Identify exactly \(\text{all}~\text{representations}\) that algebraically preserve the signed division relationship \(18~\div~(-6)\). Use valid inverse equations, and do not interpret a negative quantity as a physical number of groups because an equal-groups model requires a nonnegative group count. Report the complete set of labels.

Target: \(18~\div~(-6)\)

Representations:
A. the number that makes \((-6)~\times~?~=~18\)
B. \(18\) divided into groups of \(-6\)
C. \(18\) divided by \(6\)
D. the number that makes \(6~\times~?~=~-18\)
E. \((-6)(-3)\)
F. a total of \(18\) split into equal groups of \(-6\)
G. \(18~+~(-6)\)
H. \(3\) groups of \(-6\)

Open full size