Solved Problem on Properties of Integers
Problem 1: Identify the correct properties of integers in the following:
a) x + y = y + x
b) x × (y – z) = (x × y) – (x × z)
Solution:
a) x + y = y + x is the Commutative property of integers.
b) x × (y – z) = (x × y) – (x × z) is the Distributive property of integers.
Problem 2: Evaluate the expression: (-20 × 15) + (-20 × 18) using the properties of integers.
Solution:
The given expression is (-10 × 15) + (-10 × 18). Using the distributive property of integers, which states (a × b) + (a × c) = a × (b + c). So, here we can take (-10) as common out of both the terms. We get -10 × (15 + 18).
⇒ – 10 × 33
= – 330
Problem 3: Does 0 is the identity element for the subtraction of integers as well as we can subtract 0 from any integer to get the same integer as the answer. State the reason.
Solution:
The identity element for subtraction is not 0, though. It is true that any integer gets the same integer as the answer if 0 is subtracted from it. However, it should also be true in reverse for it to qualify as an identity factor. Any integer can be subtracted from 0 to yield its additive inverse.
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