Properties of Division of Integers Division of integers is a mathematical operation that tells us how many times one number (the dividend) can be divided by...
Properties of Division of Integers
Division of integers is a mathematical operation that tells us how many times one number (the dividend) can be divided by another number (the divisor). There are several properties of division that apply to integers, which help us understand how division behaves with different numbers.
Closure Property:
The result of dividing any integer by another integer is always an integer. This means that the division of any two integers, regardless of their signs, will always result in an integer.
Division Property:
The dividend divided by the divisor remains unchanged if the divisor is positive or negative, but the dividend divided by the negative divisor is the negative of the dividend divided by the positive divisor.
Identity Property:
Dividing any number by itself results in the identity element, which is 1. The identity property applies to both positive and negative divisors.
Division by Zero:
Division by zero is undefined, meaning that we cannot determine the value of the quotient in this case.
Distributive Property:
(a + b) ÷ c = (a ÷ c) + (b ÷ c)
Cancellation Property:
(a - b) ÷ c = (a ÷ c) - (b ÷ c)
Examples:
12 ÷ 3 = 4, as 3 goes into 12 exactly 4 times.
-6 ÷ 2 = -3, as 2 goes into -6 3 times and leaves a remainder of 2.
15 ÷ 3 = 5, as 3 goes into 15 5 times.
24 ÷ 4 = 6, as 4 goes into 24 6 times