work out (for mathematical calculations) (e.g. The total bill for three people is $60. That works out at $20 each)
work out means develop, progress (e.g. Good luck for the future. I hope everything works out well for you)
work out means do physical exercises (e.g. Jon works out at the gym three times a week)
work something out means calculate, think about a problem and find the answer (e.g. I can’t work it out in my head)
write something down means write something on paper because you may need the information later (e.g. I can’t remember Bob’s address. I wrote it down, but I can’t find it)