Answer:
2/3
Step-by-step explanation:
Let x be the number of books that Millicent has. So the number of books that Harold has is x/2. And the number of book that Harold is bringing to the new home is (x/2)/3 = x/6.
The home has enough room for another half of Millicent's books, which is x/2. So the total books capacity of the new home is
Since x is also the number of books in Millicent's old library capacity, we can conclude that the fraction of Millicent's old library capacity to the new home's library capacity is 2/3, or 2 thirds