For example,

If I needed to generate a random number. I use a good source of entropy to generate r.

Then I add values a, b and c whom are generated from bad entropy such that new entropy = r + a + b + c

How would the overall entropy look like?

The plus sign means to add and not concatenate. I believe that if we concatenated, then this would lead to an overall bad entropy because if we assume that each a,b,c,r each contribute 64 bits to 256 bits of entropy. We would in reality only have 64 bits of good entropy from r. This is my intuition with concatenation.