Help with errors in a research


New Member
Hi all,
I am new to this forum and I am really glad that I found it. Hope I'll be able to offer some help as well.

My problem is fairly simple, but I couldn't find the answer anywhere and my attempts were very poor.

I am doing analyses on some soil samples and I am getting an analytical error from the mass spec for each sample. for example: 1+/- 0.2.

Now, the problem starts when, in some samples, I need to divide the sample into 2 different portions so I get: Total sample (a+b): 1+/- 0.2, sample b: 0.8+/- 0.4., relative proportion error for b is 0.55+/-0.05, and for a is 0.45+\-0.05
Then, in order to get my final value I need to calculate:
(Value of total sample, a+b)=(value of sample a, this is what I am looking for)*relative proportion(a)(+/-error on the proportion)+(value of sample b)*relative proportion(b)(+/-error on the proportion).

This all mess is happening because I cannot extract some mineral (a) in the soil, and these are the ones I am interested in. So I am left with:
(value of sample a)=(((a+b)+/- error)-((b+/- error)*relative proportion))/(relative proportion(a)(+/-error on the proportion)).

I would like to know how should I calculate the finale error for sample a.

Please let me know if I wasn't clear enough.

Any help will be GREATLY appreciated.