Playing around with some numbers may help:

from math import remainder, fmod

# in case x is a multiple of y
remainder(20, 4)    # 0.0
fmod(20, 4)         # 0.0

# in any other case
remainder(20, 3)    # -1.0
fmod(20, 3)         # 2.0

So what we see here is that the remainder, as stated in the docs, returns the difference between x and the closest integer multiple of y. As 20 lies between 18 and 21 (the 6- and 7-multiples of 3), it chooses whichever is closer to x. In this case it is 21, so the difference between x and 21 is -1.0.

In contrast, fmod returns the result of 20 mod 3, which is 2.0. I explicitly do not use the % operator, as the docs state that the result may differ.

As Thomas K said, use math.fmod for modulo, or if you really want you can define it yourself:

def cmod(x, y):
    return abs(x) % abs(y) * (1 if x > 0 else -1)

And this function should emulate C-style division:

def cdiv(x, y):
    return abs(x) / abs(y) * cmp(x, 0) * cmp(y, 0)

You said that you must use the / and % operators. This is not possible, since you can't override the operator for built-ins. You can however define your own integer type and operator overload the __div__ and __mod__ operators.