Question

First, rewrite 9/10 and 23/25 so that they have a common denominator.

Answer 1

The lowest common multiple of 10 and 25 is 50, so set that as the denominator.

9/10=45/50 (multiply by 5)
23/25=46/50 (multiply by 2)

46/50 > 45/50 therefore
23/25 > 9/10.

Hope this helps :)

Answer 2

The cheap answer is, well, all we do is, grab the denominator of one and multiply the other by it, top and bottom, and grab the denominator of the other, and multiply the first one by that one too, that way, both will have the same denominator, and then you can simply check the numerator to see who's larger, let's do so.

$\bf \cfrac{9}{\boxed{10}}\qquad \qquad \cfrac{23}{\boxed{25}} \\\\\\ \cfrac{9\cdot \boxed{25}}{10\cdot \boxed{25}}\implies \cfrac{225}{250}\qquad \qquad \qquad \cfrac{23\boxed{10}}{25\cdot \boxed{10}}\implies \cfrac{230}{250}\\\\ -------------------------------\\\\ \textit{so, which is larger then?}\qquad \cfrac{225}{250}~or~\cfrac{230}{250}?$

surely you can tell.