Can anybody give me give me some idea how to tackle this:
1/ (2/5) - 1/ (2/3)
There is a way to avoid the ":" stuff. Consider the fraction:
$\displaystyle \frac{1}{\frac{2}{5}}$
We need to remove the fraction in the denominator of the "overall" fraction. How would you do this? Well, note that if we multiply $\displaystyle \frac{2}{5}$ by 5 the result is an integer: 2. But what we multiply in the denominator we must also multiply in the numerator. So:
$\displaystyle \frac{1}{\frac{2}{5}} = \frac{1}{\frac{2}{5}} \cdot \frac{5}{5} = \frac{1 \cdot 5}{\frac{2}{5} \cdot 5} = \frac{5}{2}$
(No offense Krizalid. I hate ratio notation with a passion. )
-Dan