I tried to decipher something like this once. I actually discovered ways, theoretically, in which 1+1=1, 1+1>2, and 1+1<1.
Ignoring volume, when you mix two liquids, a new, singular liquid is formed. To demonstarte, take yellow-dyed water and mix it with blue-dyed water. If all variables are in correct proportion, you will then have green-dyed water. 1+1=1.
In the above case, when looking at volume, you would naturally see that 1unit+1unit=2units. However, due to chemical imbalances, there are times when the volume may remain constant, so again 1+1=1. Atomically, however, there are gaseous byproducts created, due to conservation of mass. In fact, there might be several byproducts, whereas 1+1=1+G1+G2... and thus, 1+1>2.
I got to thinking about genetics in my contemplations. 1 male + 1 female = 1 child. Really, though, it's 1 sperm + 1 egg = 1 zygote, and, on the microscopic level, 1/2+1/2=1, or 1+1=2.
In Downs Syndrome, however, the equation is as such: 23/46+24/46=1 human, so, 47/46=1. Additionally, one might consider how the Downs individual might be deficient in certain ways (physical development, mental capacity) so that 23/46+24/46<1, which would mean 47/46<1. In a sense, the simplified math of male+female=child would equate to 1+1<1, as the child is less than the parents involved.
This is where I ended my inquiry, however, as the idea of a "fractional person" sounded too macabre and much like Jim Crow laws or Nazi propaganda.
Any further thoughts from the peanut gallery?