webwork question

Had issues with Section4.1 Rosen7: Problem 5  as practice indicates that

you are rounding up (ceiling) but this is not the case on the actual

homework problem.  The homework problem did not like decimal spots, number

R number, or number plus fraction.

Please let me know how this problem was suppose to be answered.

Last answer:

AnSwEr0001: 2

AnSwEr0002: 0

AnSwEr0003: -6

AnSwEr0004: 2

AnSwEr0005: 7

AnSwEr0006: 2

AnSwEr0007: -4

AnSwEr0008: 0

AnSwEr0009: 3

AnSwEr0010: 8

AnSwEr0011: -5

AnSwEr0012: 0

AnSwEr0013: 9

AnSwEr0014: 28

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OK, first of all, the webwork uses the '÷' sign for what the book calls 'div'.  The mathematical theorem that is the background for all of this is that given any integer a and natural number b, there is an integer d and a natural number r such that 0≤r<b such that

                         a=d*b+r

Note the important fact that r is strictly non-negative, so that d*b has to be smaller than a.  When a is negative, this means that d*b is more negative.  For instance, in problems 3 and 4, which were -26÷4 and -26 mod 4,  this means that d*4 has to be the largest multiple of 4 less than -26, so that d=-7 not -6, while r has to be 2.