Multiplying Fractions.

Again the credit is not mine. :) But some fun stuff!!

irageo : Was thinking about multiplications, too.
irageo : Might be easiest to start with something like 1/x * 1/y
irageo : 1/3 times 1/2... 1/6
irageo : 1/2 times 1/2... 1/4
irageo : 1/4 times 1/3... 1/12
irageo : 3/4 times 1/3... Well, 3/4 is just 3 1/4's, isn't it? 3* 1/4.
irageo : so 3/4 times 1/3 must be 3 times as much as 1/4 times 1/3...
irageo : 3/12
irageo : 1/4 times 2/3...
irageo : Well, 2/3 is 2 1/3's... 2* 1/3, right?
irageo : So 1/4 times 2/3 must be twice as much as 1/4 times 1/3...
irageo : 2/12!
irageo : Now... the tricky bit...
irageo : 3/4 times 2/3!
irageo : I wonder if there's any pattern here... some shortcut we could take...
irageo : I'd do a few problems the long way around first, though
irageo : Let them try and work out the "shortcut" themselves
kaspirant: I did that the other day with borrowing fractions...they were so amazed when i showed them the shortcut. I love doing that.
irageo : But here's the thing
irageo : about shortcuts
irageo : Unless you know WHY they work, it's worse than not having it at all.
kaspirant: Right and the reason that it is necessary to teach 'the long way' to understanding first.