Associative Property of Integers
The associative property of integers under addition and multiplication states that no matter how the integers are grouped, the outcome of addition and multiplication of more than two integers is always the same. This suggests that we have, for any three integers x, y, and z.
- x + (y + z) = (x + y) + z = (x + z) + y
- x × (y × z) = (x × y) × z = (x × z) × y
Note: Since the order of the numbers is crucial in subtraction and division and cannot be modified, the associative feature of integers does not apply to these operations.
For example, 3 – (8 – 9) = 3 – (-1) = 4. Now, if we change the order to 8 – (3 – 9) = 8 – (-6) = 14. Therefore, 3 – (8 – 9) ≠ 8 – (3 – 9).
Example: Mention which operation satisfies the associative property.
Solution:
Addition: Satisfy the associative property.
Subtraction: Do not satisfy the associative property.
Multiplication: Satisfy the associative property.
Division: Do not satisfy the associative property.
Properties of Integers
Properties of Integers are the fundamental rules that define how integers behave under various operations such as addition, subtraction, multiplication, and division. As we know, integers include natural numbers, 0, and negative numbers. Integers are a subset of rational numbers, where the denominator is always 1 for integers. Therefore, many of the properties that hold for rational numbers also hold true for integers.
This article explores the concept of Properties of Integers including Closure Property, Associative Property, Commutative Property, Distributive Property, Identity Property, and Inverse Property. So, let’s start learning about all the properties of integers in this article.
Table of Content
- What are the Properties of Integers?
- Closure Property of Integers
- Associative Property of Integers
- Commutative Property of Integers
- Distributive Property of Integers
- Identity Property of Integers
- Inverse Property of Integers