## Wednesday, 14 September 2011

### Are Equivalent Fractions Really Equivalent?

We teach pupils that 6/7 is the same as 12/14 is the same as 120000/14000 etc. But is it really?

This thought struck me in a faculty meeting this afternoon. The head of maths said that the maths department had the highest proportion of U grades at A level in the school. He then said, "But we did have a much higher intake than other subjects". Everyone immediately said things like "ah, yes" and "true, that needs to be taken into account" and "well there you go". So the message I was hearing loud and clear was: if 7 people out of 42 got a U grade, that's not as bad as 1 person out of 6, and hence the two fractions aren't equivalent.

When you see adverts for shampoo or whatever on TV, it might say 70% of women agree, and then it always says at the bottom, 109 out of 156 women agreed. Now if that figure was 10900 out of 15600, would you be more likely to believe that it's a good shampoo? I would. We all know that the bigger the sample, the more reliable the findings. So the two fractions aren't really equivalent.

Of course equivalence is an undisputed term. It means they have the same value. The thing is, the word "value" can have multiple meanings. The mathematical meaning, which is obvious, and the other one, the one that refers to how much value we give to something, as in, how much we think something is worth. We think 1/6 is worth more than 7/42 when it comes to U grades. We think 10900/15600 is worth more than 109/156 when it's to do with data collection. Mathematically, of course they're the same.

Happy hump day everyone!
Emma x x x