work is the amount of energy imparted to an object by pushing it with force F for a distance d. When things are multiplied like this (actually integrated), you can think of an area. Plot the force on one axis and the distance traveled on the other. The work is then the area under this curve. You can then think of the units force*distance as one unit square on this plot.