I don't think that's right, because simplifying means that you just make the number or equation or whatever it is simpler, it shouldn't change the value of the "thing" being simplified.
For example, the exact value of your original problem was (approximately):
(5 * sqrt(13)) / (25) = 0.7211
after you "simplified" it, you got:
(5 * sqrt(13)) / (5) = 3.605
clearly, you must not have simplified correctly, because the two values aren't the same. I'm not sure what the "quotient property" is, but I do know you can simplify the 5/25 in your problem to 1/5, because both values equal 0.2! So, if you simplified it, you would get:
(sqrt(13)) / (5) , which equals: 0.7211 - meaning you simplified correctly!
http://tinyurl.com/2l9oql
Try simplifying these (to fractions, not decimals):
5/25
3/9
6/24
72/81
1/4
6/3
Hope this helps and that I didn't give you any wrong information!