This is a little tricky. If you actually divide -50 by 7, you will get -7 1/7 ...
but...
when we talk about dividing and leaving a remainder, we want the number we find as a multiple to be LESS that the number we are dividing up (the dividend). Then the remainder counts "up" to the dividend.
This is easy if we're talking about positive numbers. For example, if I divide 34 by 10 and leave a remainder... I get 30 as my multiple, which is 10 x 3... and a remainder of 4, which counts up from 30 to 34.
Note that "up" means we're counting from left to right on the number line. This means we are finding a number that is a multiple of the divisor and is less than or equal to the divisor. SO, with negative numbers, "less than" means that it is to the left on the number line.
So back to -50 divided by 7. 7x(-7) is -49... but that is BIGGER than -50. So we have to go with 7 x (-8) = -56, with a remainder of 6, which we add to -56 to get -50.
It feels all wrong but you just have to get your head around "left is smaller" and the fact that -56 is SMALLER than -50.
--Louise
