Which is the best reason why 2/5 is the exact quotient for 1/4÷ 5/8 ?

If u do the inverse and switch the 5/8 to 8/5 cause of (KCF- keep change flip) then u would get
[tex] \frac{1}{4} \times \frac{8}{5} [/tex]
Then u would cross divide (basically asking yourself) to find the greatest factor u can multiply with two numbers if u can if u can only find one do one
how many times can 4 go into 4? which is 1
And how many times can 4 go into 8 which is 2 which is
[tex] \frac{1}{1} \times \frac{2}{5} [/tex]