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.


For example:

(i) 7542 ÷ 1 = 7542

(ii) 372 ÷ 1 = 372

(iii) 1522 ÷ 1 = 1522

(iv) 1502 ÷ 1 = 1502

(v) 1084 ÷ 1 = 1084

(vi) 1745 ÷ 1 = 1745

(vii) 28456 ÷ 1 = 28456


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.

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



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

Properties of Division


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. 

● Operations On Whole Numbers

● Addition Of Whole Numbers.

● Subtraction Of Whole Numbers.

● Multiplication Of Whole Numbers.

● Properties Of Multiplication.

● Division Of Whole Numbers.

● Properties Of Division.








5th Grade Math Problems 

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