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A fraction is a fair cut

The bottom is the cut. The top is how many pieces you mean.

Why this exists

Two people and one loaf. The word “one” is too coarse. You need a name for a piece, and the piece has to be a fair cut or the name starts a fight.

A fraction is that name. It always talks about equal pieces of one whole. If the pieces aren’t equal, it isn’t the fraction you wrote.