Floor division and modulo with negative number

Question

print(-2//4)

The output is -1. I do not understand the logic. Why the negative modulo?

Answer 1

(-2) ÷ 4 gives -1 remainder 2.

The relation that has to be correct is that for integers a and b

a = (a//b) * b + (a%b)

In this case, b is 4, and the remainder a%b must be between 0 (inclusive) and 4 (exclusive). So the only values for a//b and a%b that work are

a//b = -1
a%b = 2

which gives

-2 = -1 * 4 + 2
a   a//b  b  a%b

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TLDR

The precise value of (-2) / 4 is -0.5. The greatest integer not greater than -0.5 is -1.