Here is another version of the Quotient-Remainder Theorem:

Given any integers $n$, $d$ with $d\neq 0$, there exist unique integers $q$, $r$ satisfying

(1) $\mathrm{ n = dq + r }$

(2) $\mathrm{-d/2 < r \leq d/2}$

Find the quotient and remainder (using the theorem above!) for the following pairs of integers:


n = 11, d = 2
q= , r = .


n = 11, d = 3
q= , r = .


n = -11, d = 3
q= , r = .


n= 54 d = 7
q= , r = .


n= -54 d = 7
q= , r = .


n= 52 d=8
q= , r = .


n = -52 d = 8
q= , r = .