I stumbled upon this blog today, and am pleased that someone out there in cyberspace has tackled this thorny issue.
The blogger says, “What is this sitution (sic) describing? This seems the one most difficult for teachers and students alike. We all know what it means to divide a length into (by?) two pieces, but what sense does it make to divide it into 1/2 a piece.”
The conclusion is: “dividing fractions is simply fractions which have fractions instead of integers in the numerator and denominator.”
Other ways of tackling this include those found at
Do these approaches make it clearer for you?