Maths help required for a 100% book

If you work out the book percentage you have (1/8)*100 + (1/1.08)*100 = 12.5 + 92.59259
                                                          = 105.09259%

100% to 105.09259% is an increase of 1.0509259


So 8.0 * 1.0509259 = 8.4074072

and  1.08 * 1.0509259 = 1.135

I think that bottom part is wrong. Think you have to change the 8.0 to a fraction then multiply by 1.0509259. Increasing odds like this is not something I've had to do before.