# Why operation * not defined in Q

by pakkanen
Tags: defined, operation
 P: 12 1. The problem statement, all variables and given/known data Show that l/m * k/n = (l+k)/(m2+n2) can not be defined as an operation in Q when l,k € Z and m, n € Z\{0} I do not know what is the issue here? Should I know something about Q that this not fulfilled by the operation *?
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P: 2,658
 Quote by pakkanen 1. The problem statement, all variables and given/known data Show that l/m * k/n = (l+k)/(m2+n2) can not be defined as an operation in Q when l,k € Z and m, n € Z\{0} I do not know what is the issue here? Should I know something about Q that this not fulfilled by the operation *?
Hint: What happens if you negate $l$ and $m$?
 P: 12 Ok.. So the same operation can produce two different results?? So that l/m * k/n = (l+k)/(m2+n2) ≠ (-l+k)/((-m)2+n2) = -l/-m * k/n = l/m * k/n