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Learning Fractions

Piper (my second grader) is learning fractions while we cook in the kitchen, and it is fascinating to see the ways in which fractions are not intuitive. For example, if you remove one egg from a four-egg recipe, it seems intuitive to her to remove one whole cup from the one-and-a-half cups of flour to match.

On the other hand, if you reduce a four-egg recipe to one egg, she gets the intuition right.

That matches the ancient history of fraction notation where Egyptians were able to write "1/n" instead of generalizing to "m/n". That system is very complicated and is no longer used today.

But the ancient Babylonians had a fractional decimal notation using base 60 that is still used in angles and hours today (minutes and seconds). And the Romans were had a notation for "m/12" that shows up in our American inches today.

The idea of allowing both numerator and denominator to be written was a Hindu innovation. Thanks to the Hindus, it is now possible to successfully pull off a cookie recipe no matter how many eggs are in the refrigerator.

Posted by David at January 2, 2009 02:01 PM