how to teach reduce terms

When my child try  reduce 99/141, bigger number easily cause calculation mistake, she thinks she could not divide by 3. I think it could be very beneficial if she know Divisibility rule.

http://en.wikipedia.org/wiki/Divisibility_rule
You don't need teach all numbers, only prime number less than 20, which is 2, 3, 5, 7, 11, 13, 17, 19
Any idea to make problem easily done?