There are few properties of division like other basic operations (such as addition, subtraction and multiplication) which are helpful in better understanding of the concept and ideas. These properties will help the learners in easier understanding and even for the purpose of self checking the division problems done. Each of the properties is narrated below:

**1. If any whole number (other than zero) is
divided by itself then the answer or the quotient is one.**

**For
Example:**

(i) 5 ÷ 5 = 1

Again, as we know that division is an inverse of multiplication hence 5 = 5 × 1

(ii) 25 ÷ 25 = 1

Again, as we know that division is an inverse of multiplication hence 25 = 25 × 1

**2. If any whole number (other than zero) is
divided by 0 then it is undefined or meaningless**

**For
Example:**

(i) 47 ÷ 0 = undefined

(ii) 5 ÷ 0 = undefined

(iii) 225 ÷ 0 = undefined

**3. If zero divided by a non- zero whole number,
the answer is zero.**

**For
Example:**

(i) 0 ÷ 5 = 0

(ii) 0 ÷ 10 = 0

(iii) 0 ÷ 50 = 0

**4. If any non zero whole number is divide by 1,
then the quotient will be the whole number itself.**

**For
Example:**

(i) 5 ÷ 1 = 5

(ii) 23 ÷ 1 = 23

(iii) 15 ÷ 1 = 15

**5. If any whole number (other than zero) is
divided by another non-zero whole number, the quotient is not necessarily a
whole number.**

**For
Example:**

(i) 25 ÷ 2 = 12.5

(ii) 10 ÷ 3 = 3.333

(iii) 27 ÷ 4 = 6.75

So, in these cases we can see that a whole number is divided by another whole number and the result is not a whole number. The answer is in decimal.

**6. If there are three whole number out of the
three one is dividend, another divisor and other is quotient. Now if the
divisor and the dividend is not zero then divisor multiplied by quotient is
dividend.**

**For
Example:**

(i) 25 ÷ 5 = 3

Here, 25 is the dividend, 5 is the divisor and 3 is the quotient.

Now according to the property divisor multiplied by quotient is the dividend

So, 5 × 3 = 15

(ii) 50 ÷ 10 = 5

Here, 50 is the dividend, 10 is the divisor and 5 is the quotient.

Now according to the property divisor multiplied by quotient is the dividend

So, 5 × 10 = 50

iii) 39 ÷ 13 = 3

Here, 39 is the dividend, 13 is the divisor and 3 is the quotient.

*Division Equation: Dividend = Divisor × Quotient + Remainder*

* *

Now according to the property divisor multiplied by quotient is the dividend

So, 13 × 3 = 39

169 ÷ 7

Dividend = Divisor × Quotient + Remainder

= 7 × 24 + 1

= 168 + 1

= 169

**7. If there are three whole numbers (other than
zero) p, q and r. If q × r = p, then p ÷ r = q and p ÷ q =r**

**For
Example:**

(i) 8 × 6 =48

Then, 48 ÷ 6 = 8 and

48 ÷ 8 = 6

(ii) 9 × 5 = 45

Then, 45 ÷ 5 =9 and

45 ÷ 9 = 5

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