Negative × Negative = Positive

Why does a negative times a negative give a positive? Let's think about money. Imagine you owe someone five dollars. That's negative five. Now imagine this debt gets erased twice.

• Owe $5 = negative 5
• Erase twice = multiply by negative 2

If your debt disappears, you gain money. That's positive! Let me show this with a number line. Start at zero. Negative three means go left three steps. Do it twice.

• Gain = positive result

After two jumps of negative three, we land on positive six. Here's the pattern with a number line. Negatives flip direction.

• Negative 3 times negative 2 = positive 6

Negative times positive goes left. Negative times negative flips back right. Let's check: what is negative four times negative five? Negative times negative always gives positive because two flips return you forward.

• Flip twice = back to positive