Settle the Signs First
With negative numbers in play, a product or quotient of nonzero numbers is negative exactly when an odd number of its factors are negative, and its size depends only on the absolute values. So a problem about unknown signed numbers starts by narrowing the sign candidates from a product or quotient, then brings in the other conditions -- a sum, an order, a quadrant, a reciprocal pair -- to decide which case holds, and only then compares sizes. Elementary ordering never needed this first step.
grade 7–8 Number system Eliminate PossibilitiesMake a Systematic List
Progression (6)
g7 1. Recover each letter's sign from a quadrant Number system
g7 2. ac=1 makes a and c same-sign reciprocals Number system
g7 3. Product and sum signs fix how many are negative Number systemOperations
g7 4. Fix the signs, then compare reciprocals Number system
g7 5. Split by common divisors, count |b| values Number system
g8 6. Let the sign decide the exponent's parity ExpressionsNumber system