For starters, you need to emphasise that division does NOT mean "splitting into equal smaller pieces". They will be expecting to get smaller numbers, so will be surprised when they get an answer for .
You need to emphasise that division mean "how much" or "how many".
So means "How many quarters in 2?" In other words, .
means "How much of a half is in a quarter?" In other words, .
Then you can get them to estimate an answer for harder questions, like , before formalising with "stay, change, flip".
And when you want to formalise, here is a proof...
Suppose you knew that , how would you find ?
Method 1: Divide both sides by , so .
Method 2: Multiply both sides by , giving .
Therefore to divide fractions, keep the first fraction the same, change the divide to a times, and flip the second fraction. "Stay, Change, Flip".