What are integers and what are their properties?

Integers are a set of whole numbers and their opposites (negatives). Think of them on a number line: they include all the positive numbers (1, 2, 3,...), all the negative numbers (-1, -2, -3,...), and zero (0).

Key Properties to Remember:

• Closure Property: Adding, subtracting, or multiplying any two integers will always give you another integer. For example, 5 + (-2) = 3.
• Commutative Property: You can swap the numbers when adding or multiplying, and the result stays the same. For example, (-4) * 3 = 3 * (-4). This does not apply to subtraction or division.
• Associative Property: When adding or multiplying three or more integers, you can group them in any order. For example, (2 + 3) + 4 = 2 + (3 + 4).

Always use a number line to visualize integer operations. Moving right is addition, and moving left is subtraction. This simple trick can prevent common sign errors.