Commutative Property of Integers
The only distinction between the commutative and associative properties of integers is that only two integers are used in the former. According to the commutative property of integers under addition and multiplication, the outcome of adding and multiplying two integers is always the same, regardless of the sequence in which they are added.
This implies, if there are two integers x and y, we have,
- x + y = y + x
- x × y = y × x
Note: This property does not hold true with subtraction and division operations.
Example: Which operation performing with 2 and 5 holds true for a commutative property? Explain with an example.
Solution:
Operation | Calculation | Result |
---|---|---|
Addition | 2 + 5 = 5 + 2 = 7 | Verify Commutative property |
Subtraction | 2 – 5 ≠ 5 -2 | Not Verify Commutative property |
Multiplication | 2 × 5 = 5 × 2 = 10 | Verify Commutative property |
Division | 2/5 ≠ 5/2 | Not Verify Commutative 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