I am not sure what the purpose of a drop is for cell formatting. Drop downs are used for inputting values with data validation.
Additionally, you have very strangely merged cells so a formula copy down or conditional formatting copy is not going to work or nearly impossible.
And when I unmerged column Q, the records that were there went into column P. I do not want to attempt what your asking. But, the only thing I can say is you can't "number format" text, so if you convert $L$3 into text that is all you have. You can use conditional formatting on column Q(if that is really what it is) by having a formula that says "If this cell is a number" then format it as fractions (you need to choose if quarters, eigths etc.).