Simple question about averages and proportions/ratios

I'd like to get the global average of 2 numbers in their proportions. How's that possible?

Here is the example of what I want:

a = 3084
a1 = 0.35

b = 2349
b1 = 0.52


I want to get a1 + b1's average based on the ratios we get by:

a + b = 5433

a_percent = 0.567

b_percent = 0.433


So I want to get the average of a1 & b1 based on the ratio of 0.567 : 0.433

If I simply get the average of a1 + b1 then it's going to be 0.435 but it's not calculating the ratios.

Sorry if my description is so basic, I haven't learned anything like this before, so I don't know how to express myself. Just let me know if you need anything else.

$$\text{average}_\text{weighted} =\text{a_percent}\times a_1 + \text{b_percent}\times b_1$$ $$\text{average}_\text{weighted} =0.567\times 0.35 + 0.433\times 0.52 \approx 0.42.$$
Since the relative weights ($$0.567$$ and $$0.433$$) are near $$0.5$$, the weighted average is near the 'normal' average ($$\frac{a_1+b_1}2 = 0.5\times a_1 + 0.5 \times b_1 = 0.435$$).
Since the weight for $$a_1$$ is bigger than $$0.5$$, one would presume that the weigthed average is slightly nearer to $$a_1$$ than the normal average, which is correct.