Properties of Addition and Subtraction of Integers An integer is a whole number (both positive and negative) that we use to represent quantity and size. Addi...
An integer is a whole number (both positive and negative) that we use to represent quantity and size. Addition and subtraction of integers involve combining or separating these quantities based on their relative values.
Key properties of addition and subtraction of integers:
Commutative property: Adding or subtracting two integers is the same regardless of the order of the numbers. For example, 5 + 3 = 3 + 5.
Associative property: Adding or subtracting three or more integers can be grouped together and added or subtracted simultaneously. For example, (5 + 2) + 3 = 5 + (2 + 3).
Distributive property: When adding or subtracting integers, we can distribute the value of the number being added or subtracted to another number. For example, 5 + (2 + 3) = (5 + 2) + 3.
Identity property: Adding or subtracting zero to an integer always results in the original number unchanged. For example, 5 + 0 = 5 and 5 - 0 = 5.
Inverse property: Adding or subtracting the opposite integer (the number that gives you the original number when added or subtracted) results in zero. For example, 5 - 5 = 0 and 10 + (-10) = 0.
These properties allow us to simplify expressions by combining or separating similar terms. For example, 5 + 2 - 3 = (5 + 2) - 3. Similarly, 10 - 5 + 3 = 10 - (5 - 3).
These properties are crucial in various mathematical calculations and real-world scenarios involving quantities and sizes. By understanding and applying these properties, we can manipulate and solve complex mathematical problems involving addition and subtraction of integers