that half of 8.82oz is the amount of additional water to be added
No, that's not quite it. The amount of water added is however much the original amount calls for MINUS half of the amount of 1:1 solution added. Because half of that solution is lye and half is water.
So, as another example.
I had a recipe that called for 8.0 oz water, 4.2 oz lye.
To use my 1:1 lye solution(so half lye, half water), I take a look at the amount of lye required and double it: 4.2x2 = 8.4. So I know that I need to measure out 8.4oz of lye solution in order to meet 4.2oz lye.
With 8.4oz of solution, just as there is half (4.2oz) of lye, so there is water.
I know that my 8.4oz of solution gives me 4.2 oz of water. So to determine how much more water to add, I take the original amount called for: 8.0 oz and subtract the amount of water i know is present in my solution - 4.2
8.0-4.2= 3.8. I need to add 3.8oz to meet the water requirement of 8.0 oz.
So to summarize: I double the amount of lye required to know how much solution to use. 8.4oz of 1:1 lye solution. Then subtract the original amount of lye called for(or, half the amount of solution) from the original water requirement to determine how much extra water/liquid.
8.4oz of solution, and 3.8 oz of water.
You can also check your math by adding together the originally called for amounts of lye and water (8.0 + 4.2 = 12.2) and then add together your calculated amounts of lye solution and additional water (8.4 +3.8=12.2)
Does that help at all (or did i make it worse?
)
I think I see the problem.
@The Efficacious Gentleman wrote
Required water - half of the 50/50 amount
Which I think is being misinterpreted as "Required water EQUALS half of the 50/50 amount", but what is written and meant is "Required(by the recipe) water MINUS half of the 50/50 solution amount." to get the amount of added water.