What are Properties of Integers?
As we already discussed the integers are the fundamental number in Maths, which includes both positive and negative whole numbers including 0. There are various properties of integers which define the behaviour of integers under various different operations.
The 6 properties of integers are:
- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- Identity Property
- Inverse Property
The following table covers all the properties in brief:
Property |
Addition |
Subtraction |
Multiplication |
Division |
---|---|---|---|---|
Closure |
a + b ∈ Z |
a – b ∈ Z |
a × b ∈ Z |
a ÷ b ∈ Z |
Commutative |
a + b = b + a |
a – b ≠ b – a |
a × b = b × a |
a ÷ b ≠ b ÷ a |
Associative |
(a + b) + c = a + (b + c) |
(a – b) – c ≠ a – (b – c) |
(a × b) × c = a × (b × c) |
(a ÷ b) ÷ c ≠ a ÷ (b ÷ c) |
Distributive |
a × (b + c) = a × b + a × c |
a × (b – c) = a × b – a× c |
– |
– |
Identity |
a + 0 = 0 + a = a |
– |
1 × a = a × 1 = a |
– |
Inverse |
a + a-1 = a-1 + a = 0 |
– |
a-1 × a = a × a-1 = 1 |
– |
Let’s explore the various properties in detail:
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