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I am sure you have seen different “proofs” of this unequal equality: $1=2$.

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 $5/8=5/4$, hence, $8=4$. Now divide both side by 4 and voila, here it is:

$1=2$

### One Response to “1=2 Explained!”

1. Maryam

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