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]]> Comment on Learning Fractions With Fun Fraction Games by MPL http://findmathtutor.com/?p=40&cpage=1#comment-21 MPL Mon, 18 Jan 2010 08:53:30 +0000 http://findmathtutor.com/?p=40#comment-21 Well, there's a few ways of justifying cross canceling, which is really just a way to speed up the process. If you already agree that (a/b)*(c/d) = (a*c)/(b*d), then from there you know that (a*c)/(b*d) = (c*a)/(b*d) = (c/b)*(a/d), and then the cancellation is done inside the rearranged fractions, not across fractions. Maybe a better way to put it is that you know that if some number divides another, say x divides y, then x divides any multiple of y. So if you're multiplying two fractions, a/b and c/d, and a and d are both divisible by some common factor f, then f will divide a*c and divide b*d, so you can cancel it out sooner, rather than later. I'm afraid neither of those explanations are particularly intuitive though. Well, there’s a few ways of justifying cross canceling, which is really just a way to speed up the process.

If you already agree that (a/b)*(c/d) = (a*c)/(b*d), then from there you know that (a*c)/(b*d) = (c*a)/(b*d) = (c/b)*(a/d), and then the cancellation is done inside the rearranged fractions, not across fractions.

Maybe a better way to put it is that you know that if some number divides another, say x divides y, then x divides any multiple of y. So if you’re multiplying two fractions, a/b and c/d, and a and d are both divisible by some common factor f, then f will divide a*c and divide b*d, so you can cancel it out sooner, rather than later.

I’m afraid neither of those explanations are particularly intuitive though.

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