Adjusted nominator for a more reflective ratio change

Question

Two variables change every year, e.g. $a_1=500$, $a_2=600$ and $b_1=1000$ and $b_2=800$. Their ratio change is $$YoY=a_2/b_2-a_1/b_1=600/800-500/1000=0.25$$ The negative change in the denominator is a negative event and I want to reflect this, so e.g. in the example above $YoY$ is smaller if the change in the denominator is negative and vice versa. One solution I tried was called adjusted nominator: $$YoY=a_2*(b_2/b_1)/b_1$$ With the same values as above, it gives $-0.02$ as a result, which is less then $0.25$, thus it reflects the negative change in the denominator. What are the best tools for this scenario?