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Multiplying integers

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Multiplying Integers

Multiplying integers uses the same multiplication facts as whole numbers, plus a sign rule: two numbers with matching signs multiply to a positive answer, and two numbers with different signs multiply to a negative answer. Learn the rule with a worked example, negative 3 times negative 4 equals 12.

The sign rules for multiplying integers

Multiplying integers works exactly like multiplying whole numbers — the only extra step is figuring out the sign of the answer. Two rules cover every case: matching signs give a positive answer, and different signs give a negative answer.

Sign rules for multiplying integers A table of sign rules: positive times positive equals positive, positive times negative equals negative, negative times positive equals negative, and negative times negative equals positive. Worked example: negative 3 times negative 4 equals 12. SignsResult (+) × (+)positive (+) × (−)negative (−) × (+)negative (−) × (−)positive −3 × −4 = 12
Matching signs (both positive or both negative) give a positive result; mixed signs give a negative result.

Worked example

For −3 × −4: multiply the numbers as if they were positive (3 × 4 = 12), then apply the sign rule. Both signs are negative, which is a matching pair, so the answer is positive: −3 × −4 = 12.

Why two negatives make a positive

Think of multiplying by a negative number as flipping direction. Multiplying a negative number by another negative flips its direction a second time, landing back on the positive side. One flip (mixed signs) stays negative; two flips (matching negatives) return to positive.

Related skills

The same sign logic applies to dividing integers. Once you are comfortable with both, applying integer operations combines multiplication, division, addition, and subtraction in one problem.

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