Practice Problems on Properties of Integers
Problem 1: Determine whether the following statement is true or false: If a and b are even integers, then a + b is also an even integer.
Problem 2: Prove that for any integer a, a + 0 = a.
Problem 3: If m and n are positive integers such that m > n, prove that m^2 – n^2 is divisible by (m – n).
Problem 4: Show that the product of three consecutive integers is divisible by 6.
Problem 5: Determine whether the integer 27 is a perfect square.
Problem 6: Find two consecutive odd integers whose sum is 44.
Problem 7: Solve for x: 3x – 7 = 2x + 5.
Problem 8: Determine the prime factorization of the integer 36.
Problem 9: Find the greatest common divisor (GCD) of 18 and 24.
Problem 10: Prove that the sum of two even integers is always even.
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