Multiplying fractions – showing why

It was a long time ago, so I can’t be certain, but when I first learned to multiply fractions, it was a procedure that involved turning mixed numbers into improper fractions, multiplying numerators and denominators with maybe some cancelling down along the way. It was a procedure with no understanding.

Screen Shot 2016-10-28 at 08.53.59.png

You could just apply that procedure to these questions. But there is scope for a greater depth of understanding not to mention some creativity in showing why these work.  Bar models are one way to demonstrate and calculate. Here are two examples:

screen-shot-2016-10-28-at-08-29-52screen-shot-2016-10-28-at-08-29-42

A worthwhile exercise is to go through each of these questions attempting a drawing to show why (squared paper is a must).

Depending on your class, you will probably need to show some examples first. Or maybe you would prefer to give the completed statements so the focus is on drawing the representation rather doing the calculations.

Here is the lyx file for these questions and the pdf.

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