**Properties of Addition**

###
**Order property of addition**

If we
change the order of the addends, the sum remains the same.

**Example:**8146 + 3564 = 11710 and 3564 + 8146 = 11710

Thus, 8146
+ 3564 = 3564 + 8146 = 11710

###
**Grouping
of addends**

When three
or more numbers are added, the sum remains the same regardless of the way
addends are grouped.

**Example:**(6489 + 2734) + 4698 = 9223 + 4698 = 13921

6489 + (2734
+ 4698) = 6489 + 7432 = 13921

Thus, (6489
+ 2734) + 4698 = 6489 + (2734 + 4698) = 13921

###
**Property
of zero**

The sum
of any number and 0 is the number itself.

**Example:**9754 + 0 = 9754 and 0 + 9754 = 9754

Thus, 9754
+ 0 = 0 + 9754 = 9754

###
**Property
of one**

The sum
of any number and 1 is always the successor of the number.

**Example:**4867 + 1 = 1 + 4867 = 4868

##
**Properties of Subtraction **

###
**Property of zero**

If 0 is
subtracted from a number, the difference is the number itself.

**Example:**95,633 – 0 = 95,633

###
**Property
of one**

If 1 is subtracted
from a number, the difference is the predecessor of the given number.

**Example:**32,577 – 1 = 32,576

###
**Subtraction
of a number from itself**

If a
number is subtracted from itself, the difference is zero.

**Example:**96,762 – 96,762 = 0

##
**Properties of Multiplication **

###
**Order
property of multiplication**

Even if
the order of multiplicand and multiplier is changed, the product remains the
same.

**Examples:**52 × 43 = 43 × 52; 524 × 62 = 62 × 524; 345 × 52 = 52 × 345

###
**Property
of one**

Any
number multiplied by 1 gives the number itself as the product.

Examples:
7413 × 1 = 7413; 2735 × 1 = 2735; 5230 × 1 = 5230

###
**Property
of zero**

Any
number multiplied by 0 gives 0 as the product.

**Examples:**6231 × 0 = 0; 3745 × 0 = 0; 2837 × 0 = 0

·
The product of a number
(either odd or even) with an even number is always an even number.

**Examples:**325 × 2 = 650; 562 × 4 = 2248; 2252 × 8 = 18016

·
The product of
two odd numbers is always an odd number.

**Examples:**323 × 3 = 969; 561 × 7 = 3927; 727 × 9 = 6543

##
**Properties of Division **

·
When a non-zero
number is divided by 1, the quotient is the number itself and the remainder is
zero.

**Examples:**45 ÷ 1 = 45; 328 ÷ 1= 328; 4629 ÷ 1= 4629

·
When a number is
divided by itself, the quotient is 1 and the remainder is zero.

**Examples:**210 ÷ 310 = 1; 4762 ÷ 4762 = 1; 23612 ÷ 23612 = 1

·
Division by zero
has no meaning.

·
When 0 is
divided by any number, the quotient is always 0.

**Examples:**0 ÷ 26 = 0; 0 ÷ 7540 = 0; 0 ÷ 76241 = 0

**Related Topics:**