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➖✖️➖ Negative Multiplication Pattern Lab

Why does a negative number times a negative number
make a positive number?

Simply memorizing “negative times negative is positive” is easy to forget. Instead, follow the pattern as the multiplier decreases one step at a time, and you can see for yourself why the answer has to turn out that way. Use the slider to decrease the multiplier and check the rule.

3 × (multiplier)2

Understanding the pattern: 3×3=9, 3×2=6, 3×1=3, 3×0=0 — each time the multiplier decreases by 1, the result decreases by 3. If this rule continues, 3×(-1) is -3, subtracting 3 from 0, and 3×(-2) is -6. So far, “positive × negative = negative” follows naturally.

Now apply the same idea to negative × negative: (-3)×3=-9, (-3)×2=-6, (-3)×1=-3, (-3)×0=0 — again, each time the multiplier decreases by 1, the result “increases” by 3 (moving toward less negative numbers). If you continue this pattern, (-3)×(-1) increases by 3 from 0 to +3, and (-3)×(-2)=+6. For the rule to remain consistent, negative × negative must be positive.

➖✖️➖ Negative Multiplication Quiz

Question 1/3 · 0 correct