9/10 - 5/8?

In order to add or subtract two fractions, we have to find a common denominator. A common multiple of 10 and 8 is 40. 10 x 4 = 40 and 8 x 5 = 40.
But it will do us no good to just multiply the denominators with 4 or 5 respectively. We have to expand the fraction, multiplying nominator AND denominator:
((9 x 4) / (10 x 4)) - ((5 x 5) / (8 x 5))
We multiply the fraction with a handy "1" which is the neutral element of multiplication and thus doesn't change the value though changing the form:
((9 / 10) x (4 / 4)) - ((5 / 8) x (5 / 5))
We get:
(36 / 40) - (25 / 40) = 11 / 40

And we're done. As 11 is a Prime Number and not a factor of 40, we cannot cancel the fraction further. We can, however, calculate the proper decimal fraction and get 0.275

That's it.