I guess it is saying that people are going straight to the "trick" (multiply the reciprocal) instead of understanding that they are applying the fact that: a /

I guess it is saying that people are going straight to the "trick" (multiply the reciprocal) instead of understanding that they are applying the fact that: a / (b/c) = a * (c / b) (a in Q, b,c in N and b <> 0) And that they therefore have a less rich understanding of when the rule is applicable and when it isn't appropriate. (Such as a situation where b is actually zero, perhaps if it's "hidden" in another form like x-y.