Math question

Soooooo…

There is a pattern that I want to make, but, I want to use a much finer yarn, and I am going to put a stripe in it, and it’s going to be a v-neck, instead on a scoop, and the v is going to be ribbed. With all of that aside, what kind of math do I do to determine cast on, stitches worked, etc, with the original gauge, and the gauge of the yarn that I want.

Here you go!

If you happen to be math averse, here’s a conversion calculator.