# Properties of Division

The properties of division are discussed here:

1. Division by 1 Property:

If we divide a number by 1 the quotient is the number itself.

In other words, when any number is divided by 1, we always get the number itself as the quotient.

When any number is divided by 1, we always

get the number itself.

**For example:**

(i) 7542 ÷ 1 = 7542

(ii) 372 ÷ 1 = 372

(iii) 1522 ÷ 1 = 1522

(iv) 1502 ÷ 1 = 1502

(v) 34 ÷1 = 34

(vi) 16÷1 = 16

(v) 1084 ÷ 1 = 1084

(vi) 1745 ÷ 1 = 1745

(vii) 28456 ÷ 1 = 28456

(viii) 34 ÷1 = 34

(ix) 16÷1 = 16

2. Division by itself Property:

If we divide a number by the number itself, the quotient is 1.

In other words, when any number is divided by the number itself, we always get 1 as the quotient.

When any number is divided by the number itself,

we always get 1 as the quotient.

**For example:**

(i) 275 ÷ 275 = 1

(ii) 105 ÷ 105 = 1

(iii) 572 ÷ 572 = 1

(iv) 1027 ÷ 1027 = 1

(v) 1426 ÷ 1426 = 1

(vi) 1654 ÷ 1654 = 1

(vii) 18520 ÷ 18520 = 1

(viii) 7 ÷ 7 = 1

(ix) 24 ÷ 24 = 1

3. Division any Number by 0 Property:

Division of a number by 0 is meaningless.

**For example:**

(i) 35 ÷ 0 = no meaning

(ii) 65 ÷ 0 = no meaning

(iii) 29 ÷ 0 = no meaning

(iv) 47 ÷ 0 = no meaning

(v) 86 ÷ 0 = no meaning

**Note:** The divisor can never be zero. Division by zero is not

possible.

4. Division of 0 by any Number Property:

0 divided by a number gives 0 as the quotient.

*In other words*, when 0 is divided by any number, we always get 0 as the quotient.

**For example:**

(i) 0 ÷ 25 = 0

(ii) 0 ÷ 100 = 0

(iii) 0 ÷ 4255 = 0

(iv) 0 ÷ 15246 = 0

(v) 0÷2 = 0

(vi) 0 ÷ 75 = 75

5. Division by 10, 100 and 1000 Property:

**For example:**

(i) When a number is divide by 10, the digit in the once place is the remainder.

867 ÷ 10;

*Quotient* = 86 and *Remainder* =7.

(ii) When a number is divided by 100, the number formed by the tens and once place is the remainder.

2764 ÷ 100;

*Quotient* = 7 and *Remainder* = 456.

Questions and Answers on Properties of Division:

**1. Fill in the blanks.**

(i) 23 ÷ 23 = ………

(ii) 21 ÷ ……… = 21

(iii) 15 ÷ 1 = ………

(iv) ……… ÷ 15 = 0

(v) 0 ÷ 12 = ………

(vi) 8 ÷ ……… = 1

(vii) 65 ÷ 65 = ………

(viii) ……… ÷ 12 = 1

**Answer:**

**1. **(i) 1

(ii) 1

(iii) 15

(iv) 0

(v) 0

(vi) 8

(vii) 1

(viii) 12