Question

15 1/4 acres of land are to be divided into lots of at least 2/3 acres each What is the maximum number of lots that can be created?

Answer 1

This is simply    15   1/4    ÷   2/3

For there to be maximum lots, it should be divided by 2/3.

It should not be greater than 2/3 

This is simply    15   1/4    ÷   2/3

(15*4 +1)/4   ÷  2/3

61/4  ×  3/2 = 183/8 = 22.875

Maximum number of lots created = 22

Answer 2

Well, if you want the maximum number of splits, then you want to make
each individual split as small as possible. 
That's 2/3 acre.  How many will that give you ?

                  (15 and 1/4) divided by (2/3)

             =      (15.25)  /  (0.666...)  =  22.875 pieces .

The maximum number of 2/3-acre lots you can sell is 22 lots.

Then you have 58.3% of an acre of land left over that you can't sell
because it's less than 2/3 acre.  Sadly, that 58.3% of an acre is just
about the size of the lot that I've been living n for almost 30 years. 
You really know how to rub it in, dontcha !