Division is one of the basic mathematical operations. Basically, division is the ratio between two numbers. The question is how do we perform division operation for two natural numbers? Imagine you have 15 chocolates and you need to distribute those chocolates to your friends. At that moment, you have 5 friends who are eager to get chocolates from you. How you are going to distribute those chocolates equally to your friends? By divide 15 by 5 and, in mathematical language, this is how you need to write:

15 \div 5 or 15 : 5 or \frac { 15 }{ 5 }

All the above syntaxes are correct and if you see any of the syntaxes above, it means you need to perform the division operation. When you are dividing, basically you are trying to split the first number into equal parts and the number of equal parts is decided by the second number. In the above example, you need to split 15 into 5 equal parts. If you give 3 chocolates to each of your friends, that means you equally divide 15 chocolates within your friends, hence:

15 \div 5 = 3


15 is the dividend,

5 is the divisor,

and 3 is the quotient.

Types of Divisions

The above division might look easy but things get complicated as you move forward and that is why you should be aware of types of divisions. There are two types of division that you might encounter.

1. Exact Division

If you divide a number and the answer that you receive is zero that means it is an exact division. An exact division will always have the remainder zero.

D = d \div c

15 = 5 \times 3

2. Not Exact Division

If you divide a number but in the end, you still get a number which isn't divisible by the divisor, that is the case of not exact division. The number which isn't divisible by the divisor is called the remainder. In simple words, a division is not exact when the remainder is not zero.

D = d \times c + r

17 = 5 \times 3  + 2


Properties of the Division of Natural Numbers

Like every mathematical operation, division of natural numbers also has some properties. Below are all the properties:

Property No.1: Doesn't Follow Closure Property

This property tells that if you divide two natural numbers this will result in a new number which will not always be a natural number.

a\div b\notin N

2 \div 6 \notin Z

Property No.2: It is not Commutative

When you are dividing two natural numbers, the order does change the division.

a : b \neq b : a

6 : 2 \neq 2 : 6

Property No.3: Zero Dividend

If you divide zero by any number, the result will always be equal to zero.

0 \div a = 0

0 \div 5 = 0

Property No.4: Zero Divisor

Any number divided by zero will always result in infinity.


Dividing Integers,   Dividing Decimal Numbers.

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