Operations with Integers - Multiplication of Integers

To multiply two integers with the same sign, multiply their absolute values and place a positive sign ($+$) before the product. Example: $(+a) \times (+b) = ab$ and $(-a) \times (-b) = ab$.

To multiply two integers with unlike signs, multiply their absolute values and place a negative sign ($-$) before the product. Example: $(+a) \times (-b) = -ab$ and $(-a) \times (+b) = -ab$.

The product of an even number of negative integers is positive. For example, $(-a) \times (-b) \times (-c) \times (-d) = abcd$.

The product of an odd number of negative integers is negative. For example, $(-a) \times (-b) \times (-c) = -abc$.

Commutative Property: Multiplication is commutative for integers, meaning $a \times b = b \times a$ for any integers $a$ and $b$.

Associative Property: For any three integers $a, b,$ and $c$, the grouping of factors does not change the product: $(a \times b) \times c = a \times (b \times c)$.

Distributive Property: Multiplication distributes over addition and subtraction: $a \times (b + c) = (a \times b) + (a \times c)$ and $a \times (b - c) = (a \times b) - (a \times c)$.

Multiplicative Identity: The integer $1$ is the identity for multiplication. For any integer $a$, $a \times 1 = 1 \times a = a$.

Multiplication by Zero: Any integer $a$ multiplied by zero results in zero: $a \times 0 = 0 \times a = 0$.