Exactly what I was thinking. Maybe it could be formalized this way? (with t = 1 table)

1/3 * (1 table) + 1/3 * (1 table) = 2/6 * (2 tables)

or

1/3 * t + 1/3 * t = 2/6 * 2 * t

but 2/6 * 2 = 2/3 so you get

1/3 * t + 1/3 * t = 2/3 * t

which is correct.