Operations with Integers - A Quick Recap of Integers

Integers are a set of numbers consisting of whole numbers and their negatives: $\mathbb{Z} = \{ \dots, -3, -2, -1, 0, 1, 2, 3, \dots \}$.

On a number line, adding a positive integer moves the point to the right, while adding a negative integer moves it to the left.

The absolute value of an integer $a$, denoted by $|a|$, is its numerical value regardless of its sign. For example, $|-5| = 5$ and $|5| = 5$.

When adding two integers with the same sign, add their absolute values and keep the common sign. For different signs, subtract the smaller absolute value from the larger one and use the sign of the integer with the larger absolute value.

The additive inverse of any integer $a$ is $-a$, such that $a + (-a) = 0$.

Rules for Multiplication and Division: $(+) \times (+) = (+)$, $(-) \times (-) = (+)$, $(+) \times (-) = (-)$, and $(-) \times (+) = (-)$. Same rules apply for division.

Properties include the Commutative Property ($a + b = b + a$), Associative Property ($a + (b + c) = (a + b) + c$), and the Distributive Property of multiplication over addition ($a \times (b + c) = a \times b + a \times c$).