Identify exactly \(\text{all}~\text{representations}\) with the same multiplication meaning as \((-4)(3)\). Include \(\text{every}~\text{representation}\) that models \(3~\text{groups}~\text{of}~-4\), not merely an expression with the same final value. Report the complete set of labels.
Target: \((-4)(3)\)
Representations:
A. \(3~\text{groups}~\text{of}~-4\)
B. \((-4)~+~(-4)~+~(-4)\)
C. \((-3)(4)\)
D. \(0~-~4~-~4~-~4\)
E. \(12~\div~(-3)\)
F. a total change of \(-12\) split equally among \(3~\text{groups}\)
G. \((-4)~+~3\)
H. A temperature drops \(4^{\circ}~\text{each}~\text{hour}\) for \(3~\text{hours}\)
What this problem is really about
Translate the target into its precise multiplication meaning: three groups of negative four. For every representation, identify the operation, number of groups, and signed amount per group before calculating anything. Keep only models that preserve all three features; an expression with the same total can still describe different grouping or a division relationship.