Multiply integers

Integer multiplication extends whole-number multiplication to positive, negative, and zero factors: the product’s magnitude is the product of the absolute values, with a positive result for like signs, a negative result for unlike signs, and zero when either factor is zero. Understanding these sign relationships, including their basis in patterns and the distributive property, supports multiplication of rational numbers and simplification of algebraic expressions; abstract number systems and more advanced generalizations are not included.

Detailed Explanation: Multiply integers

To multiply integers:

Multiply the absolute values as if they were whole numbers.
Decide the sign:
- Same signs → positive
- Different signs → negative
- Either factor is zero → zero
Write the product with the correct sign.

Worked example: $\left(-6\right)(4)$

Step 1: Multiply the absolute values.

\vert {-6} \vert \times \vert 4 \vert = 6 \times 4 = 24

Step 2: Decide the sign.

The factors have different signs: one is negative and one is positive. Therefore, the product is negative.

Step 3: Write the answer.

\left(-6\right)(4) = -24

A helpful way to remember the sign rules is that multiplying by a negative reverses a sign. One negative factor causes one reversal, giving a negative result; two negative factors cause two reversals, giving a positive result. If either factor is $0$ , the product is always $0$ .

Learn by doing: Multiply integers

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Negative Integer Multiplication and Division

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