Question

Find the reciprocal of the expression. 10b/2b + 8

Answer 1

Comment
I think you need brackets to clarify what you mean. I think it should be written as 
10b/(2b + 8) 

If that is the case the reciprocal is

(2b + 8)/10b You just turn everything up side down. There are technical ways of doing this, but the easiest way is just to do what I just did. 

Put the numerator in  the denominator,
Put the denominator in the numerator.

You could simplify this a bit.
2b/10b + 8/10b
which reduces further.

1/5 + 4/5b 
Just to make sure you understand where that b is, I will do this in

Latex.$\frac{2b + 8}{10b} = \frac{2b}{10b} + \frac{8}{10b} = \frac{2}{10} + \frac{4}{5b} = \frac{1}{5} + \frac{4}{5b}$

Alternate answer
If you do mean what your wrote then the reciprocal is 2b / 10b + 8 which is 1/5 + 8 = 8 + 0.2 = 8.2 

The 8 has nothing to do with the reciprocal under these conditions.

The answer
I have given you all the choices I can think of without going into decimals. If you have choices, please list them under the comments.