Hadley decided to paint 4/5 of the rooms in her home last year. By the end of the year, Hadley completed 2/3 of the rooms. How much of Hadley's home was painted last year?
Since 2/3 of her home was painted, then 4/5 - 2/3 = 12/15 - 10/15 = <<12/15-10/15=2/15>>2/15 of Hadley's home was painted last year. Answer: \boxed{2/15}.
To find out how much of Hadley's home was painted last year, we need to find the total fraction of the rooms that were painted.
Hadley decided to paint 4/5 of the rooms in her home last year.
So, the fraction of rooms painted is 4/5.
By the end of the year, Hadley completed 2/3 of the rooms.
So, the fraction of rooms completed is 2/3.
To find the total fraction of rooms painted, we'll multiply these two fractions:
(4/5) * (2/3) = (8/15)
Therefore, 8/15 of Hadley's home was painted last year.