Why cant the reminder of a division be negative?
89171
You cant just add or substract whatever is left. You invalidate the function of "division" by partially dividing then filling in the rest of the numerator. The number left over after something has been divided is called the modulo, and is useful for programming functions. You cant do an incomplete division(only dividing 20/5 instead of the 2/5 also) and then speculate as to why it cant be negative when doing a full division. It invalidates the definition.
1133031
When you are adding a negative number to a positive number, try thinking through it this way:\n\nTake two steps backwards then five steps forward. Where are you in relationship to where you started?
890832
Gary, that's a good one, but one mistake...\nyou said that a=b, thus you cannot divide by (a-b) b/c that equals zero, and you cant divide by zero.
596523
If you are approaching zero from the left, then -1 divided by 0 is positive infinity.\nIf you are approaching zero from the right, then -1 divided by 0 is negative infinity.\n-1 divided by 0 is undefined because you get different results when coming in from the right side of 0 and the left side of 0.\nI learned this in Calc 1 (possibly Calc 2).\nThere are different levels (degrees) of infinity.
882621
My old math teacher showed me this.\n\nSince A=B, then A-B=0, and you can't divide by 0
750843
you cannot divide by 0 = a-b\n&#92;
1137443
It's undefined.  You can't divide any number by 0.
344009
No, because it doesn't.\nThere's a number of "proofs" out there that rely on dividing by 0, even when it's not obvious that's what's going on.\nDivide by zero, and you can prove anything!
1019179
Yes, negative x positive always equals negative.  \n        negative x negative always equals negative\n        positive x positive always equals positive
811215
If the value in an absolute value is positive, it remains the same. If it is negative, it is multiplied by -1.\n\nEither a<x, a = x, or a > x. (I think this is called trichotomy?)\n\nIf a = x, then both sides equal 0.\n\nIf a > x, then a-x is positive, and x - a is negative, so...\na - x =  -1(x - a)\n\na - x If a > x, then x-a is positive, and a - x is negative, so...\n-1(a - x) =  x - a\nx - a = x - a\n\na - x = a - x\n\nQED
604013
there is no answer becuase it is impossible to divide by 0
477027
aint is not supposed to be used. It is a double negative
486386
Subtracting a negative number is the equivalent of adding a positive number.\n\nInterestingly, if you were multiplying two negative numbers, the answer would be a positive.
543316
I believe that would be like -3 and +3. Negative numbers and positive numbers are on opposite sides of the zero, therefore they are opposite points on the number line.
27071
The problem with negative numbers is that they don't actually exist.  We talk about negative values but it's technically impossible to have a negative amount of anything.\n\nI've found the easiest way to make students understand negatives is to talk about what happens when you owe a certain amount.\n\nFor instance, if I have four apples and you want to get five apples from me, I can give you four but then I have no more.  Therefore, I will owe you one apple.  This apple - which I do not have but which I owe you - is like a negative number.\n\nWhen all else fails, go for the number line.  Numbers extend on to infinity in BOTH directions, from zero and up, and down as well.  If your eight year old can understand infinity, negatives shouldn't be too hard.\n\nNegative numbers, by the way, are generally sixth-grade material.  Don't be frustrated if your child doesn't understand yet!  Some things will take time.
653428
Because -2 squared = (-2)(-2)\n\nA negative times a negative equals a positive.
190233
When you divide by 3, the remainder must be 0, 1 or 2. \nThen the remainder is 1 , since -5 = 3x(-2)+1\n\nThere are many incorrect answers here, so I will explain clearly.\n\nThe definition of the division of the integer  is :\n\nIf a = b*q + r   (0 ≤ r < |b| ),  then a ÷ b = q remainder r\nIt means the remainder must be non-negative integer.\n\nWell -5 = 3 * (-2) + 1,  then the remainder must be 1.\n\n-2 is wrong !!!!\n\nsource : I am a maths prof.