Multiplication of Integers
Learning the rules for multiplying positive and negative integers.
Core concept
For example, (-3) × (-4) = 12 (same sign, so positive), while (-3) × 4 = -12 (different signs, so negative). This rule can be understood intuitively: multiplying a negative number represents 'reversing direction' on a number line, so multiplying by two negatives reverses direction twice, ending up positive again — similar to how two 'no's can sometimes mean 'yes' in double-negative sentences.
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• Same sign × same sign = positive result (e.g., (-3)x(-4)=12).
• Different signs × different signs = negative result (e.g., (-3)x4=-12).
• Multiplying by a negative can be thought of as 'reversing direction' on a number line.
• Two reversals (multiplying by two negatives) return to the original positive direction.