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# Properties of Division

Mathematical operators help us to solve the problems with Numbers and get the result. Division is one of the basic mathematical operators. Division is the reverse process of multiplication. Division means equal distribution of any object in any number of parts. The number which is divided is called dividend, the number of parts in which the number is to be divided is called divisor and the result we get is called quotient. After division, some part is left over; it is given the name remainder. The '÷' sign is normally used for division. Here are some of the properties of division:

1. Closure Property

Closure property does not holds true for division, which means that if a and b are Natural numbers, then a / b is not always a natural number.

e.g, 3 ÷ 5 = 0.6

2. Commutative Property

The Commutative Property does not hold true for division i.e, when two natural numbers are divided, the result changes with the change in the order of the natural numbers.

e.g, 3 ÷ 5 5 ÷ 3

3. Associative Property

The Associative Property does not hold true for division i.e, when three natural numbers are divided, the result changes as the Position of the brackets of the operators changes.

e.g, 3 ÷ (5 ÷ 2) (5 ÷ 3) ÷ 2

4. Identity Property

The identity property states that there is a natural number '1' such that when this number gets divided with any other natural number then the result will be the other natural number.

e.g, 3 ÷ 1 = 3

5. Property of 0 Division by any Number

When 0 is divided by any
natural number, the result is always zero.

e.g, 0 ÷ 3  = 0

6. Divisibility by Zero

Any number when divided by zero, gives no result.

e.g, 3 ÷ 0 = infinity