Which is the best reason why 3/5 is the exact quotient for 1/2 divided by 5/6

So when ur trying to divide fractions that can't really "happen" for one u may not get the correct answer so u (KCF) which would mean "keep change flip" so this is what u should get

See what we did there? We switch the second fraction and instead of division we did multiplication so then if u multiply across you should get

Then find the greatest common factor which is 2 then divide both of them by two straight across then u would get

Cause 6 divided by 2 =3
And 10 ÷2 =5