Dividing Fractions

Ran across an basic fraction division problem on an old AMC 8 today.

Problem #12 from the 1989 AMC 8 (AJHME).

The problem is easy to state:

Evaluate \frac{ 1 - 1/3 }{1 - 1/2}

When my son dove in to the problem he immediately remembered the “flip the denominator” rule. That rule makes pretty much takes care of solving the problem. BUT, after he got the answer I asked him if he knew why the rule was true. He said that he didn’t know.

So, we spent the last couple of minutes in the video talking about why it was true:

When I first introduced fraction division to him, we looked at flipping the denominator and also a second approach involving snap cubes. I guess the “flipping the denominator” rule is a lot easier to remember, but I still remember the fun we had making this video 🙂

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