I'll use this thread for quick small questions that come up while I'm studying.
is $\displaystyle \frac{b}{b+7}$ the same as $\displaystyle \frac{1}{7}$ ?
NO! IT CAN'T!
That is the conclusion the earlier posts are trying to steer you towards!!
Try putting in some values of b (apart from b = 1). Do you get 1/8?? Answer Plato's question: If b = 2, is $\displaystyle \frac{2}{2+7}$ the same as $\displaystyle \frac{1}{7}$? What about when b = 3? etc.
When you divide the top and bottom of a fraction by something, ALL of the top and ALL of the bottom get divided by that something.
Thanks, that's what I hadn't completely understood, if I divide $\displaystyle \frac{b}{b+7}$ by b, I get $\displaystyle \frac{1}{1+\frac{7}{b}}$, not $\displaystyle \frac{1}{7}$ or $\displaystyle \frac{1}{8}$.
Phew... this got longer than I thought, thank you everybody for the help.