Multiplying and dividing with signs

Multiplying and dividing with negatives comes down to one rule about signs, separate from the numbers themselves.

The sign rule

Multiply or divide the numbers as usual, then decide the sign:

• Same signs → positive (positive × positive, or negative × negative)
• Different signs → negative (positive × negative, or negative × positive)

So:

• (−4) × (−3) = +12 (same signs)
• (−4) × 3 = −12 (different signs)
• (−12) ÷ (−4) = +3, but (−12) ÷ 4 = −3

Why two negatives make a positive

Think of multiplying by −1 as "flip direction." One −1 flips you; a second −1 flips you back to where you started — positive. That's why (−)(−) = (+), every time.