Consider the following 4 results
7 % 3 = 1
-7 % 3 = 2
7 % -3 = -2
-7 % -3 = -1
I'm struggling to see why these outputs have been selected as such
7 % 3 is clear. Imagining | as 0, I can chunk up 7 into 3 groups of 3, and I have 1 left over going away from |
|*** *** *** *
Of course, we could say this is -1 as in "take away 1 from your numerator to make it divisible" or we could say it's -2 or 2, they all represent in some way how far off we are from having a perfect divisor.
The convention for -7 % 3 is odd to me, but I can reason about it. I would've thought it was -1 (3 groups of 3 and a remaining -1), but it's 2. I guess that's just convention.
* *** *** ***|
I'm really struggling reasoning about 7 % -3 and -7 % -3, though. Can someone explain this to me so I can intuitively understand this operation more quickly?
Side note, if I were creating a remainder operator, it would have these results
7 % 3 = 1 # remaining 1
-7 % 3 = -1 # remaining -1
7 % -3 = -1 # -ve version of 7 % 3
-7 % -3 = 1 # same as 7 % 3