. . . we all take our AFM landing distance for that weight and temp and divide by 60 to meet the following regulation:
. . .
I agree with the person who said you're confusing yourself. I think you don't understand the basic math, specifically algebra.

First of all I believe you meant "divide by .6" not by 60. 60 and .6 are very different numbers - this is important for a professional pilot to understand.

60% is 6/10 or .6 of a value.
60% of 1000 is 600

An example:
Your part 135 conformed Piper cub has a landing distance (according to the dog-eared and faded chart devoted to landing distances in the AFM(POH))
of: 600'
You've got a client who wants to land at an airport that has 1000' available landing distance.
Think of this equation:
your aircraft landing distance (ACD) must be less than or equal to 60% of the available landing distance (ALD) express it this way:
ACD = ALD x .6
This is an algebraic expression. If you went to a public Junior High school in the NorthEast you were taught to recognize that:
ACD = ALD x .6
is the same formula as:
ACD / .6 = ALD

so

You can calculate this either way: 60% of available runway of 1000' yeilds 600' of runway that you may use for calculating usable runway
1000' x .6 = 600'
OR
Divide your Cub's landing distance of 600' by .6
600' / .6 = 1000'

Of course even though you're 'legal' to accept this trip it would never happen because the Cub's got a broken landing light and your POI still hasn't approved the MEL.