at 11:46 feedback 2 Answers active oldest votes up vote 2 down vote Addition and subtraction are well-behaved, since the "circle group" is an abelian group . Multiplication doesn't work: $2/3$ is the same as $-1/3$ and $3/5$ is the same as $-2/5$, but $(2/3)\cdot(3/5)$ doesn't end up being the same