WHY? 4%10=4 -4%10=6

Answer 1

Because in Python the remainder must be less than the divisor AND positive (Java and javascript choose the sign of the numerator instead).

In Python, taking the modulo formula as:
x=qc + r (total = q*divisor + remainder)
Rewritten as:
x - qc = r (total - q*divisor = remainder)

You know 'x' and 'c', you're trying to find 'r', so all you can change is 'q'.

For your examples:
1) 4%10=4
4 - 0(10) = 4 (q=0)

2) -4%10=6
-4 - (-1*10) = 6 (q=-1)

Reference, with additional negative examples:
http://math.stackexchange.com/questions/519845/modulo-of-a-negative-number

edit: adding 2 codes due to another question...

https://code.sololearn.com/c7o8hur596jS/?ref=app
https://code.sololearn.com/c0VcyWYMEfed/?ref=app

Answer 2

Good to know. In C++ and Javascript, negative numbers modulo m produce a number between -(m-1) and 0 instead of doing a true modulo. And I dislike it, I have to do (n%m + m)%m as a workaround.

Answer 3

It's just the matter of mathematics.

a % d = r ,means:
a = (k * d) + r ,that k is an integer and r is a positive integer
so we have:
-4 = (k * 10) + r
now if we consider k = -1,
-4 = -10 + r ==> r = 6

Answer 4

still don't understand. how do I solve this
7%(5//2)

Answer 5

@Kirk Schafer. Thank you. Excellent answer! I understand.
But unfortunately, I believe this is a BUG in Python, because I lost time!
In C++, Java (and other) remainder of division is correct. In Python, uses the formula " x=qc + r (total = q*divisor + remainder)" without knowing it, the code causes the program error.
My son was not able to solve this simple school problem (find the maximum negative number and not finishing 4. http://www.sololearn.com/app/python/playground/cS6vzGj2g6mf/ ).
My solution to this problem be SURE to use abs:

abs (x)%y

It would be nice if it took into account in this lesson and drew the attention of the students.
P.S. Sorry for my English .

Answer 6

da jopa eto, zabey

Answer 7

because 4 can not divided completely, so in 0 times division it will give 4 as a remainder.
-4%10=6
-4+10=6

Answer 8

but shouldn't 4/10 be producing a decimal quotent n a reminder of zero?

Answer 9

@Sidi Victor to get the answer type in : print(7%(5///2)). Enter that without codes for solving it. They have left out the part about print command that must be placed before anything that is to be displayed.

Answer 10

Why does Python assume that q=-1? Is it to make the remainder positive AND less than the divisor? If that's so, then does that mean that Python looks for the closest number to the quotient that will give a remainder that is positive AND less than the divisor? Because -4/10 has a quotient of 0. So that means if Python finds it to be -1, it looks for the closest number to 0 to create a remainder that satisfies the rules...?