Integers

Integers are a set of whole numbers and their opposites. They include positive numbers, negative numbers, and zero. The set of integers can be represented as {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Properties of Integers

Integers have some important properties:

Addition and Subtraction: When adding or subtracting integers, the rules are:
- - Adding two positive integers results in a positive integer.
- - Adding two negative integers results in a negative integer.
- - Subtracting a positive integer from a negative integer results in the addition of the two numbers with the sign of the larger number.
Multiplication and Division: When multiplying or dividing integers, the rules are:
- - Multiplying or dividing two integers with the same signs results in a positive integer.
- - Multiplying or dividing two integers with different signs results in a negative integer.
Ordering: Integers can be ordered from least to greatest or greatest to least on a number line.

Examples

Here are some examples of integer operations:

Addition: 3 + (-5) = -2

Subtraction: 8 - 12 = -4

Multiplication: (-4) * 6 = -24

Division: 15 / (-3) = -5

Conclusion

Understanding integers and their properties is important in many areas of mathematics, including algebra and number theory. Mastery of integers is a fundamental skill for students as they progress in their mathematical education.