**Properties of division of integers :**

In Math, the whole numbers and negative numbers together are called integers. The set of all integers is denoted by Z.

Z = {... - 2, - 1,0,1,2, ...}, is the set of all integers

Here, we are going to see the following four properties of division of of integers.

(i) Closure property

(ii) Commutative property

(iii) Associative property

Let us look at these properties of subtraction of integers in detail.

Observe the following examples :

(i) 15 ÷ 5 = 15/5 = 3

(ii) (-3) ÷ 9 = -3/9 = -1/3

(i) 7 ÷ 4 = 7/4 = 1.75

(ii) 1 ÷ 2 = 1/2 = 0.5

From the above examples we observe that integers are not closed under division.

Observe the following examples :

15 ÷ 5 = 15/5 = 3

5 ÷ 15 = 5/15 = 1/3

Therefore, 15 ÷ 5 ≠ 5 ÷ 15

From the above example, we observe that integers are not commutative under division.

Observe the following examples :

12 ÷ (6 ÷ 2) = 12 ÷ 3 = 4

(12 ÷ 6) ÷ 2 = 2 ÷ 2 = 1

Therefore, 12 ÷ (6 ÷ 2) ≠ (12 ÷ 6) ÷ 2

From the above example, we observe that integers are not associative under division.

We know that division is the inverse operation of multiplication.

Positive integer / Positive integer = Positive number

Negative integer / Negative integer = Positive number

Negative integer / Positive integer = Negative number

Positive integer / Negative integer = Negative number

For example,

250 / 50 = 5

(-144) / (-12) = 12

(-120) / 20 = -6

100 / (-25) = -4

Division of any number (except 0) by zero is meaningless because division by zero is not defined.

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