PLEASE HELP I have a question regarding scale factors and scale factors in relation to dilations. Why do we multiply for basic scale factor but divide when it comes to dilations? It seems that math should be consistent across all areas, but this is something that does not make sense to me.

For example (this comes straight from the textbook), when working with regular scale factor, if we say that the scale factor of △ABC to △FGH is 2, then we know that we must divide AB by 2 in order to get the length of FG. This means that if AB=6 and the scale factor is 2, then we must divide AB, which is 6, by our scale factor, which is 2. This would give us FG=3.

On the other hand, if we say that a reduction occurs between △ABC and △FGH, then it means that the scale factor for △ABC to △FGH with that exact same triangle (with all of the values we found)'s scale factor would be 1/2, because we would **multiply** AB by 1/2 to get FG.

Why do we do this? Why would math not stay consistent across its entirety? Unless something I've said contradicts the correct way to solve, please don't explain how to find scale factor, as I already know how. It is the lack of consistency that I am curious about! Thank you!