While teaching dividing fractions this year I started with a paper activity to capture their attention. I held up 4 peices of paper and asked what 1/2 of 4 was. I then wrote the step that 1/2 x 4= They reminded me to multiply the numerators and the denominators. And the last step to simplify. They redidly gave me the answer that 1/2 times 4 was 2. The students were then ready to restate that mutiplying by 1/2 and dividing by 2 were the same thing. The point was made that dividing by a fraction was the same thing as multiplying by it's reciprocal.
Ex. 4 divided by 1/2 (four sheets of paper torn in 1/2 gives you 8 sheets of paper) therfore it is the same as 4 times 2 (multiply be the reciprocal!)