Monday, September 08, 2008

I'll Show You Improper

I just want to state for the record that whatever jerk it was who gave fractions greater than one the name 'improper fraction' should be kicked square in the nuts.

I was trying to help Jack subtract some compound numbers (compound numbers being things like one-and-three-quarters and seven-and-five-eighths and so forth). If, for example, you are subtracting one and five-eights from two and one-fourth, it's helpful to convert both numbers into fractions before subtracting.

The easiest way to do this is to convert 2 1/4 to 9/4, and 1 5/8 to 13/8, then convert 9/4 to 18/8, then subtract 13/8 from 18/8. The result is 5/8. Simple, right?

However, Jack was very reluctant to do that because he'd been taught, and taught well, that you couldn't write a fraction as nine fourths. That was improper. So every time we got to a point where you'd have a 18/8 or 9/4, he would say that he couldn't do that because that was an improper fraction, and convert it back to a compound number.

This an unfortunate side-effect of elementary education. They wanted to have an easy way to tell kids not to write their fractions upside down, so they called them 'improper'. But there's no fundamental mathematical reason for banning fractions larger than one. Fractions, after all, are just another way of writing a division problem. So rather than teach that, we've generated a rule that's fundamentally incorrect to keep kids from making a simple mistake, and then having to un-learn that rule later.