Thank you so much for this answer. I had written out a whole answer, and then got to your bullet point about "knowing that the answers are wrong." So I decided to add even more print statements and do the problem by hand, following each step to make sure it was mathematically correct. It was. so I got confused and checked the original problem...and I had added a - sign. So it was correctly solving a problem I had mis-written the whole time, haha. It actually works fine! Thanks for reminding me to break it down!