Scalar multiplication of an expression containing equality

Question

Suppose:

expr=(a x + a y==0);
expr/a
(*Out:=(a x + a y==0)/a*)

I want a eliminated to obtain expr=(x+y==0). None of Expand, Simplify, FullSimplify work. Any suggestions?

Answer 1

Use Thread[]:

expr = a x + a y == 0;
Thread[expr/a, Equal] // Simplify
   x + y == 0