Hiw do i use mental math to determine if a ratio is simplified?

See if the top and bottom are both divisible by a common factor.
5/15 can be simplified to 1/3 because the top and bottom are divisible by 5.
If you know your divisibility rules, this should be easy.
Also worth noting: You only need to check if it's divisible by primes. If it's not divisible by 2, it won't be divisible by 4, because 2 is a factor of 4.