Maintain relationship between two numbers, when their sum equals 1

Question

I have a question that I hope won't seem too silly.

I have four numbers that add up to one: A= 0.4 B= 0.3 C= 0.15 D= 0.15

Now, assume that numbers C and D are removed and that I want to maintain the same ratio between numbers A and B and have them add up to 1. In other words, I need to find a way of maintaining the relationship between A and B but increase them both so that A+B=1 as opposed to A+B=0.7 as it is when I remove numbers C and D.

I think it involves exponential functions but I can't figure out the mechanics exactly. Any help would be greatly appreciated.

Thank you!

Answer 1

If you want to maintain the ratio $\frac BA$ and make them sum to $1$, you multiply them by $\frac 1{1-C-D}$