I am sure you have seen different “proofs” of this unequal equality: .

Here is my version that would be based on the answers given to this question

**What fraction is shaded?**

here and here . One answer is 5/8, seeing the figure as something that is made up of 8 small squares, five of which have been shaded. The other answer is 5/4, taking each bigger square as a unit (as a whole), seeing the figure as one whole and one fourth of that whole. This results in 1 and 1/4 that is the same as 5/4. Using the pizza metaphor, the first answer is like seeing the whole figure like a big pizza, the second answer is taking each four-piece square as a pizza. Basically, both interpretations are correct and just two different ways of numerically representing the same thing. Thus, we should have , hence, . Now divide both side by 4 and voila, here it is:

Fraction of what? Unit is different in these two condition!