Inverse Property of Integers
Inverse property of integer is the property in which the by performing the inverse operation we get the inverse of the integer. It is valid for only Addition and Multiplication operation but not for subtraction and division.
Two integers whose sum is zero are called additive inverse of each other. By reversing the integer’s sign, one can derive the additive inverse of an integer. For instance, the additive inverse of a number +5 is -5 and a number -3 is +3.
Example: Find the additive inverse of 56.
Solution:
To find the additive inverse of a number we need to reverse its sign
So, additive inverse of 56 is -56.
Two integers whose product is one are called multiplicative inverses of each other. Thus, the multiplicative inverse of any negative number is its reciprocal.
For example, (-3) × (-1/3) = 1, therefore, the multiplicative inverse of -3 is -1/3.
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