If I examine what you said they do understand [transforming a=bc] and don't understand [transforming a=b/c] I suspect they don't have a good understanding and skills of fractions. Transforming the first doesn't require understanding of fractions and operations with fractions, while transforming the second type does.
Basically it's just a mnemonic to remember how to multiply binomials in a bit different order that one would usually do.
I think there's no need to teach FOIL. If they know the distributive property, they can learn multiplication of polynomials easily. Then they have to gather similar terms, but that's simple as well. It's basically just accounting. The FOIL method though, is not scalable to more than binomials and thus not a good way to teach multiplication of polynomials.
> For example, if we have (simple) formula > a = b/c > and if we want to find formula for "c" > then > I would (in my mind) move "c" from denominator (from the right side) > into multiplication with "a" (onto left side) AND > I would move "a" from multiplication (from the left side) into > denominator (onto right side). > So, I get c = b/a . > Actually, "c" and "a" changed their positions. > > When I try to explain it to my kids, they become confused complitely > (7th grade)!! > Some of you said that your kids can accept it. How old are they? > > In the other hand, > if we want to find formula for "b" (in upper example a=b/c), > we should just to move "c" (as I described before) > and then to change both sides of formula, > so we get > b = ac . > > These two methods haven't got equivalent steps, and it confuses kids > as well. > > But, transforming formulas like a=bc is easy for them - they know > to move "b" and "c" correctly, that is they remember to put them into > denominator.