# Pizza Math

This gem is timely to my thinking about ratios and units:

It seems to have situated itself broadly enough across the Internet that I don’t know if it’s real or a fabrication, but it seems plausible enough. There are, at least, lots of non-teachers who are equally convinced that the question is a trick because, naturally, $$\frac{5}{6} > \frac{4}{6}$$.

The child in this case is correct. Marty could easily have started with more pizza than Luis. The very point of the problem, I imagine, is to reinforce that fractions represent ratios of things and are not units in and of themselves. For a teacher to assign this problem and miss that point is very troubling.

Addendum: This problem is in conflict with the rest of the problems on the page. The exercises on the page treat fractions as unitless things that can thus be compared: 4/6 > 1/6, for instance. It is true that 4/6 of x units of y thing is greater than 1/6 of x units of y thing, but it is not true that 4/6 of x units of y thing is definitely greater than 1/6 of z units of w thing.

That said, I can see why a teacher might have made the mistake that’s shown, if they’re in such a fixed mindset that they can’t even accept the answer when it’s explicitly given to them.